question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>The problem: A car with a mass of 1200 kg and speed 10 m/s runs into a traffic barrier at an angle of 45 degrees, and is thrown outwards at an angle of 45 degrees relative to the barrier with a speed of 5.0 m/s How big was the change in momentum of the car during the collision?</p>
<p>I tried decomposing the momentum, but failed to get the right answer. Can someone explain to me how I can solve this question without using the fact that Pinitial and Pfinal make a right triangle?</p>
<p>Additionally, someone made the following solution to this problem:</p>
<p>$$\vec{p_e} = 1200 kg \cdot 5 m/s [{1 \over \sqrt{2}} , {1 \over \sqrt{2}}] \\
\vec{\Delta p} = \vec{p_e} - \vec{p_f} = 1200 [-{5 \over \sqrt{2}}, {15 \over \sqrt{2}}] kg m/s \\
|\vec{\Delta p}| = 1200 \sqrt{({5 \over \sqrt{2}})^2 + ({15 \over \sqrt{2}})^2} kg m/s = 1,3 \cdot 10^4 kgm/s$$</p>
<p>Can someone please explain to me how vectors and trig are used to solve this? I especially don't understand what the following means, and where it came from: $$[{1 \over \sqrt{2}} , {1 \over \sqrt{2}}] \\$$</p>
| 10,740 |
[
-0.024992801249027252,
-0.045225292444229126,
-0.028999995440244675,
0.008745747618377209,
0.06680554151535034,
0.0037703539710491896,
0.011124623008072376,
-0.008466815575957298,
0.0031573367305099964,
0.01612844318151474,
0.0008987595210783184,
0.062360573559999466,
0.04576219618320465,
0.01295547466725111,
0.023795094341039658,
0.010038275271654129,
-0.000886184221599251,
-0.02428249828517437,
0.0436955988407135,
-0.038791995495557785,
-0.02101909928023815,
-0.02976383827626705,
0.008462820202112198,
-0.037383705377578735,
-0.022258078679442406,
0.015584580600261688,
0.013623697683215141,
-0.013025828637182713,
0.013224628753960133,
0.04157246649265289,
0.007793582510203123,
-0.014278554357588291,
0.03247177600860596,
-0.032885413616895676,
-0.0012415091041475534,
0.01694425940513611,
-0.004161721095442772,
-0.01150358747690916,
-0.00642112921923399,
0.007565423846244812,
-0.06572488695383072,
-0.009804617613554,
-0.014620632864534855,
0.09078820794820786,
-0.028443027287721634,
0.04054545611143112,
0.012969189323484898,
-0.013711857609450817,
0.013191317208111286,
-0.038320157676935196,
0.09908830374479294,
0.0029535419307649136,
0.03395112231373787,
0.031228458508849144,
-0.016963794827461243,
-0.014430076815187931,
0.026759039610624313,
0.0543082132935524,
-0.037612393498420715,
-0.0537276454269886,
0.013979097828269005,
-0.04174792766571045,
-0.03726321831345558,
0.015746688470244408,
-0.018831294029951096,
0.03245428204536438,
-0.021275203675031662,
-0.04405011609196663,
0.026562979444861412,
-0.01168432179838419,
0.01352305244654417,
0.0015954338014125824,
0.021814711391925812,
-0.010349453426897526,
0.019755132496356964,
-0.05351995304226875,
0.04731025546789169,
0.004363335203379393,
0.01826753467321396,
0.0470130480825901,
0.006903436034917831,
-0.0071802507154643536,
0.0269798394292593,
0.03535434976220131,
0.03540067374706268,
-0.029226278886198997,
0.05239613726735115,
0.025296369567513466,
0.01965925469994545,
0.009878898970782757,
0.00670244824141264,
0.015102031640708447,
0.012930069118738174,
-0.0058057126589119434,
-0.022719169035553932,
0.051655326038599014,
-0.0001636213273741305,
0.03994886949658394,
-0.002657947363331914,
-0.002900599967688322,
-0.0031645861454308033,
-0.02037188410758972,
0.0198365431278944,
0.05789729207754135,
0.0009318114025518298,
0.005380293354392052,
-0.026870666071772575,
-0.014405407942831516,
-0.03267846256494522,
-0.010653453879058361,
-0.020459655672311783,
0.0006378082325682044,
-0.003761118743568659,
-0.0026846725959330797,
-0.019504094496369362,
-0.05005395784974098,
-0.012025122530758381,
0.015176965855062008,
0.05011569336056709,
0.03615538030862808,
0.05120116472244263,
-0.05595306307077408,
0.0060151382349431515,
-0.0319010354578495,
-0.06639467179775238,
0.02418321743607521,
0.021660884842276573,
0.00439288467168808,
-0.022209983319044113,
0.0173161830753088,
0.010023503564298153,
-0.010130566544830799,
0.02453644387423992,
0.00494820112362504,
0.010634883306920528,
-0.041086919605731964,
-0.0951162800192833,
-0.08080577105283737,
0.037346210330724716,
0.015677668154239655,
-0.0190848670899868,
-0.07217993587255478,
0.027856921777129173,
0.009448835626244545,
0.06792819499969482,
-0.0008426347631029785,
0.021731195971369743,
0.017778268083930016,
0.022259803488850594,
-0.006226183380931616,
0.016557514667510986,
-0.00011462326801847667,
-0.017684001475572586,
-0.0011825250694528222,
0.011527111753821373,
-0.07812917232513428,
0.020541995763778687,
0.005895122420042753,
-0.019730620086193085,
-0.03422529622912407,
0.05245504155755043,
-0.0010524543467909098,
-0.017509350553154945,
-0.0032801434863358736,
-0.04998582974076271,
0.030618783086538315,
0.045661456882953644,
0.010124758817255497,
-0.02135678194463253,
0.026237929239869118,
0.02180350571870804,
0.03132336959242821,
-0.014684765599668026,
0.012733006849884987,
0.0682704895734787,
-0.010561102069914341,
-0.004623777698725462,
0.011590486392378807,
0.005647300276905298,
-0.023521101102232933,
-0.03299384191632271,
-0.04596365988254547,
-0.011648764833807945,
0.036474376916885376,
0.019172757863998413,
0.05168912559747696,
-0.006385866552591324,
-0.004047259222716093,
-0.025347750633955002,
-0.021788526326417923,
-0.016681334003806114,
-0.048876747488975525,
0.05650577321648598,
-0.0491173081099987,
0.003475659294053912,
0.03479532152414322,
-0.038514722138643265,
0.04105492681264877,
-0.027354253455996513,
0.008986072614789009,
-0.009551619179546833,
0.05324708670377731,
0.06019063666462898,
0.02589615248143673,
-0.02009587734937668,
0.05101240426301956,
0.06336761265993118,
0.017940400168299675,
-0.015114902518689632,
-0.0007121260860003531,
0.014842904172837734,
-0.008817719295620918,
-0.007210193667560816,
-0.007282009813934565,
0.004012231715023518,
-0.014611960388720036,
-0.0005467095761559904,
-0.026826053857803345,
0.0210279393941164,
0.05195363983511925,
-0.029440104961395264,
0.07025051862001419,
0.06987667828798294,
0.045957643538713455,
-0.0013616367941722274,
0.037547796964645386,
-0.024126162752509117,
0.03898373991250992,
-0.0010391315445303917,
-0.023703783750534058,
-0.03062443807721138,
0.007722986396402121,
0.02024124190211296,
0.021419504657387733,
-0.03654591366648674,
-0.011070099659264088,
0.05536988750100136,
-0.00851750560104847,
0.06805089861154556,
0.037001222372055054,
0.013274029828608036,
-0.05531308427453041,
0.04675484448671341,
0.00903278961777687,
0.014508906751871109,
-0.03294483572244644,
-0.002935679629445076,
0.007685299031436443,
0.016182558611035347,
0.015771036967635155,
-0.04748798534274101,
0.02382933348417282,
0.011603332124650478,
0.07525360584259033,
-0.007678403053432703,
-0.02087935246527195,
0.05663370341062546,
0.006885118782520294,
-0.006631617434322834,
0.017752958461642265,
0.012495031580328941,
0.0009240051731467247,
-0.0485999621450901,
0.012217076495289803,
-0.015686865895986557,
-0.01143391989171505,
-0.027000974863767624,
0.01608206517994404,
0.01248922199010849,
-0.025430671870708466,
-0.0035883395466953516,
0.019899288192391396,
-0.02682720497250557,
-0.023739969357848167,
-0.007543141022324562,
0.019958892837166786,
-0.0019232707563787699,
0.020174497738480568,
-0.029840627685189247,
-0.006068281829357147,
-0.013512811623513699,
-0.011292454786598682,
0.006747241597622633,
0.003077895613387227,
-0.0653083324432373,
0.023834945634007454,
-0.024242214858531952,
-0.030285678803920746,
0.060851093381643295,
-0.008099362254142761,
-0.015875378623604774,
0.017201079055666924,
-0.02770805172622204,
-0.025874115526676178,
-0.0087776193395257,
-0.011684190481901169,
0.019085422158241272,
-0.010851984843611717,
-0.010739441961050034,
0.035334374755620956,
0.011559061706066132,
-0.033548157662153244,
0.03777536004781723,
-0.06801065057516098,
-0.01737600937485695,
-0.041905760765075684,
0.012098061852157116,
0.015753233805298805,
-0.008613633923232555,
0.019021296873688698,
0.012307931669056416,
-0.003618558868765831,
0.0308745838701725,
-0.035220712423324585,
-0.00978065188974142,
-0.03952513262629509,
0.007410252001136541,
0.053745247423648834,
-0.0034166155382990837,
-0.01636616699397564,
0.09874222427606583,
0.0164695605635643,
-0.05356656014919281,
-0.022964967414736748,
0.01549650076776743,
-0.00945235975086689,
-0.03372777998447418,
0.004963818471878767,
0.04417848959565163,
-0.016572944819927216,
0.012451346963644028,
-0.01103722769767046,
0.03661826252937317,
0.07681655138731003,
-0.006816912908107042,
-0.023888275027275085,
0.0048688300885260105,
-0.0004617803206201643,
0.0155892763286829,
0.03454397991299629,
0.033910274505615234,
-0.0444316603243351,
0.028595073148608208,
0.02719067595899105,
0.05193350464105606,
0.0475851371884346,
-0.055543575435876846,
0.05389392003417015,
0.022719649598002434,
-0.007183546666055918,
-0.03609152510762215,
0.0487007275223732,
0.02018655650317669,
-0.04591304436326027,
0.01815534383058548,
0.007727584335952997,
0.01444505900144577,
-0.06035362556576729,
-0.03647485002875328,
0.006529772654175758,
0.05198332294821739,
-0.010493668727576733,
-0.05240993574261665,
-0.0310070663690567,
0.021204819902777672,
0.034762948751449585,
-0.017802102491259575,
0.004510591272264719,
-0.009661098010838032,
0.030508598312735558,
0.05277503281831741,
0.00025675995857454836,
-0.034559689462184906,
0.04837656766176224,
-0.05249129608273506,
-0.026493748649954796,
0.015230112709105015,
0.009193078614771366,
-0.009982503019273281,
0.059649884700775146,
0.01435963436961174,
0.027968093752861023,
0.033577896654605865,
0.026794642210006714,
-0.0552845299243927,
0.035057201981544495,
-0.00048357844934798777,
-0.03718290105462074,
-0.01240547839552164,
-0.0059013464488089085,
0.025960754603147507,
-0.006130264140665531,
0.01614455133676529,
0.009605581872165203,
0.009264822117984295,
-0.05082593858242035,
0.032554931938648224,
-0.030565716326236725,
-0.014590815640985966,
0.014780131168663502,
0.018866775557398796,
0.06375443190336227,
-0.02493732050061226,
0.03661832585930824,
0.07157181948423386,
-0.03504763916134834,
-0.01855197176337242,
-0.019574400037527084,
-0.026029378175735474,
0.0014818833442404866,
0.031199034303426743,
0.0034300428815186024,
0.02511575073003769,
0.042311668395996094,
0.05125543475151062,
-0.02485012449324131,
0.04708532989025116,
0.014356800355017185,
0.03777889534831047,
-0.011722417548298836,
-0.07728859782218933,
-0.008154790848493576,
-0.05716651678085327,
0.019462883472442627,
-0.05245314911007881,
0.00590803287923336,
0.046798139810562134,
0.0012202078942209482,
-0.028742967173457146,
0.05164887756109238,
-0.004578378517180681,
0.02611655183136463,
-0.01462500263005495,
-0.06561033427715302,
-0.014221101999282837,
-0.02169024385511875,
-0.03409598767757416,
0.025996441021561623,
0.0066925096325576305,
-0.011860262602567673,
0.014889722689986229,
0.05511506646871567,
0.009987441822886467,
-0.028753885999321938,
0.03275549039244652,
-0.01532394252717495,
0.010773672722280025,
-0.047481685876846313,
-0.0004865745722781867,
-0.011387279257178307,
0.02411814033985138,
0.05973434075713158,
-0.008034884929656982,
-0.02086493745446205,
-0.07617519050836563,
-0.0017433834727853537,
0.02316318079829216,
0.04575444012880325,
-0.03308485820889473,
0.021122531965374947,
-0.0430707223713398,
-0.03100363165140152,
0.05100323632359505,
-0.008519504219293594,
0.03640839457511902,
-0.03183441981673241,
0.013497953303158283,
-0.010236719623208046,
-0.006554157938808203,
-0.0399814136326313,
-0.005632504820823669,
-0.05962669104337692,
0.0395432710647583,
0.004274651873856783,
-0.042008742690086365,
-0.010345865972340107,
0.0014088492607697845,
0.025293273851275444,
0.044252749532461166,
0.0035054455511271954,
-0.0048828087747097015,
-0.015718773007392883,
0.03918025270104408,
-0.05750300735235214,
-0.03317219391465187,
-0.01625148206949234,
0.0046601202338933945,
-0.022609861567616463,
0.01989423856139183,
-0.05526520684361458,
-0.06072603538632393,
0.0007559758378192782,
-0.006291376426815987,
0.011525310575962067,
0.018859468400478363,
-0.02099086530506611,
0.04565545544028282,
0.032877787947654724,
-0.0035714523401111364,
0.026723386719822884,
0.021624267101287842,
-0.012675747275352478,
0.012876552529633045,
-0.020663026720285416,
0.03592704236507416,
0.022365570068359375,
-0.00814361497759819,
-0.023770438507199287,
0.02902408316731453,
-0.041275687515735626,
0.05429527536034584,
0.00811587180942297,
0.026377148926258087,
-0.05830102413892746,
-0.03821864351630211,
0.008442550897598267,
0.038411859422922134,
-0.0053183091804385185,
0.003671230049803853,
-0.026124821975827217,
-0.015558532439172268,
0.04596525430679321,
-0.00983527209609747,
0.013096550479531288,
-0.0011491624172776937,
0.011249637231230736,
-0.013435848988592625,
-0.005220027174800634,
-0.000395978830056265,
-0.04113500192761421,
-0.03514670580625534,
0.03137865290045738,
-0.053198378533124924,
0.05199229344725609,
0.0012792659690603614,
0.01588953286409378,
0.04069024324417114,
-0.05713438615202904,
-0.03582803159952164,
0.01152255479246378,
-0.016101891174912453,
0.03975401446223259,
-0.0554138645529747,
0.02832041122019291,
0.025078605860471725,
0.014607597142457962,
-0.017675504088401794,
-0.04810518026351929,
0.04210623353719711,
0.001367567921988666,
-0.026760844513773918,
-0.03914328292012215,
-0.02795405685901642,
-0.003924248274415731,
-0.04122423753142357,
-0.0012725858250632882,
0.06150798499584198,
-0.06035495176911354,
0.007231122348457575,
0.011046275496482849,
-0.010083743371069431,
0.033434100449085236,
0.012745496816933155,
0.028078578412532806,
-0.0029064600821584463,
-0.019961416721343994,
-0.006963660009205341,
0.04132503271102905,
0.01897607184946537,
-0.025259189307689667,
-0.02343234047293663,
-0.0019694450311362743,
-0.0037257815711200237,
0.034980032593011856,
-0.024352118372917175,
0.060461413115262985,
0.006599927321076393,
-0.0021219784393906593,
0.012822684831917286,
0.019399644806981087,
0.02630019187927246,
-0.0036597761791199446,
0.03992880880832672,
-0.009006010368466377,
0.015607600100338459,
-0.034428901970386505,
-0.03156948462128639,
0.023948926478624344,
-0.009048666805028915,
0.03420555219054222,
-0.028834180906414986,
0.06676218658685684,
-0.03144054114818573,
0.046539612114429474,
0.01572246663272381,
0.022411884739995003,
0.03936222568154335,
-0.003788524540141225,
0.0009353725472465158,
0.02379688061773777,
0.012788678519427776,
0.004537559114396572,
-0.02988838031888008,
-0.04968929663300514,
0.009062444791197777,
0.07117409259080887,
-0.031188523396849632,
0.0422571562230587,
0.03898174688220024,
0.00997984316200018,
0.0031267614103853703,
-0.022089580073952675,
-0.01680753566324711,
0.010704289190471172,
0.028217118233442307,
0.038809794932603836,
-0.030645057559013367,
0.0167367085814476,
0.01783045381307602,
0.015984630212187767,
-0.0005012233159504831,
-0.010723566636443138,
0.030117159709334373,
0.011153505183756351,
0.016125282272696495,
-0.004324459470808506,
-0.01203493308275938,
0.00924016535282135,
0.021668238565325737,
0.014773624017834663,
-0.04925742745399475,
-0.03141573816537857,
0.1005469411611557,
0.03236211836338043,
0.016865599900484085,
-0.0397966168820858,
-0.005449344869703054,
0.002447478473186493,
0.003969545476138592,
0.03624000772833824,
-0.021568538621068,
-0.018200835213065147,
0.022651201114058495,
0.04654492810368538,
0.021731048822402954,
0.019150687381625175,
-0.05093971639871597,
-0.021972011774778366,
-0.020358633249998093,
-0.035043563693761826,
-0.05564367026090622,
0.02192675694823265,
0.008476748131215572,
0.010554179549217224,
0.04000208154320717,
-0.04249793291091919,
0.02709467150270939,
-0.009525490924715996,
0.02514500543475151,
-0.03280675783753395,
0.07772382348775864,
-0.023303071036934853,
-0.005823075771331787,
0.008954459801316261,
-0.0379331111907959,
0.09099249541759491,
0.017187895253300667,
-0.0065855165012180805,
0.004477140959352255,
-0.002517363987863064,
-0.044968631118535995,
-0.01407840009778738,
-0.030464403331279755,
0.013958369381725788,
-0.007746955845504999,
-0.00881054438650608,
0.0044661881402134895,
0.05347691476345062,
0.03759249672293663,
-0.02542434260249138,
0.04005993902683258,
-0.03748467192053795,
-0.04217008873820305,
-0.014159666374325752,
0.026531221345067024,
-0.02465265616774559,
-0.0025908041279762983,
-0.016408737748861313,
0.04057387635111809,
-0.029201876372098923,
-0.006484664045274258,
-0.04699711129069328,
-0.03584369644522667,
-0.003347784746438265,
0.011137044988572598,
-0.03223685547709465,
0.06914450228214264,
0.022096388041973114,
-0.011740718968212605,
-0.03402149677276611,
0.051045894622802734,
0.03779023513197899,
0.013285980559885502,
-0.02716090902686119,
0.037419643253088,
-0.032527536153793335,
0.0025326055474579334,
-0.014167415909469128,
0.02679663710296154,
-0.05168848857283592,
0.002292726654559374,
-0.047118570655584335,
0.08967287093400955,
-0.012718826532363892,
0.023665376007556915,
-0.014346156269311905,
0.015663525089621544,
-0.003556119743734598,
-0.07224250584840775,
0.0252535343170166,
0.02529963292181492,
0.011939086019992828,
0.009913399815559387,
-0.026995323598384857,
-0.012342219240963459,
0.010352506302297115,
0.0449489951133728,
0.024011172354221344,
0.015292494557797909,
-0.019040165469050407,
0.014827516861259937,
-0.009310669265687466,
0.03962892293930054,
-0.05175364390015602,
-0.020667443051934242,
-0.019299667328596115,
-0.007831876166164875,
-0.03857102245092392,
-0.0002722521312534809,
0.03746234253048897,
0.017662812024354935,
-0.0037248623557388783,
0.0007073582382872701,
-0.02434142492711544,
-0.00787433609366417,
-0.02892373502254486,
0.03292100504040718,
-0.013456156477332115,
-0.04099474847316742,
-0.0126448143273592,
-0.005560758989304304,
-0.01658201776444912,
0.0700850859284401,
-0.012915155850350857,
-0.01624900847673416,
-0.011864073574543,
0.015819240361452103,
0.010945037007331848,
-0.011833791621029377,
-0.015454204753041267,
0.003351175459101796,
-0.011899439617991447,
0.02162127010524273,
0.018561141565442085,
0.0417778454720974,
0.03879111260175705,
-0.007285556755959988,
0.005929118953645229,
0.030135324224829674,
-0.02483413927257061,
0.014415881596505642,
0.023145213723182678,
-0.04783711954951286,
0.0028489509131759405,
-0.00337419961579144,
0.018963860347867012,
-0.01065833494067192,
0.021953804418444633,
-0.013656554743647575,
-0.02958223782479763,
-0.016403771936893463,
0.00991035159677267,
-0.007012581918388605,
0.018645625561475754,
-0.05435320734977722,
0.020629743114113808,
-0.04419747367501259,
0.000324591324897483,
-0.022115647792816162,
0.0046377768740057945,
0.016782348975539207,
-0.023458316922187805,
-0.037085045129060745,
0.031360331922769547,
-0.003883760655298829,
0.016986869275569916,
0.012350358068943024,
0.03916007652878761,
-0.04220586642622948,
-0.05031774938106537,
-0.007151785306632519,
-0.004450799431651831,
0.04812408983707428,
-0.06057887151837349,
-0.001602641656063497,
0.06837932020425797,
-0.03668369725346565,
-0.02732846885919571,
0.02208244800567627,
0.04456237703561783,
0.06097758561372757,
-0.0008126585162244737,
-0.01751515083014965,
-0.033536575734615326,
0.0600118488073349,
-0.02946009673178196,
-0.03797924518585205,
-0.008935446850955486,
-0.033999860286712646,
-0.050979770720005035,
-0.059562310576438904,
0.004331196192651987,
0.002442452358081937,
-0.00356422271579504,
0.026639005169272423,
0.0170527882874012,
-0.02444775402545929,
0.017515793442726135,
0.037434615194797516,
0.015435623936355114,
0.0022857424337416887,
0.028061823919415474,
-0.0015808928292244673,
0.0009445411269553006,
0.029778119176626205,
-0.016769377514719963,
0.001757402322255075,
0.0024997014552354813,
0.0038106513675302267,
-0.06767398864030838,
-0.011993455700576305,
0.04153124988079071,
-0.032084960490465164,
0.09346046298742294,
-0.08939775079488754,
0.002719623502343893,
0.026946578174829483,
-0.08487918227910995,
-0.03866080939769745,
-0.04877821356058121,
-0.04944552481174469,
0.00953326839953661,
-0.009443500079214573,
0.01536889374256134,
0.048734765499830246,
0.0049865469336509705,
0.0006977672455832362,
0.011174182407557964,
-0.01941588893532753,
-0.005748861934989691,
-0.0375179797410965,
0.0164684746414423,
0.022878091782331467,
-0.012009521014988422,
-0.007563635241240263,
0.055471763014793396,
-0.01945803314447403,
0.006711144465953112,
0.013821677304804325,
-0.03497367724776268,
0.023905044421553612,
0.008344757370650768,
0.02388690784573555,
-0.007675752975046635,
-0.002326534129679203,
-0.005529387854039669,
-0.011880212463438511,
0.009952884167432785,
-0.0023483706172555685,
-0.010453203693032265,
-0.021800465881824493,
0.043237295001745224,
0.002614916767925024,
0.029140768572688103,
-0.036772944033145905,
-0.008697363547980785,
0.017368843778967857,
-0.013470887206494808,
-0.00798484031111002,
0.008440826088190079,
0.008324434980750084,
0.008612927980720997,
-0.039083026349544525,
0.016519268974661827,
-0.04298297315835953,
-0.0027091531082987785,
0.008076279424130917,
-0.007138981018215418,
0.0029062717221677303,
0.006060248240828514,
-0.0002267998206662014,
-0.012284431606531143,
-0.010438586585223675,
-0.004235240630805492,
-0.02357158251106739,
-0.0529613196849823,
-0.03434373810887337,
0.016275372356176376,
-0.018886305391788483,
-0.009462524205446243,
-0.02545803226530552,
-0.02761090360581875,
-0.0012484157923609018,
0.039324209094047546,
0.020674023777246475,
0.006589023396372795,
0.0097089484333992,
-0.0037249058950692415,
-0.07637891173362732,
0.0172103438526392,
-0.006016658153384924,
-0.05720552057027817,
-0.032635949552059174,
-0.041428472846746445,
-0.01635867729783058,
0.022634197026491165,
0.035886265337467194,
-0.016348354518413544,
-0.011540400795638561,
-0.00819322932511568,
-0.023799022659659386,
-0.012950693257153034,
-0.02451700158417225,
-0.018479814752936363,
-0.023517487570643425,
-0.027415262535214424,
0.02666751854121685,
0.018936365842819214,
0.0400872603058815,
-0.008581666275858879,
0.00973496213555336,
0.007299845572561026,
0.00304985698312521,
-0.017558777704834938,
-0.06062693893909454,
0.0029292083345353603,
-0.015460464172065258,
-0.007977073080837727,
0.05669141188263893,
0.007138113956898451,
0.023206550627946854,
0.05450747534632683,
-0.03390039503574371,
-0.05524511635303497,
0.0162289347499609,
-0.033399809151887894,
-0.04550667107105255,
-0.04507216811180115,
-0.03976132720708847,
0.07294070720672607,
-0.0624391995370388,
-0.009396107867360115,
0.015611271373927593,
-0.06521322578191757,
-0.00309566012583673,
0.04916972294449806,
0.05860956385731697,
0.013687876984477043,
-0.0002430210297461599,
0.044065218418836594,
0.025269389152526855,
-0.06625880300998688,
-0.02154904045164585,
-0.0033149337396025658,
0.06059213727712631,
0.0050619360990822315,
-0.00749411853030324,
0.054513897746801376,
-0.023480013012886047,
0.0025457662995904684,
-0.017410608008503914,
0.0060851238667964935,
0.0040303440764546394,
-0.019128261134028435,
-0.013067223131656647,
-0.0035037961788475513,
0.01811361312866211,
0.038849443197250366,
-0.009998633526265621,
0.044362571090459824,
-0.03650951385498047,
0.006971178576350212,
-0.000026046298444271088,
0.03761890158057213,
-0.022330695763230324,
0.019337236881256104,
0.000318037171382457,
0.020287951454520226,
-0.005018049851059914,
-0.03369325026869774,
-0.02203887142241001,
-0.01445993036031723,
0.021520692855119705,
-0.00609985738992691,
-0.013616256415843964,
-0.013709332793951035,
-0.005955396220088005,
-0.024056239053606987,
-0.024573296308517456,
-0.015272831544280052,
-0.03546203672885895,
0.017254319041967392,
0.03740298002958298,
-0.001137158484198153,
-0.06400440633296967,
-0.008720455691218376,
0.004811764694750309,
0.05868140608072281,
-0.023416668176651,
-0.003564246464520693,
-0.007741042412817478,
0.012856113724410534,
0.0004312251112423837,
-0.014705728739500046
] |
<p>A ladder $AB$ of mass $m$ has its ends on a smooth wall and floor (see figure). The foot of the ladder is tied by an inextensible rope of negligible mass to the base $C$ of the wall so the ladder makes an angle $\alpha$ with the floor. Using the principle of virtual work, find the magnitude of the tension in the rope. </p>
<p>My equations:</p>
<p>I assume length of ladder = $L$</p>
<p>$x$-direction: $$N_2 = mg$$</p>
<p>$y$-direction: $$N_1 = T$$</p>
<p>torque equation about $B$: $$ T_{about B}=T_{mg}+T_{A} = \frac{L}{2}(mg)cos\alpha-LN_1 sin\alpha=0$$
Therefore, $$\frac{L}{2}(mg)cos\alpha-LT sin\alpha=0$$</p>
<p>And we get $$T= \frac{1}{2}(mg)cot\alpha$$</p>
<p>which is the answer. </p>
<p>However, I am supposed to find this using the principle of virtual work. To do this, I guess I would have to displace the ladder downward at $A$ and rightward at $B$, in which case the normal forces $N_1$ and $N_2$ do no work. I then conclude that the work done by the gravitational force $mg$ along the downward displacement of the center of mass of the ladder counterbalances the tension times the horizontal displacement at $B$. However, finding the displacement of the center of the ladder as the ladder slides downwards doesn't seem to be an easy task, so I must be on the wrong track. The final equation I have to deal with seems to be $$mg.\delta y_{com}-T.\delta x_{at B}=0$$</p>
<p>Any inputs would be appreciated. </p>
<p><img src="http://i.stack.imgur.com/yhIPX.jpg" alt="enter image description here"></p>
| 10,741 |
[
0.0029591803904622793,
0.01784099079668522,
-0.021579347550868988,
-0.006387495901435614,
0.03674423322081566,
0.007535019889473915,
-0.06161433085799217,
-0.019013410434126854,
-0.012999184429645538,
-0.026267100125551224,
0.03344185650348663,
0.052438199520111084,
0.03993513435125351,
0.05830254778265953,
0.01745864376425743,
-0.03044036589562893,
0.024844763800501823,
-0.0242506954818964,
0.007973612286150455,
-0.059286583214998245,
-0.0048884735442698,
-0.007904510013759136,
0.0085484329611063,
0.015708953142166138,
-0.021724337711930275,
0.020057274028658867,
0.05204106494784355,
-0.024722393602132797,
-0.04963700845837593,
0.07771453261375427,
-0.0020055146887898445,
-0.01803688146173954,
-0.019430456683039665,
-0.012588563375175,
0.00940180104225874,
0.042389027774333954,
-0.04502083361148834,
-0.04539572820067406,
0.008741430938243866,
0.06672200560569763,
-0.01089527178555727,
0.01358290109783411,
-0.0036817053332924843,
0.07521219551563263,
-0.03969144448637962,
0.040885768830776215,
-0.02971574477851391,
0.00814405269920826,
0.06015627831220627,
-0.056923069059848785,
0.06123243272304535,
-0.007415375206619501,
0.02148931846022606,
-0.01566159725189209,
-0.02944745495915413,
-0.021043993532657623,
0.027560701593756676,
0.04442444443702698,
0.005492372438311577,
-0.06720190495252609,
-0.012497431598603725,
-0.003073369851335883,
-0.0708998292684555,
-0.061718035489320755,
-0.020537085831165314,
0.0064249602146446705,
-0.005108762066811323,
0.026987509801983833,
0.035008274018764496,
-0.03985271602869034,
0.009743582457304,
-0.014985905960202217,
0.023837797343730927,
-0.046863727271556854,
0.004279067274183035,
-0.023226924240589142,
-0.01195614505559206,
0.05752772465348244,
-0.003523078514263034,
0.046427857130765915,
0.012694007717072964,
-0.013541377149522305,
0.038542699068784714,
0.07004444301128387,
-0.008895901031792164,
-0.044199779629707336,
0.0652075782418251,
0.005024479236453772,
0.020792270079255104,
0.004551705904304981,
0.05413223057985306,
0.014072428457438946,
0.011095799505710602,
0.004898932762444019,
0.01266523078083992,
-0.0020903986878693104,
0.010805261321365833,
0.024322763085365295,
0.04054010286927223,
-0.024668486788868904,
-0.012745589017868042,
-0.05384252592921257,
0.008563155308365822,
0.08805517852306366,
0.024824710562825203,
-0.004022881388664246,
0.024588124826550484,
0.005059160757809877,
0.03413467854261398,
-0.027997149154543877,
-0.05097338929772377,
0.017485354095697403,
0.012384871952235699,
-0.017594004049897194,
-0.01972835138440132,
-0.04729337617754936,
0.010255664587020874,
-0.010905442759394646,
0.07307043671607971,
0.02185455895960331,
-0.006133889313787222,
-0.033731475472450256,
0.03361491486430168,
-0.0029240997973829508,
-0.049003470689058304,
0.0054368325509130955,
-0.0023084678687155247,
-0.0450003445148468,
-0.0322120375931263,
0.026508215814828873,
0.06433717161417007,
-0.02371162548661232,
-0.012239730916917324,
-0.002568762982264161,
0.06759458780288696,
-0.022268112748861313,
-0.0892675518989563,
-0.0575745664536953,
0.034562356770038605,
0.0026756897568702698,
-0.00267593446187675,
-0.027243852615356445,
-0.019059767946600914,
0.04811341315507889,
0.05556362494826317,
0.019309155642986298,
0.015458110719919205,
0.020673533901572227,
-0.007776410784572363,
-0.01030020136386156,
0.027270488440990448,
-0.03547972813248634,
0.017217056825757027,
-0.040418706834316254,
-0.015988856554031372,
-0.043194256722927094,
0.031839195638895035,
0.019289931282401085,
-0.005368654150515795,
-0.016807273030281067,
0.04711068794131279,
0.023794900625944138,
-0.010721941478550434,
0.031845174729824066,
-0.005522874649614096,
-0.019757956266403198,
0.06493602693080902,
0.007115733344107866,
-0.023807479068636894,
0.046980299055576324,
0.0004142406687606126,
0.029412200674414635,
0.015341133810579777,
0.013534367084503174,
0.021816428750753403,
-0.04356919229030609,
-0.018632372841238976,
-0.0050194524228572845,
0.011903192847967148,
0.014013303443789482,
-0.021425889804959297,
-0.07289252430200577,
-0.017323100939393044,
0.019103581085801125,
-0.005455716047435999,
0.04908081144094467,
0.008349308744072914,
-0.006061851978302002,
-0.020588239654898643,
-0.0032244031317532063,
-0.01866213046014309,
-0.05938442796468735,
0.033748578280210495,
0.01137477532029152,
-0.012327544391155243,
-0.020055396482348442,
0.022195229306817055,
0.0034486392978578806,
-0.02097960188984871,
0.002499972004443407,
0.04467673972249031,
0.03137350082397461,
0.03684691712260246,
0.0061162193305790424,
0.06587417423725128,
0.01964675262570381,
0.07130128145217896,
0.04068783298134804,
0.03971196711063385,
-0.04406057298183441,
0.00786562543362379,
-0.011939728632569313,
-0.035719603300094604,
0.03859659656882286,
0.011024698615074158,
0.032478101551532745,
0.00581633485853672,
-0.007376519031822681,
-0.0025962498039007187,
0.04198737069964409,
0.020318659022450447,
0.06544716656208038,
0.06184157729148865,
0.022540533915162086,
0.040845733135938644,
0.036204587668180466,
0.00912078283727169,
0.035266775637865067,
-0.005805549677461386,
-0.04815516248345375,
-0.02371109463274479,
-0.014572454616427422,
-0.007194071542471647,
0.04289399832487106,
-0.01914411410689354,
0.011466190218925476,
0.028509873896837234,
0.020008806139230728,
0.032587189227342606,
0.021282507106661797,
-0.02127734199166298,
-0.04061553627252579,
0.0022558323107659817,
0.024697335436940193,
0.009320450946688652,
0.03784292936325073,
0.010889503173530102,
0.045223213732242584,
0.01581404358148575,
-0.021558552980422974,
0.0034604170359671116,
0.03173670172691345,
0.015349547378718853,
0.016971087083220482,
0.02356405183672905,
-0.01902696117758751,
0.06297191977500916,
0.0010602979455143213,
0.025057099759578705,
0.05330226570367813,
-0.02372725121676922,
0.005472932942211628,
0.001878340495750308,
-0.004461247473955154,
0.04671912267804146,
0.004836536478251219,
-0.006327103357762098,
-0.01040189154446125,
0.03500024229288101,
-0.008716808632016182,
0.03236228972673416,
0.0020678716246038675,
-0.01232244074344635,
-0.004914096090942621,
-0.04743534326553345,
-0.010929392650723457,
0.035593464970588684,
0.04851219803094864,
-0.04720280319452286,
-0.0008900039829313755,
-0.01598338410258293,
-0.02962327189743519,
0.0050766668282449245,
-0.006990408059209585,
-0.03436910733580589,
0.004765622783452272,
-0.041109975427389145,
-0.011487990617752075,
0.07859453558921814,
0.023739192634820938,
-0.0186043418943882,
0.047123879194259644,
0.0008758694166317582,
-0.010904352180659771,
-0.045055925846099854,
-0.0034168248530477285,
0.009737275540828705,
-0.06773587316274643,
-0.002703780774027109,
0.015938133001327515,
0.0017937516095116735,
-0.01890767365694046,
0.02327430248260498,
-0.05606502294540405,
-0.08067432790994644,
0.008241175673902035,
0.02852822281420231,
-0.011662062257528305,
-0.010451069101691246,
0.025936761870980263,
-0.021626833826303482,
0.004101279657334089,
-0.019852187484502792,
-0.04647049680352211,
-0.04494494944810867,
0.00959170050919056,
-0.0067750453017652035,
0.014842364005744457,
-0.009976132772862911,
-0.0442788302898407,
0.09177087247371674,
0.0391768254339695,
-0.0014947622548788786,
-0.010219602845609188,
-0.02386605180799961,
0.020775968208909035,
0.008604412898421288,
0.02860867790877819,
0.01892535760998726,
-0.04228712618350983,
0.0014466812135651708,
-0.0016186527209356427,
0.012435701675713062,
0.042718492448329926,
0.01811104826629162,
-0.00045641695032827556,
0.04716111719608307,
0.009137771092355251,
-0.0018589405808597803,
0.05179199203848839,
-0.006814055610448122,
0.03761561959981918,
0.011070246808230877,
-0.008000640198588371,
-0.006864813156425953,
-0.0422370582818985,
-0.06435209512710571,
0.049426302313804626,
-0.024198412895202637,
0.031029194593429565,
-0.030723631381988525,
0.048871226608753204,
0.015421184711158276,
-0.028332456946372986,
-0.01527134608477354,
0.004709311295300722,
0.02965289168059826,
-0.0050772083923220634,
-0.0013025706866756082,
0.056283481419086456,
0.034332167357206345,
0.020977526903152466,
-0.020390324294567108,
-0.012354938313364983,
0.006291798781603575,
0.04506140574812889,
-0.02383238635957241,
-0.058458905667066574,
0.0017219536239281297,
0.07311870902776718,
-0.0019586593843996525,
-0.005414074286818504,
-0.036367155611515045,
-0.026079796254634857,
-0.035840149968862534,
0.002309185452759266,
-0.01989014819264412,
0.06436861306428909,
-0.00886786449700594,
0.0308385007083416,
0.02941509522497654,
0.04072720557451248,
0.02900039404630661,
0.02025279402732849,
-0.08928506821393967,
0.02880837209522724,
-0.015061884187161922,
-0.02505827136337757,
0.03366059809923172,
-0.005820986814796925,
0.03997108340263367,
-0.007377183064818382,
-0.050158675760030746,
0.0036889417096972466,
0.016658028587698936,
-0.04691937565803528,
-0.008802833966910839,
-0.01731787994503975,
-0.023411065340042114,
-0.003119108034297824,
-0.0010205853031948209,
0.003983077127486467,
-0.01965991035103798,
-0.006702762562781572,
0.03723873570561409,
-0.012012992054224014,
-0.005282570607960224,
-0.006736457347869873,
-0.046721477061510086,
0.02657162770628929,
-0.002416526898741722,
0.006910290103405714,
0.03198368847370148,
-0.03794236108660698,
-0.02728000469505787,
0.011465691030025482,
0.04072829335927963,
-0.008596831001341343,
-0.006914913188666105,
-0.010867675766348839,
-0.03834926709532738,
-0.019903244450688362,
0.008617200888693333,
0.04491518437862396,
-0.025940315797924995,
-0.0008860898087732494,
0.04392420873045921,
0.01873438060283661,
0.0010244924342259765,
0.0641760304570198,
0.05506576597690582,
0.048781245946884155,
0.015438783913850784,
-0.046591438353061676,
-0.01548800989985466,
-0.030008191242814064,
-0.019267547875642776,
0.0012589195976033807,
-0.02665792405605316,
-0.01768621616065502,
-0.029593734070658684,
0.05343767628073692,
0.07694406062364578,
0.01685129478573799,
0.03848255053162575,
-0.03717753291130066,
0.010097396560013294,
0.0006212793523445725,
0.0015021447325125337,
0.021120985969901085,
-0.026121782138943672,
0.05514705553650856,
-0.022845538333058357,
-0.006154551170766354,
-0.07439578324556351,
-0.07163120806217194,
0.011627578176558018,
0.04538138210773468,
-0.020057303830981255,
0.013924116268754005,
-0.020125724375247955,
-0.04358713701367378,
0.01636591926217079,
-0.031783327460289,
0.06600221246480942,
-0.009149151854217052,
0.035296499729156494,
-0.006924972403794527,
-0.018828965723514557,
-0.04493672773241997,
-0.02067168615758419,
-0.02129141427576542,
0.004967872519046068,
-0.03236955776810646,
-0.01579117216169834,
0.018651623278856277,
-0.019801238551735878,
0.038470689207315445,
0.031179901212453842,
-0.008673643693327904,
-0.04777434468269348,
-0.002596256323158741,
0.04362482205033302,
-0.03578045964241028,
-0.06007450446486473,
0.013040941208600998,
-0.01240369863808155,
-0.04299601912498474,
-0.008238204754889011,
0.007497979793697596,
-0.0502207987010479,
0.04683087393641472,
0.008107547648251057,
0.044755324721336365,
0.024181926622986794,
0.01650746539235115,
0.01915823481976986,
0.04356641322374344,
-0.003913852386176586,
0.03684345632791519,
0.03927264362573624,
-0.02528553456068039,
-0.006177361123263836,
-0.01656476780772209,
0.02216799557209015,
-0.003281576558947563,
-0.008068555034697056,
-0.02294817380607128,
0.019795246422290802,
-0.03839318826794624,
0.04588963836431503,
0.0008603117894381285,
0.026276977732777596,
-0.038828492164611816,
-0.036312684416770935,
0.021290671080350876,
0.034034136682748795,
0.029382307082414627,
-0.018192779272794724,
0.009761601686477661,
-0.019025705754756927,
0.015959907323122025,
-0.010082540102303028,
-0.018596742302179337,
0.009240706451237202,
-0.008709746412932873,
0.02459903620183468,
-0.0038962827529758215,
-0.04135392978787422,
-0.0358709841966629,
0.005858424585312605,
0.004403435159474611,
-0.06419447809457779,
0.014753093011677265,
0.01176777295768261,
0.036031655967235565,
0.00877134408801794,
-0.026145707815885544,
-0.05810168385505676,
0.01694469340145588,
-0.021511418744921684,
0.003727767150849104,
-0.011158193461596966,
-0.007928251288831234,
0.011120043694972992,
-0.007755091413855553,
-0.013950632885098457,
-0.03467075526714325,
-0.013326598331332207,
-0.006299557629972696,
0.01415480300784111,
-0.008868350647389889,
0.0009828145848587155,
0.019427992403507233,
-0.033035386353731155,
0.00431108707562089,
0.08190077543258667,
-0.03917469084262848,
0.04713066667318344,
0.05255085974931717,
0.03668287768959999,
0.016518695279955864,
0.004138822201639414,
-0.006606020033359528,
-0.024634886533021927,
-0.015003632754087448,
-0.01916113682091236,
0.025268888100981712,
0.026465799659490585,
-0.047241635620594025,
-0.029743636026978493,
0.043160125613212585,
0.016267454251646996,
0.05341210588812828,
-0.013433738611638546,
-0.00803170446306467,
-0.008395504206418991,
0.04590365290641785,
-0.004858524072915316,
0.0032831509597599506,
0.029797464609146118,
0.02244170941412449,
0.02814418077468872,
-0.023739658296108246,
0.008863596245646477,
-0.0355260968208313,
-0.05086877569556236,
-0.022267064079642296,
0.01024922076612711,
-0.02757091633975506,
0.02568521909415722,
0.058253053575754166,
-0.019748738035559654,
-0.006162111647427082,
0.006378096528351307,
-0.014381710439920425,
0.0168031994253397,
-0.0023577490355819464,
0.02244112454354763,
0.03751932084560394,
-0.024605195969343185,
-0.04398537799715996,
-0.0078011672012507915,
-0.005112362559884787,
0.012088488787412643,
0.05786745995283127,
0.008855709806084633,
0.08376437425613403,
-0.020312292501330376,
0.01637849397957325,
0.0018571955151855946,
0.013285534456372261,
0.0028807346243411303,
0.0026809964329004288,
0.03793348744511604,
0.0060460008680820465,
-0.05691464990377426,
-0.03141781687736511,
0.055302198976278305,
-0.004279792308807373,
-0.03325992077589035,
-0.005084634758532047,
0.005192977841943502,
0.022998826578259468,
-0.017154768109321594,
-0.022275157272815704,
-0.01823384128510952,
0.04790183901786804,
0.01521238125860691,
0.04269209876656532,
0.00889897532761097,
-0.03252113237977028,
0.027886489406228065,
0.024580547586083412,
0.02655217982828617,
-0.02531169354915619,
-0.00824125949293375,
-0.06974972784519196,
0.011107263155281544,
0.007172818761318922,
0.0059636617079377174,
-0.0049033258110284805,
0.020144550129771233,
0.013815830461680889,
-0.050823524594306946,
0.03873744606971741,
-0.05554651468992233,
-0.046690769493579865,
-0.019810618832707405,
-0.01773981750011444,
-0.06796219199895859,
0.029329681769013405,
0.0014993430813774467,
-0.014596867375075817,
0.06790133565664291,
-0.058488260954618454,
0.013351290486752987,
0.0008682809420861304,
0.006593169178813696,
-0.014152266085147858,
0.0766608789563179,
-0.030507249757647514,
0.023609507828950882,
-0.013465371914207935,
0.007677176967263222,
0.14808301627635956,
0.042348772287368774,
0.036266252398490906,
-0.038430940359830856,
-0.007905462756752968,
0.007786143571138382,
-0.0021631452254951,
-0.034799885004758835,
0.007636386435478926,
-0.013210952281951904,
-0.023676186800003052,
-0.004500941839069128,
0.04991048946976662,
-0.03604419156908989,
-0.0414816215634346,
0.020152559503912926,
-0.038094934076070786,
-0.04935012757778168,
0.00651557045057416,
-0.021416937932372093,
-0.013421139679849148,
-0.011899659410119057,
-0.02397240325808525,
0.014793707057833672,
-0.01661684177815914,
-0.042498793452978134,
-0.008404678665101528,
-0.037350282073020935,
0.008100025355815887,
-0.010732008144259453,
-0.0752154067158699,
0.012300706468522549,
-0.007985386997461319,
-0.026126330718398094,
0.00442234193906188,
0.04916277527809143,
0.004939063917845488,
-0.019804969429969788,
0.029984986409544945,
0.0596296489238739,
-0.015709534287452698,
0.008701171725988388,
0.0030446669552475214,
0.009711934253573418,
-0.07117047160863876,
0.02743721753358841,
-0.041087083518505096,
0.027673352509737015,
-0.006177383009344339,
0.014088766649365425,
0.03284478560090065,
-0.04035999998450279,
0.005965877324342728,
-0.0037433390971273184,
0.020145071670413017,
-0.000824193877633661,
0.022600410506129265,
-0.03643229231238365,
0.015493366867303848,
-0.002620141487568617,
0.007273481227457523,
0.02675274945795536,
-0.02847621776163578,
-0.020032307133078575,
-0.002528655808418989,
-0.031198330223560333,
-0.01136210560798645,
0.07744161039590836,
-0.012792909517884254,
-0.004130884539335966,
-0.002782715717330575,
-0.018382586538791656,
0.0131119629368186,
0.005278927739709616,
-0.034941088408231735,
0.039433836936950684,
0.016853757202625275,
0.014371834695339203,
-0.0328405387699604,
-0.058900877833366394,
-0.059934698045253754,
0.0026192371733486652,
-0.0330502912402153,
0.002985264640301466,
-0.031594522297382355,
-0.01029922440648079,
0.03212719038128853,
0.04653138667345047,
0.010438580997288227,
0.017415473237633705,
0.04488920420408249,
0.0054038939997553825,
0.039777252823114395,
-0.02643507719039917,
-0.030658748000860214,
0.004675986710935831,
-0.0034862072207033634,
-0.02088131010532379,
-0.006661244202405214,
-0.01652630791068077,
0.046123478561639786,
-0.02684173360466957,
-0.03866659104824066,
0.0339248850941658,
-0.035961929708719254,
-0.0039059026166796684,
0.004419049713760614,
-0.012095289304852486,
0.0034024061169475317,
0.037083227187395096,
0.025181634351611137,
-0.06515304744243622,
0.00209123850800097,
-0.0035612129140645266,
-0.0029997650999575853,
-0.003636343637481332,
0.034600887447595596,
-0.018408626317977905,
0.013704677112400532,
-0.019042085856199265,
0.022496139630675316,
-0.066573865711689,
-0.024709049612283707,
-0.011915753595530987,
-0.03698750212788582,
-0.005366164725273848,
0.006209071725606918,
-0.05793721601366997,
0.012057230807840824,
-0.010918610729277134,
0.004389146342873573,
-0.009168693795800209,
0.023704785853624344,
-0.008559894748032093,
-0.02329774759709835,
0.01422854233533144,
-0.0008604458416812122,
0.02891133353114128,
0.004684124141931534,
-0.03036312200129032,
0.020295413210988045,
0.03391709551215172,
-0.017495999112725258,
0.024757107719779015,
-0.027007628232240677,
0.007356582209467888,
0.010976935736835003,
-0.03500812128186226,
-0.0011158442357555032,
0.017059849575161934,
-0.042260847985744476,
-0.005292051006108522,
-0.08364170789718628,
-0.05302438884973526,
-0.03474760800600052,
-0.044873300939798355,
-0.03237656503915787,
-0.02044748328626156,
-0.008673962205648422,
-0.02523741126060486,
0.012026051059365273,
-0.02301948145031929,
-0.03356984257698059,
0.007117528468370438,
-0.0026073565240949392,
-0.005945794750005007,
0.04414935037493706,
0.009950928390026093,
0.005751513410359621,
0.010473952628672123,
-0.012776967138051987,
0.03362305089831352,
0.0012235668255016208,
-0.00217461003921926,
-0.0978407934308052,
-0.04178273677825928,
-0.024605227634310722,
0.028660066425800323,
0.05433429777622223,
-0.02931479550898075,
-0.009878144599497318,
0.022177385166287422,
-0.06808922439813614,
0.04305046796798706,
-0.022234879434108734,
0.003057237947359681,
0.007624633144587278,
-0.015425445511937141,
0.013047104701399803,
0.023091401904821396,
-0.033877257257699966,
0.050992365926504135,
-0.009725922718644142,
0.02115226536989212,
-0.025651518255472183,
-0.021473919972777367,
0.04786161333322525,
0.03354612737894058,
-0.012457353062927723,
-0.002059350023046136,
0.04062415286898613,
-0.02744809351861477,
-0.015642419457435608,
0.03637831285595894,
-0.040367789566516876,
0.02206992357969284,
-0.00349823129363358,
0.0212933961302042,
-0.021431103348731995,
0.058705754578113556,
-0.0060133314691483974,
0.031153066083788872,
-0.009997098706662655,
0.021423418074846268,
0.029166826978325844,
-0.0006236305343918502,
-0.027649112045764923,
0.0006398861296474934,
0.03572307899594307,
-0.0012901072623208165,
-0.012016868218779564,
0.010875069536268711,
-0.055254776030778885,
-0.001997746527194977,
0.02340269275009632,
-0.011839333921670914,
-0.024767685681581497,
-0.024541186168789864,
-0.02072213403880596,
-0.014470092952251434,
0.01949586160480976,
0.0192507803440094,
-0.0023278139997273684,
-0.029096819460392,
0.001461129984818399,
0.03835908696055412,
-0.0008608616190031171,
0.018637312576174736,
0.01897343248128891,
-0.04800913482904434,
-0.059972941875457764,
-0.013220925815403461,
-0.03075101226568222,
-0.016076713800430298,
0.02085469663143158,
-0.019030818715691566,
-0.008393563330173492,
-0.007621495984494686,
0.02197004109621048,
0.009487491101026535,
-0.02149483561515808,
-0.01809117943048477,
-0.030696706846356392,
-0.0698380097746849,
0.03828131780028343,
-0.007532840128988028,
-0.05475680157542229,
-0.004837291315197945,
-0.011204262264072895,
0.005448079202324152,
-0.012135723605751991,
0.041307877749204636,
-0.03692648559808731,
0.0035468689166009426,
0.015033644624054432,
-0.03628816083073616,
-0.008055291138589382,
-0.0046600899659097195,
0.024364624172449112,
0.013304957188665867,
-0.0030268304981291294,
0.022136088460683823,
0.00788069050759077,
-0.004159324336796999,
0.007788779214024544,
0.027399370446801186,
-0.029551023617386818,
0.009750002063810825,
-0.014188428409397602,
-0.011979425325989723,
-0.010603316128253937,
-0.003199438564479351,
-0.016380252316594124,
0.05245091766119003,
-0.0028614855837076902,
0.01073927991092205,
0.013541257940232754,
-0.05324195697903633,
-0.03208639472723007,
0.017751120030879974,
0.013703595846891403,
0.0062403809279203415,
-0.021481558680534363,
-0.009167350828647614,
0.02889196388423443,
-0.03520023450255394,
-0.010384994558990002,
0.0025034905411303043,
0.000545988732483238,
-0.020101366564631462,
0.027665449306368828,
0.012751669622957706,
0.015077340416610241,
-0.0068579064682126045,
0.07015842199325562,
0.010810786858201027,
0.017375905066728592,
0.05303274840116501,
-0.018308842554688454,
0.0009994815336540341,
-0.0255785770714283,
-0.022469496354460716,
0.06896263360977173,
-0.021949395537376404,
0.07658329606056213,
-0.016061358153820038,
-0.003571470268070698,
-0.01009286753833294,
-0.029080640524625778,
0.026302777230739594,
-0.01794595457613468,
-0.0194392129778862,
0.029100729152560234,
-0.015464389696717262,
0.07592078298330307,
-0.02874068170785904,
0.04149722307920456,
-0.009553363546729088,
0.028238801285624504,
0.025623595342040062,
-0.022384624928236008,
-0.008702688850462437,
0.00558561971411109,
-0.017157385125756264,
-0.010137506760656834,
0.007999362424015999,
-0.03937956318259239,
-0.01670208014547825,
0.004773394670337439,
0.021093962714076042,
0.02920220047235489,
0.009325726889073849,
0.016457397490739822,
-0.05427207797765732,
-0.06170351803302765,
-0.031300630420446396,
0.063404880464077,
0.060434240847826004,
-0.019346680492162704,
-0.01635749451816082,
0.014033266343176365,
-0.0015451249200850725,
0.04001981019973755,
-0.031918156892061234,
-0.043360233306884766,
-0.002770659513771534,
0.01904415525496006,
0.030017230659723282,
-0.008663871325552464
] |
<p>I just cooked a meat pie in the oven. Almost immediately after pulling it out of the oven, I felt that the crust was only slightly warm, but when I cut it open the filling felt very warm. I can't understand how the crust could be at a lower temperature. My understanding was that the oven heats the air, then the air heats the crust and the crust heats the filling inside. As long as the air is hotter than the crust (should be always), there is no way for the crust to lose heat, except by heating the filling and there is no way for the filling to gain heat, without being heated by the crust. According to this logic, the filling can't be hotter than the crust. Given this situation, why does the filling feel hotter than the crust?</p>
| 10,742 |
[
-0.0030734678730368614,
-0.024869119748473167,
0.0012831200147047639,
-0.008436672389507294,
-0.012247512117028236,
0.026882555335760117,
0.006643970031291246,
-0.012353837490081787,
-0.0009636605391278863,
0.01038949005305767,
0.015342502854764462,
0.026556823402643204,
0.03886966407299042,
-0.0033385506831109524,
0.00016345108451787382,
-0.004321523476392031,
-0.019474400207400322,
-0.002368853660300374,
0.0058239479549229145,
-0.01892390288412571,
-0.02119339071214199,
0.023393364623188972,
-0.02687055803835392,
-0.008929906412959099,
-0.04671958461403847,
0.007188726216554642,
0.018475420773029327,
-0.006754119880497456,
0.07069356739521027,
0.030252618715167046,
0.006339477840811014,
-0.020122742280364037,
-0.024980172514915466,
0.028340645134449005,
0.05934867262840271,
-0.010214138776063919,
-0.039891231805086136,
0.008266358636319637,
-0.02749866060912609,
0.026318946853280067,
0.007326650898903608,
0.0042526600882411,
-0.00041925377445295453,
0.017197085544466972,
0.015870779752731323,
-0.012502492405474186,
0.0017078920500352979,
-0.001748827868141234,
0.061021339148283005,
-0.059763096272945404,
0.035710424184799194,
-0.02292121946811676,
0.02216794714331627,
0.09018375724554062,
0.025452956557273865,
0.006461024284362793,
0.07934366911649704,
0.05019199103116989,
-0.03148043155670166,
-0.059785086661577225,
-0.04060317203402519,
-0.03616150841116905,
-0.03577284887433052,
-0.002806241624057293,
-0.022314397618174553,
0.02180013619363308,
-0.012833554297685623,
-0.023487024009227753,
0.0065278890542685986,
0.018749630078673363,
0.034922875463962555,
0.005112270824611187,
0.021664435043931007,
-0.016029760241508484,
0.012635084800422192,
-0.01583821140229702,
0.034293800592422485,
0.00016329345817212015,
0.05615825951099396,
0.03464875370264053,
0.010352888144552708,
0.01807338185608387,
0.03744274005293846,
0.026399705559015274,
-0.007722680922597647,
0.00013774787657894194,
0.0741681233048439,
-0.00616411492228508,
0.015516173094511032,
0.055147457867860794,
-0.008354928344488144,
0.01604708656668663,
-0.007875114679336548,
-0.029398510232567787,
0.0027266221586614847,
-0.01687675341963768,
-0.01903642900288105,
0.058712996542453766,
-0.003249181667342782,
0.007237504236400127,
0.0028428719379007816,
0.022534780204296112,
0.02498357929289341,
0.0884813666343689,
0.0013189370511099696,
-0.02459494210779667,
-0.039055176079273224,
0.033040083944797516,
0.041563719511032104,
0.0034041928593069315,
-0.06453938037157059,
-0.009361088275909424,
-0.014895467087626457,
0.011911558918654919,
0.011833369731903076,
-0.040268126875162125,
-0.00762720825150609,
-0.036061838269233704,
0.0022056037560105324,
0.020828699693083763,
0.04469408467411995,
-0.014342447742819786,
0.0032418067567050457,
-0.027954276651144028,
-0.10045963525772095,
0.028367212042212486,
0.0027812481857836246,
-0.002439234871417284,
-0.026561791077256203,
0.03746962547302246,
-0.02283654920756817,
-0.04092928767204285,
-0.004155764821916819,
-0.0018702431116253138,
0.03709166496992111,
-0.010545616038143635,
-0.08861038088798523,
-0.06620507687330246,
0.02987692691385746,
0.009107074700295925,
-0.01314803771674633,
-0.09093271940946579,
0.0005172909586690366,
0.02734389156103134,
0.06171964854001999,
0.01959572732448578,
-0.019150128588080406,
-0.03265228867530823,
-0.0001369037345284596,
0.0021903777960687876,
-0.02366727776825428,
-0.057807326316833496,
0.00031100574415177107,
-0.01849689893424511,
0.015477757900953293,
-0.04331424832344055,
0.05843276157975197,
0.016332337632775307,
-0.018023867160081863,
-0.021053733304142952,
0.02028665505349636,
-0.0362125001847744,
-0.018215857446193695,
-0.01960133947432041,
0.019031690433621407,
-0.02078162506222725,
0.1098073348402977,
0.001379568362608552,
-0.034071601927280426,
0.038885705173015594,
-0.001328089041635394,
0.01755703054368496,
-0.03982480987906456,
0.04160001873970032,
0.048340555280447006,
-0.0007233174983412027,
-0.025424925610423088,
0.004001963883638382,
0.040924787521362305,
0.0804661214351654,
-0.031094329431653023,
-0.00591050973162055,
0.021769696846604347,
-0.01973498985171318,
-0.013659792952239513,
0.051423899829387665,
-0.0045987521298229694,
-0.02617306262254715,
0.020635537803173065,
-0.06657091528177261,
-0.051765572279691696,
-0.07989431917667389,
-0.025188792496919632,
-0.0290729608386755,
-0.008245481178164482,
-0.013111422769725323,
0.06063654273748398,
0.024620147421956062,
-0.06283169984817505,
-0.028623230755329132,
0.007603859528899193,
-0.027517281472682953,
0.02202882617712021,
-0.03028656542301178,
0.0263331551104784,
0.058860115706920624,
0.018475692719221115,
-0.022713765501976013,
0.015687858685851097,
-0.012510058470070362,
-0.009329292923212051,
0.0124663719907403,
-0.011051635257899761,
-0.002952049020677805,
-0.005569787230342627,
-0.030162334442138672,
0.0042848424054682255,
0.006018861196935177,
-0.036948468536138535,
0.07404101639986038,
-0.0006647227564826608,
0.08200297504663467,
0.001974591054022312,
0.009362592361867428,
-0.011625038459897041,
0.04141576215624809,
-0.002314592245966196,
0.008118430152535439,
-0.032062698155641556,
-0.03071710653603077,
-0.040062956511974335,
-0.021143220365047455,
0.052070096135139465,
0.017768707126379013,
-0.042034704238176346,
-0.00033733653253875673,
0.037068989127874374,
0.014433428645133972,
-0.0037414429243654013,
0.014611495658755302,
0.02278464287519455,
-0.013230687007308006,
0.03790029138326645,
0.006656269542872906,
0.05063645914196968,
0.040090590715408325,
0.01805482991039753,
0.017247257754206657,
0.03348102420568466,
-0.0026097402442246675,
-0.044789981096982956,
0.057587631046772,
0.016390329226851463,
0.023776208981871605,
-0.011754108592867851,
-0.0048332116566598415,
0.006575442384928465,
-0.03429045528173447,
0.05846502259373665,
-0.010328790172934532,
0.01917826011776924,
0.0054299733601510525,
-0.020303500816226006,
-0.0085136778652668,
0.011839034035801888,
0.02852906659245491,
0.009920472279191017,
0.0011939078103750944,
0.014553748071193695,
-0.031130867078900337,
-0.0153193986043334,
-0.02985883131623268,
-0.0057693771086633205,
-0.032939303666353226,
-0.014382426626980305,
-0.010288002900779247,
-0.002683050464838743,
0.01688443124294281,
-0.04433315992355347,
-0.02396458387374878,
-0.041511181741952896,
-0.004631676245480776,
0.006596022751182318,
0.006076647434383631,
-0.03543109446763992,
0.010905925184488297,
0.012404337525367737,
-0.021046599373221397,
0.043808870017528534,
0.011727624572813511,
0.005148720927536488,
-0.008051366545259953,
-0.036243122071027756,
-0.03763768821954727,
0.0007540850783698261,
-0.020761331543326378,
0.03505153954029083,
-0.012142408639192581,
0.0032363724894821644,
0.049553677439689636,
-0.009684180840849876,
-0.0053538051433861256,
0.05113476887345314,
-0.041585735976696014,
-0.05721527338027954,
-0.03284327685832977,
-0.022150153294205666,
0.03973468765616417,
-0.02541618049144745,
0.014436235651373863,
0.03203599527478218,
-0.03203151375055313,
-0.013123163022100925,
-0.00645206356421113,
-0.061547309160232544,
-0.00710729043930769,
-0.016409747302532196,
0.0120561383664608,
0.02300318330526352,
-0.051419105380773544,
0.0460846945643425,
-0.006159876007586718,
-0.019948316738009453,
0.0003177992766723037,
0.0009043222526088357,
-0.030033860355615616,
0.00084215885726735,
0.03105568140745163,
0.030737776309251785,
-0.04974464699625969,
0.03321550786495209,
0.025557417422533035,
0.06576592475175858,
0.04576331749558449,
0.022990738973021507,
-0.04656395688652992,
0.02040030062198639,
0.0022660447284579277,
-0.023054495453834534,
0.013057774864137173,
0.020852714776992798,
-0.0023723652120679617,
0.010249854065477848,
0.007913448847830296,
0.0416044183075428,
0.05629356950521469,
-0.061475515365600586,
0.03707081079483032,
0.011183594353497028,
-0.019890764728188515,
-0.04597761854529381,
0.04486965760588646,
-0.04879222810268402,
0.015160896815359592,
0.03179299831390381,
0.05370430275797844,
0.06390061974525452,
-0.024669447913765907,
-0.013326802290976048,
0.040110282599925995,
0.04722406342625618,
-0.04042436182498932,
-0.024629274383187294,
0.005118453875184059,
-0.03605642169713974,
0.047461286187171936,
0.025974411517381668,
-0.0015224087983369827,
0.05911145731806755,
0.02852092869579792,
0.0381833054125309,
0.0026592379435896873,
-0.04049063101410866,
0.0000733154229237698,
-0.05778561905026436,
-0.018468834459781647,
0.030628206208348274,
0.0703170970082283,
0.012570720165967941,
0.07905097305774689,
0.03355361893773079,
0.01060368213802576,
0.0161605067551136,
0.02647852711379528,
-0.09450696408748627,
0.05516740307211876,
0.003896299982443452,
0.0010710936039686203,
-0.02668706886470318,
-0.018657226115465164,
0.004978231154382229,
-0.024419793859124184,
0.011255196295678616,
-0.030396074056625366,
-0.004146077204495668,
-0.04723405838012695,
0.013409916311502457,
-0.025203119963407516,
-0.018530642613768578,
-0.016897052526474,
0.035473063588142395,
0.043001022189855576,
-0.011892830953001976,
0.043522052466869354,
0.055594008415937424,
-0.00012531231914181262,
-0.025510640814900398,
-0.06299398839473724,
0.0005411599995568395,
0.019099004566669464,
0.03338777273893356,
0.0020603470038622618,
0.032650627195835114,
-0.021790828555822372,
-0.0012073040707036853,
0.04493959993124008,
0.050452761352062225,
-0.02308596298098564,
-0.016867078840732574,
-0.044237881898880005,
-0.026485953480005264,
-0.03541550040245056,
-0.016677523031830788,
0.06791681796312332,
-0.03815789893269539,
0.012714613229036331,
0.004982621408998966,
0.029254036024212837,
-0.03081524558365345,
0.01934291049838066,
0.04288564994931221,
0.017043963074684143,
-0.035897146910429,
-0.03945261612534523,
-0.027855275198817253,
-0.07344444841146469,
0.02138591557741165,
0.015355398878455162,
-0.014673640951514244,
-0.02444084919989109,
-0.008471797220408916,
0.023775219917297363,
-0.04800648242235184,
0.010657659731805325,
-0.005018641706556082,
-0.022730572149157524,
0.018310265615582466,
-0.019872013479471207,
-0.012415952980518341,
0.006301751360297203,
0.006751583889126778,
0.060599878430366516,
0.01568262092769146,
-0.0254839938133955,
-0.0776568129658699,
-0.004491782281547785,
0.07496286183595657,
0.034481219947338104,
-0.027895910665392876,
0.006603180896490812,
-0.06617394834756851,
0.0014591157669201493,
0.013458340428769588,
-0.009778214618563652,
0.04938044026494026,
-0.06892887502908707,
-0.028465302661061287,
-0.008161691017448902,
-0.02693650685250759,
0.0018391745397821069,
0.004484169650822878,
0.010272089391946793,
0.013914193958044052,
-0.015179956331849098,
-0.00028154763276688755,
-0.02150736376643181,
-0.005191061645746231,
0.042320407927036285,
0.02301190234720707,
-0.0035984537098556757,
0.016010107472538948,
0.017809003591537476,
-0.00011307695240247995,
-0.02144521288573742,
-0.07521772384643555,
-0.031463585793972015,
-0.020985035225749016,
-0.006727011874318123,
0.038997799158096313,
-0.03269074857234955,
-0.04157755896449089,
0.009588518179953098,
-0.014170830138027668,
-0.047519501298666,
-0.007186900824308395,
-0.01594984345138073,
0.04796509072184563,
0.02792551927268505,
-0.003150590695440769,
0.06107054278254509,
0.022324731573462486,
-0.037416722625494,
-0.0123769361525774,
0.0075426059775054455,
0.053087566047906876,
-0.02336232364177704,
0.011555777862668037,
-0.031858500093221664,
-0.018781576305627823,
0.008323166519403458,
0.03417930006980896,
0.018836984410881996,
0.0014047888107597828,
-0.020882457494735718,
-0.06455141305923462,
-0.0019588021095842123,
0.025298457592725754,
0.026213178411126137,
0.025564249604940414,
-0.02171671949326992,
0.007367695681750774,
0.003956485539674759,
-0.022635415196418762,
0.01693148910999298,
0.019165178760886192,
0.019516171887516975,
0.022363781929016113,
-0.022731788456439972,
0.030122147873044014,
-0.03934575244784355,
-0.027527451515197754,
0.003916753921657801,
-0.03042944148182869,
0.030521107837557793,
0.00023514032363891602,
-0.012448578141629696,
0.007761488202959299,
-0.06989284604787827,
0.0022489598486572504,
-0.006859046872705221,
0.020285015925765038,
0.02349812164902687,
-0.03247186169028282,
0.06407676637172699,
0.01483375858515501,
0.004850481636822224,
-0.08468951284885406,
-0.048377521336078644,
0.02036427892744541,
0.018410252407193184,
-0.034693922847509384,
-0.019299443811178207,
-0.04414874687790871,
-0.0022216993384063244,
-0.06712226569652557,
0.010654788464307785,
0.0459616556763649,
0.023166697472333908,
0.004729937762022018,
0.02995026484131813,
0.017312277108430862,
0.03206590935587883,
0.01253143697977066,
0.0041443160735070705,
0.004593128804117441,
-0.011844051070511341,
-0.04600021615624428,
0.04996393248438835,
0.033637769520282745,
-0.020802779123187065,
-0.021980781108140945,
0.01057185884565115,
0.020814931020140648,
0.047881778329610825,
0.012253737077116966,
-0.025713758543133736,
0.014766493812203407,
0.03569295257329941,
-0.007252316456288099,
-0.041821833699941635,
0.049419522285461426,
0.030859846621751785,
0.039119161665439606,
-0.0023659460712224245,
0.0009278018260374665,
-0.010673386044800282,
-0.015250466763973236,
0.0009302711114287376,
-0.02264963649213314,
0.014516942203044891,
0.03413677215576172,
0.08861520141363144,
-0.01431361585855484,
0.004172483924776316,
0.022557886317372322,
-0.006553702522069216,
0.04128323495388031,
0.007783368695527315,
-0.017179492861032486,
0.006864736322313547,
0.021335419267416,
-0.05008029192686081,
0.005975694861263037,
-0.0051863547414541245,
-0.0003493822005111724,
0.0399712510406971,
-0.0455692782998085,
0.059265632182359695,
0.03523171320557594,
-0.034782811999320984,
0.01340482011437416,
-0.0028134677559137344,
-0.02309352718293667,
0.019726980477571487,
-0.0301008690148592,
0.03138329088687897,
-0.008456459268927574,
0.002891427604481578,
0.048041943460702896,
0.032339174300432205,
-0.004434217233210802,
-0.002074309391900897,
0.010162685997784138,
0.056057192385196686,
0.003246565582230687,
-0.008675647899508476,
-0.04115264490246773,
0.023763393983244896,
-0.018191322684288025,
0.0432976596057415,
-0.016060372814536095,
-0.02397378720343113,
0.05064947530627251,
-0.003064512275159359,
0.039235979318618774,
-0.025001918897032738,
-0.029486263170838356,
-0.014188392087817192,
0.035897377878427505,
0.012805678881704807,
0.025327356532216072,
0.04232228547334671,
0.0017559899715706706,
0.013180671259760857,
-0.013079939410090446,
-0.015279602259397507,
0.013303440995514393,
-0.021538015455007553,
-0.033466972410678864,
-0.022653380408883095,
-0.011469262652099133,
0.045832742005586624,
-0.030195316299796104,
-0.02540503442287445,
0.007555600721389055,
-0.023799924179911613,
-0.004228389821946621,
0.027746301144361496,
0.021653784438967705,
-0.00873658899217844,
0.07207050174474716,
0.008472093380987644,
0.011100511066615582,
-0.013742185197770596,
0.030385179445147514,
0.11130381375551224,
0.01805415377020836,
-0.045281194150447845,
-0.051613133400678635,
0.02011512778699398,
-0.03159702941775322,
-0.0035322904586791992,
-0.027572697028517723,
0.021911032497882843,
-0.010783128440380096,
0.03732132539153099,
0.04908500984311104,
0.06080680340528488,
-0.012821936048567295,
0.006700728554278612,
0.05593712255358696,
-0.009766903705894947,
-0.008839931339025497,
0.006537649314850569,
0.011704853735864162,
0.0012832327047362924,
0.01465823594480753,
-0.041909120976924896,
-0.0034755803644657135,
-0.03447515890002251,
0.024008940905332565,
0.005312219727784395,
-0.0388011634349823,
0.019892310723662376,
0.009918744675815105,
-0.021559294313192368,
0.006904997397214174,
0.02216237410902977,
-0.016889989376068115,
-0.01093382015824318,
0.01114178728312254,
0.05884050205349922,
-0.015734802931547165,
0.02700924687087536,
0.021393872797489166,
0.022320521995425224,
0.016805123537778854,
0.036019548773765564,
0.048533566296100616,
-0.02650860883295536,
-0.03274264559149742,
0.0009568586829118431,
0.040801987051963806,
0.014078840613365173,
0.01930776797235012,
0.016099924221634865,
0.01623612269759178,
0.002068841364234686,
-0.01470404677093029,
-0.00449548102915287,
0.013339761644601822,
0.00412764074280858,
-0.019786449149250984,
-0.07225585728883743,
-0.025307007133960724,
0.04478642717003822,
0.006034350488334894,
0.0068962848745286465,
0.012154427357017994,
-0.009070315398275852,
-0.01363097783178091,
-0.01784399524331093,
0.02223965898156166,
-0.011790699325501919,
-0.02776806615293026,
-0.013106167316436768,
0.01054049376398325,
-0.0022766219917684793,
0.0007473289733752608,
0.025750907137989998,
0.011566386558115482,
0.04293939471244812,
-0.013911808840930462,
-0.037215519696474075,
0.03899843245744705,
-0.04493064433336258,
0.006587113719433546,
-0.021285129711031914,
0.004318499006330967,
-0.03792894259095192,
-0.04659641161561012,
-0.001565445913001895,
0.027498293668031693,
-0.04026912525296211,
-0.02600783295929432,
0.007117743603885174,
-0.010537350550293922,
0.0034686552826315165,
-0.01911267824470997,
-0.0350426584482193,
0.029612749814987183,
-0.059109706431627274,
-0.02963504195213318,
0.01766560785472393,
0.03738504648208618,
-0.009101436473429203,
0.0018684756942093372,
0.006163768470287323,
0.0049174814485013485,
-0.028129685670137405,
-0.012200106866657734,
0.03449878841638565,
0.010270352475345135,
-0.015554079785943031,
-0.015176058746874332,
-0.005369885824620724,
-0.023864956572651863,
-0.05870199576020241,
-0.02280665934085846,
-0.023821791633963585,
-0.023717515170574188,
0.05384073406457901,
0.012941291555762291,
0.03662502020597458,
-0.006288980599492788,
-0.003508935449644923,
-0.01769881322979927,
-0.023735497146844864,
-0.07325375825166702,
-0.04843847453594208,
0.028775304555892944,
-0.00793401338160038,
0.0033210180699825287,
0.010800284333527088,
-0.027232429012656212,
-0.025233859196305275,
-0.00801103189587593,
0.017031576484441757,
-0.018072599545121193,
-0.05015498772263527,
0.021151280030608177,
-0.030268214643001556,
0.04642033204436302,
-0.0649411678314209,
-0.08171921223402023,
0.07028011977672577,
-0.0346997007727623,
-0.0624798983335495,
0.007778125815093517,
0.011056761257350445,
0.03063146211206913,
0.016835859045386314,
0.009586472995579243,
-0.014210567809641361,
0.06332734227180481,
-0.0023913183249533176,
-0.020275522023439407,
-0.006389599293470383,
-0.01334640197455883,
0.02081013098359108,
0.024721873924136162,
-0.0019332015654072165,
-0.01250428892672062,
-0.007513014599680901,
0.040187038481235504,
0.019735164940357208,
0.003956579603254795,
-0.027530565857887268,
0.005831473972648382,
-0.030438650399446487,
0.01146271824836731,
0.014987671747803688,
0.05060526728630066,
0.01626383699476719,
0.04825923964381218,
-0.010522383265197277,
0.04508774355053902,
-0.017223486676812172,
-0.007187549024820328,
-0.06058945879340172,
0.009866169653832912,
-0.01186930388212204,
0.002515908796340227,
0.0057941945269703865,
-0.04173506051301956,
0.00943503063172102,
0.006589280441403389,
-0.05373383313417435,
-0.009407853707671165,
0.0012524353805929422,
-0.011527182534337044,
-0.036609817296266556,
-0.04199521988630295,
0.0007741539739072323,
0.04467136412858963,
0.042701248079538345,
0.05039791762828827,
0.024899300187826157,
0.00013669107283931226,
-0.002505204640328884,
-0.006341143045574427,
-0.033094026148319244,
0.04698619619011879,
-0.03141322359442711,
-0.019821930676698685,
0.026662949472665787,
-0.008264139294624329,
-0.02109697461128235,
0.03618622571229935,
-0.033778686076402664,
-0.02879270724952221,
0.007674722000956535,
-0.02656080201268196,
-0.03965246304869652,
-0.018897050991654396,
0.020689530298113823,
0.0022255226504057646,
0.026285959407687187,
0.05484956130385399,
0.025738876312971115,
0.031254179775714874,
-0.02057385817170143,
-0.020000141113996506,
0.018861087039113045,
-0.022867148742079735,
-0.052243396639823914,
0.026921037584543228,
-0.044659145176410675,
-0.0035875586327165365,
0.0024493015371263027,
0.03536457568407059,
0.0025025897193700075,
-0.026074165478348732,
0.009770389646291733,
-0.053835924714803696,
-0.013110347092151642,
0.031744033098220825,
0.0419207438826561,
-0.02107422985136509,
-0.01004123967140913,
-0.00513524329289794,
0.03909582644701004,
0.02519167959690094,
0.021742986515164375,
-0.0042716749012470245,
-0.012809505686163902,
-0.011724322102963924,
-0.017180485650897026,
-0.018308432772755623,
-0.03592551499605179,
-0.026675846427679062,
-0.04498406872153282,
0.005345339886844158,
0.01274510845541954,
0.04251165688037872,
-0.01705123856663704,
-0.03546351566910744,
-0.02211715839803219,
-0.04442130774259567,
0.012747284024953842,
-0.020232371985912323,
-0.004477562382817268,
-0.05596408247947693,
-0.01113622821867466,
-0.005887393839657307,
-0.018121063709259033,
0.05257292836904526,
0.0271338801831007,
-0.01352640986442566,
-0.006371264345943928,
-0.0043424880132079124,
0.028442159295082092,
-0.047045689076185226,
0.029490089043974876,
-0.02603168785572052,
-0.024201538413763046,
-0.010433046147227287,
-0.003689822042360902,
-0.050437577068805695,
-0.013372174464166164,
0.03706057369709015,
-0.010468213818967342,
0.032341741025447845,
-0.02341386489570141,
-0.008545602671802044,
0.045859139412641525,
0.008891122415661812,
0.018566899001598358,
0.08316715806722641,
-0.017580261453986168,
-0.026262566447257996,
0.025619463995099068,
0.0034187408164143562,
-0.04357537999749184,
0.018697088584303856,
0.01757674664258957,
0.010907458141446114,
-0.0037081995978951454,
0.008296838030219078,
0.0059396568685770035,
-0.03537692502140999,
-0.002953981515020132,
0.03858300298452377,
-0.042556535452604294,
-0.01860210858285427,
0.0029598919209092855,
0.019429059699177742,
0.023601971566677094,
-0.028196988627314568,
-0.025116635486483574,
-0.02384159155189991,
0.016581596806645393,
0.02266315557062626,
0.05618979036808014,
-0.002346087945625186,
0.008920787833631039,
0.013339267112314701,
0.016314320266246796,
-0.014251498505473137,
0.01019972562789917,
-0.0055575137957930565,
0.04573524743318558,
-0.026171814650297165,
-0.03827434405684471,
-0.023449841886758804,
-0.02604571171104908,
-0.0008768994593992829,
-0.006451010704040527,
-0.014429113827645779,
0.06893619894981384,
0.013720371760427952,
0.010967430658638477,
-0.0012637642212212086,
-0.008100786246359348,
-0.02794744446873665,
-0.007206772919744253,
0.05502685159444809,
0.0064861103892326355,
-0.008598532527685165,
0.030394744127988815,
-0.008349866606295109,
-0.011564942076802254,
0.023218870162963867,
-0.0012553069973364472,
-0.013420766219496727,
-0.003407785203307867,
0.012051455676555634,
-0.018009759485721588,
-0.033700671046972275,
-0.004766656551510096,
0.007450960110872984,
0.08454596996307373,
0.04429524764418602,
0.03323687985539436,
0.031073179095983505,
-0.007448867429047823,
-0.009650159627199173,
0.04457768052816391,
-0.11352895200252533,
-0.05230829864740372,
-0.030946392565965652,
0.03169247880578041,
-0.011923874728381634,
-0.016701625660061836
] |
<p>This is a nice problem that I would like to share. </p>
<p><strong>Problem:</strong> In a public garden, there a statue consisting of a spherical stone and a stone cup. The ball is 1 meter in diameter and weighs at least a ton. The cup is an upside-down hemispherical shell, and the ball sits in this shell and fits it almost exactly. Water is pumped into the bottom of shell so that a thin film exists between shell and the ball. The result is a ball that is free to rotate with negligible friction.</p>
<p>You only have access to the ball near the top, so while you can push it to make it turn around any horizontal axis, you can't get enough of a grip to make it turn around the vertical axis. Can you impart a net angular momentum around the vertical axis anyway, so that the balls spins around the vertical axis?</p>
<p><strong>Source:</strong> <em>Vector Calculus, Linear Algebra, and Differential Forms</em> by Hubbard and Hubbard. </p>
| 10,743 |
[
-0.043503060936927795,
0.018739016726613045,
-0.009376159869134426,
-0.011806371621787548,
0.038430552929639816,
-0.048365697264671326,
-0.02056710235774517,
-0.0054718125611543655,
-0.0003990853438153863,
-0.0072741140611469746,
0.041740838438272476,
0.0632290169596672,
0.03467796370387077,
0.053055621683597565,
0.022857924923300743,
0.004526128992438316,
0.010920841246843338,
-0.03571481630206108,
0.00605412945151329,
-0.010410991497337818,
-0.00584813579916954,
0.002137109637260437,
0.010075602680444717,
0.013804415240883827,
-0.002835232065990567,
0.026316087692975998,
0.027796978130936623,
-0.049499742686748505,
0.014302958734333515,
0.03876280039548874,
-0.01115844864398241,
-0.02103952318429947,
0.040213968604803085,
0.017005153000354767,
0.03355822339653969,
0.017066214233636856,
-0.01683109626173973,
-0.004445538856089115,
-0.006239572074264288,
0.03154382109642029,
0.010961595922708511,
0.01564169116318226,
0.0036259680055081844,
0.08449698239564896,
0.013390257023274899,
0.04329972714185715,
0.028508199378848076,
-0.012944478541612625,
0.07635892927646637,
-0.055448051542043686,
0.05479276180267334,
0.01038462482392788,
0.04492122307419777,
0.02939215674996376,
0.0006925099296495318,
-0.033198244869709015,
0.049380023032426834,
0.07507219165563583,
-0.011521839536726475,
-0.030139585956931114,
-0.01672680675983429,
-0.02791518345475197,
-0.042703695595264435,
0.002626239089295268,
-0.013180918991565704,
0.00003340515831951052,
-0.004004444926977158,
0.0044365995563566685,
0.017963193356990814,
-0.033902525901794434,
0.017859837040305138,
0.018502091988921165,
0.038720086216926575,
-0.037998419255018234,
-0.023158948868513107,
-0.0038146325387060642,
0.003366539953276515,
-0.004614094737917185,
-0.005445179995149374,
-0.004789663944393396,
-0.02084818296134472,
0.005358976777642965,
0.036739714443683624,
0.050510093569755554,
-0.005705857649445534,
-0.03421683609485626,
0.06024598330259323,
-0.01503076869994402,
0.035695429891347885,
0.02289111167192459,
0.025471918284893036,
0.00409412058070302,
0.01945282332599163,
-0.009232386015355587,
-0.032240141183137894,
0.0012288145953789353,
0.012835707515478134,
0.05866933986544609,
0.017161671072244644,
-0.00735133420675993,
-0.027399364858865738,
0.006750805303454399,
0.006244974210858345,
0.08868270367383957,
0.015682214871048927,
-0.05356842279434204,
0.012498612515628338,
0.008736560121178627,
0.0040242839604616165,
0.012068575248122215,
-0.03501061722636223,
-0.009420467540621758,
-0.02153157815337181,
-0.0027571627870202065,
-0.0007858216413296759,
-0.005993909668177366,
-0.030932964757084846,
-0.003825015854090452,
0.02091321162879467,
0.030894635245203972,
0.03026091866195202,
-0.032281678169965744,
0.00911021325737238,
-0.054305896162986755,
-0.07999171316623688,
0.023518282920122147,
0.019821614027023315,
-0.03711048513650894,
-0.043139029294252396,
-0.012928888201713562,
0.03389555960893631,
0.005760018713772297,
-0.0047391424886882305,
-0.02532769925892353,
-0.0012581131886690855,
-0.03986118361353874,
-0.09883102774620056,
-0.05367099866271019,
0.04845771566033363,
0.0017041047103703022,
-0.08088571578264236,
-0.06546283513307571,
-0.010821814648807049,
0.033655695617198944,
0.11935433745384216,
0.015676241368055344,
0.0226957555860281,
-0.006801828276365995,
0.03937598690390587,
-0.017352920025587082,
-0.006329767405986786,
0.009104126133024693,
0.028542349115014076,
-0.0737835168838501,
-0.02966601587831974,
-0.059229034930467606,
0.019203603267669678,
0.013826224021613598,
0.011648393236100674,
-0.004420669283717871,
0.0449453666806221,
-0.04214132949709892,
0.05325945094227791,
-0.032654281705617905,
-0.00416693976148963,
-0.030925065279006958,
-0.00327523541636765,
-0.020627712830901146,
0.04093031957745552,
0.04407751187682152,
-0.00767418323084712,
0.01777840219438076,
0.002526003634557128,
0.03299708664417267,
0.040280841290950775,
-0.031055692583322525,
0.03221389651298523,
-0.015986168757081032,
0.0046775019727647305,
-0.013283811509609222,
0.012940438464283943,
-0.02086491324007511,
0.021443994715809822,
0.006783309392631054,
-0.006939583458006382,
0.026008976623415947,
-0.0005675491993315518,
-0.011382278054952621,
-0.02210838906466961,
-0.03318481892347336,
-0.022477349266409874,
-0.04579382389783859,
0.02937156893312931,
-0.0003628371632657945,
0.0035375934094190598,
0.0423940010368824,
0.02410515770316124,
0.01834207773208618,
-0.02010953053832054,
-0.025432931259274483,
-0.019695613533258438,
0.011862109415233135,
0.011937061324715614,
-0.009558193385601044,
0.024367785081267357,
0.04373473301529884,
0.044457875192165375,
-0.007220229133963585,
0.01737108640372753,
-0.023657193407416344,
-0.01788775436580181,
-0.03860541805624962,
0.0025612327735871077,
0.021330086514353752,
0.0285312719643116,
0.04271451011300087,
0.012141233310103416,
0.008449132554233074,
0.008418389596045017,
0.0023233070969581604,
-0.028449011966586113,
0.06390514224767685,
0.061028383672237396,
-0.0080980584025383,
0.007534753065556288,
0.08381684869527817,
0.010202744975686073,
-0.016602113842964172,
0.003941415809094906,
-0.023569049313664436,
-0.029369249939918518,
0.02007152885198593,
-0.02390986867249012,
0.05964278429746628,
-0.009029899723827839,
0.028223546221852303,
0.019150735810399055,
0.04268648102879524,
0.01455622911453247,
0.0074541508220136166,
-0.02348330058157444,
0.0029600821435451508,
0.029876533895730972,
0.010628982447087765,
0.0037355790846049786,
0.03706929832696915,
0.015953781083226204,
0.018891917541623116,
-0.0061835902743041515,
0.02932337112724781,
-0.03364214301109314,
-0.008246134966611862,
0.01517304964363575,
-0.002977906260639429,
0.013046068139374256,
-0.0343044251203537,
0.047508977353572845,
-0.008892319165170193,
-0.024341266602277756,
0.01809350773692131,
-0.011842701584100723,
0.035145021975040436,
-0.05355587601661682,
0.014428658410906792,
0.000362780992873013,
0.006068460177630186,
0.02945014275610447,
-0.002042805776000023,
0.06502857804298401,
-0.0346289724111557,
-0.02918163128197193,
-0.020986944437026978,
0.007488856092095375,
0.004189953673630953,
0.01188669167459011,
-0.0012055127881467342,
0.01743573322892189,
0.01835290901362896,
0.00034471723483875394,
-0.014383763074874878,
0.012015540152788162,
-0.019240638241171837,
-0.014945844188332558,
0.03799448907375336,
-0.07824816554784775,
0.014780156314373016,
-0.03630182892084122,
-0.01635231450200081,
0.04600026458501816,
0.003657969878986478,
-0.031776610761880875,
0.03172670677304268,
0.04446333646774292,
-0.0608501210808754,
-0.011468331329524517,
-0.01766229420900345,
-0.014727884903550148,
-0.04175608605146408,
0.01288880966603756,
-0.005333477631211281,
0.02200864814221859,
-0.01569928601384163,
-0.014746730215847492,
-0.0028562999796122313,
-0.043969009071588516,
0.0018517174758017063,
0.018830643966794014,
0.03490586578845978,
-0.018914291635155678,
0.014791091904044151,
0.02668336033821106,
0.0029132962226867676,
-0.03506182134151459,
-0.09428355097770691,
-0.05543392524123192,
0.02111966535449028,
-0.008823627606034279,
0.04086373746395111,
0.04033224657177925,
0.007261848542839289,
0.07585813105106354,
0.03766395151615143,
-0.051089346408843994,
0.004654997494071722,
-0.02500455640256405,
0.01706617884337902,
-0.05442181974649429,
0.008347795344889164,
0.05149991065263748,
-0.02620176039636135,
0.002082312246784568,
0.01019937265664339,
-0.0016416290309280157,
0.001515410840511322,
0.009644292294979095,
-0.020352620631456375,
0.024913329631090164,
0.014891073107719421,
-0.015545747242867947,
0.016071222722530365,
0.013971695676445961,
-0.03920500725507736,
0.004530731122940779,
0.015920046716928482,
0.03651035577058792,
0.048075057566165924,
-0.04668770730495453,
0.06055345758795738,
0.005054657347500324,
-0.007866284810006618,
-0.020225781947374344,
0.045625265687704086,
-0.02275313064455986,
-0.0050339726731181145,
0.009094500914216042,
0.010555658489465714,
0.043483100831508636,
0.004421472083777189,
-0.001715227379463613,
0.04694557934999466,
0.04996004328131676,
-0.00003104647475993261,
-0.025928661227226257,
-0.01909560337662697,
0.003558363998308778,
0.03914322331547737,
-0.021641282364726067,
0.013184788636863232,
0.0231091920286417,
0.03055550344288349,
-0.01098374929279089,
-0.00475618289783597,
-0.012065647169947624,
-0.016109522432088852,
-0.056008756160736084,
0.04341643676161766,
-0.007149616722017527,
0.02333112061023712,
0.014605299569666386,
0.0276856180280447,
0.015353857539594173,
0.012511758133769035,
-0.005601849872618914,
-0.012175171636044979,
-0.07771105319261551,
0.04401567950844765,
-0.048292338848114014,
0.0074631646275520325,
-0.00966397114098072,
0.012084202840924263,
0.03502697870135307,
-0.007637111470103264,
-0.0439264215528965,
-0.033188436180353165,
-0.010530012659728527,
-0.019067104905843735,
0.03526943549513817,
-0.018509335815906525,
-0.036553677171468735,
-0.008143935352563858,
-0.00018361110414844006,
0.04448650777339935,
-0.03220653161406517,
0.026073290035128593,
0.02900775335729122,
-0.06513026356697083,
0.011526964604854584,
0.0032497302163392305,
0.011516797356307507,
0.008056815713644028,
0.03540867939591408,
-0.004975160118192434,
0.04057832807302475,
-0.016750594601035118,
-0.03137165307998657,
-0.029485579580068588,
0.040840182453393936,
0.02406499534845352,
0.024036545306444168,
-0.04574785381555557,
-0.0595056377351284,
-0.016304805874824524,
0.015048827044665813,
0.08263510465621948,
-0.018657712265849113,
-0.005330777261406183,
-0.0006690084701403975,
-0.020286213606595993,
0.004463942721486092,
0.03302862495183945,
0.0529324896633625,
0.04186415299773216,
-0.01144007220864296,
-0.04649770259857178,
-0.015958484262228012,
-0.043993476778268814,
0.006194237619638443,
0.013042782433331013,
-0.0013364149490371346,
-0.021503405645489693,
-0.024138707667589188,
0.017984693869948387,
0.025005685165524483,
-0.013318466022610664,
0.040830180048942566,
-0.031445492058992386,
0.036754220724105835,
-0.02191474847495556,
0.018573369830846786,
0.014519506134092808,
0.048721808940172195,
0.012985442765057087,
0.0208390224725008,
0.014705074951052666,
-0.0656193196773529,
-0.02756422758102417,
0.058597128838300705,
0.05098526179790497,
0.01480386033654213,
0.006572120822966099,
-0.07213346660137177,
-0.040911346673965454,
0.06412293761968613,
-0.01623491570353508,
0.05201102793216705,
0.013250486925244331,
-0.023137999698519707,
-0.033713288605213165,
-0.05008045211434364,
-0.023251984268426895,
-0.03220941871404648,
-0.0462450236082077,
0.036805592477321625,
-0.006116409320384264,
-0.012616537511348724,
0.021568745374679565,
0.028328344225883484,
0.04785970225930214,
0.01662960648536682,
0.021075492724776268,
-0.024323828518390656,
0.0052637062035501,
-0.0012743767583742738,
-0.034499287605285645,
-0.09868811070919037,
-0.006987582426518202,
0.005238912533968687,
-0.012330924160778522,
0.03446582704782486,
-0.06096552684903145,
-0.03511428087949753,
0.021098829805850983,
-0.013013601303100586,
-0.025403233245015144,
0.00952878501266241,
-0.030253618955612183,
0.01676969788968563,
0.003330281702801585,
0.04160738363862038,
0.013197348453104496,
0.02126481384038925,
-0.015096989460289478,
-0.029200799763202667,
-0.007968067191541195,
-0.023585615679621696,
-0.006411343347281218,
-0.008289109915494919,
-0.03933636471629143,
0.014765501022338867,
-0.005598264746367931,
0.019943488761782646,
0.009933389723300934,
0.026371950283646584,
0.011960064060986042,
-0.01666361838579178,
-0.02751913294196129,
0.03405691310763359,
-0.019635476171970367,
-0.039478931576013565,
0.0017400479409843683,
-0.016492202877998352,
0.04270142689347267,
-0.007685682270675898,
-0.017040465027093887,
0.019495146349072456,
0.027715934440493584,
0.06173576042056084,
-0.030583877116441727,
0.003103102557361126,
-0.03678504377603531,
-0.024337412789463997,
-0.03491156920790672,
-0.08053766936063766,
0.08031313121318817,
-0.0218465868383646,
0.016017958521842957,
0.06894287467002869,
-0.03322837874293327,
-0.019104253500699997,
0.000301501335343346,
-0.015225573442876339,
0.0008107487228699028,
-0.005020836368203163,
0.0032298737205564976,
0.022438928484916687,
0.0020210316870361567,
-0.02320987917482853,
-0.05306881666183472,
0.0014194983523339033,
0.012268519029021263,
-0.014683907851576805,
-0.01706729456782341,
-0.0021062965970486403,
0.010378992184996605,
-0.039451923221349716,
0.000692154688294977,
0.03540698066353798,
-0.049105171114206314,
0.014832629822194576,
0.0330982506275177,
-0.007233197335153818,
0.06525018066167831,
-0.023689202964305878,
-0.015629515051841736,
0.01980416290462017,
-0.029240043833851814,
0.024126475676894188,
-0.011070732958614826,
0.04598437249660492,
-0.043630070984363556,
-0.048941124230623245,
-0.006909733638167381,
0.010827317833900452,
0.021133186295628548,
-0.013200159184634686,
0.008381504565477371,
0.035907357931137085,
0.014647581614553928,
-0.03788665309548378,
-0.006648737005889416,
0.017940640449523926,
0.0119076082482934,
0.0199482049793005,
0.03497603163123131,
0.0071732522919774055,
-0.03477228805422783,
-0.03754984214901924,
0.015498579479753971,
-0.005226476117968559,
-0.019065577536821365,
0.0003640837676357478,
0.06947532296180725,
-0.03138362243771553,
-0.01720782369375229,
0.02110769972205162,
0.00865249428898096,
0.025735314935445786,
0.010250547900795937,
-0.012095990590751171,
-0.05396044999361038,
0.009442063979804516,
-0.040148258209228516,
-0.037536874413490295,
-0.020772026851773262,
0.03448311612010002,
0.07331410050392151,
0.0020542945712804794,
0.06569487601518631,
0.058414459228515625,
0.021915743127465248,
-0.04251858592033386,
0.01139687467366457,
-0.03023654967546463,
0.018550248816609383,
-0.010786750353872776,
0.0217797439545393,
-0.0255265049636364,
0.01484348252415657,
0.0384289026260376,
0.05776100978255272,
-0.03180000185966492,
0.03683687746524811,
-0.001165195950306952,
-0.022275980561971664,
0.03633278235793114,
-0.0178859643638134,
-0.034896157681941986,
0.009911374188959599,
-0.03550369665026665,
0.052206851541996,
0.005023231729865074,
0.005369104910641909,
0.025878293439745903,
0.009387616068124771,
0.018936414271593094,
-0.04265950620174408,
-0.02570955641567707,
-0.04292076453566551,
-0.018200352787971497,
0.014757965691387653,
0.028540927916765213,
-0.025345467031002045,
0.0015537204453721642,
0.03211194649338722,
0.033031366765499115,
-0.011023083701729774,
-0.0632479190826416,
-0.05341041460633278,
0.009901333600282669,
-0.02582431025803089,
-0.04068119823932648,
0.04759107157588005,
0.03180139884352684,
0.002565189264714718,
0.03540252521634102,
-0.028550641611218452,
0.021655617281794548,
0.04328512027859688,
0.028047623112797737,
-0.011451954953372478,
0.03429718688130379,
-0.03352048993110657,
0.01272412110120058,
-0.022376777604222298,
0.01812032423913479,
0.15588268637657166,
0.005799449048936367,
0.027643432840704918,
-0.0198853500187397,
-0.019198430702090263,
-0.012911449186503887,
-0.02551623061299324,
-0.0465523786842823,
0.0009425718453712761,
-0.024913059547543526,
0.002631597686558962,
-0.017193881794810295,
0.0444926880300045,
0.007831857539713383,
0.011001582257449627,
0.04947440326213837,
-0.0422116294503212,
-0.009239650331437588,
-0.021145904436707497,
-0.04135289043188095,
-0.016121884807944298,
0.035087525844573975,
-0.0435776449739933,
0.031317465007305145,
-0.054571229964494705,
-0.014279049821197987,
-0.030184205621480942,
-0.044024255126714706,
0.060553744435310364,
0.011194849386811256,
-0.04018240422010422,
0.03998475894331932,
-0.020533304661512375,
-0.008584397844970226,
-0.018438048660755157,
0.04168945923447609,
0.036600545048713684,
-0.023335210978984833,
0.036908939480781555,
0.040009744465351105,
0.03594842553138733,
0.015218386426568031,
0.00535530736669898,
-0.011236662976443768,
-0.027273839339613914,
0.021287882700562477,
-0.07819326221942902,
0.03839993104338646,
-0.04686325043439865,
0.005871236324310303,
0.009121999144554138,
-0.07685082405805588,
-0.00561621505767107,
-0.066470667719841,
-0.00810180976986885,
-0.01473826915025711,
0.051656194031238556,
0.020169919356703758,
0.0027416751254349947,
0.017737630754709244,
0.01892787590622902,
0.0411493219435215,
0.008002335205674171,
-0.02785266935825348,
0.019162891432642937,
-0.015986133366823196,
0.02356269769370556,
0.04145074263215065,
-0.01936239004135132,
-0.04641150310635567,
-0.06694816797971725,
-0.013168456964194775,
-0.02154921554028988,
0.03425817936658859,
-0.0016610766761004925,
0.023754984140396118,
-0.0004731997032649815,
-0.00011774660379160196,
-0.002882699714973569,
-0.02017737366259098,
-0.04253973439335823,
0.004335818346589804,
-0.041929882019758224,
-0.021698037162423134,
-0.015113423578441143,
-0.022073490545153618,
-0.010947322472929955,
0.02004467509686947,
-0.024090347811579704,
-0.039014264941215515,
0.025772934779524803,
0.03940299153327942,
0.012367560528218746,
-0.0064911614172160625,
-0.060927823185920715,
-0.02441541850566864,
-0.02752653695642948,
0.022566858679056168,
0.0002892876509577036,
0.03771710395812988,
0.06952220946550369,
0.01890603080391884,
-0.00783355813473463,
0.019187698140740395,
-0.02551637776196003,
0.020561713725328445,
0.030417373403906822,
-0.01732577569782734,
-0.01079958863556385,
-0.0064781419932842255,
-0.028662657365202904,
-0.044468387961387634,
-0.03686900436878204,
-0.032771266996860504,
-0.03117138333618641,
-0.020933907479047775,
0.011958129703998566,
-0.03401963412761688,
0.007450345903635025,
0.0059945248067379,
0.05389750376343727,
0.0040131788700819016,
0.034665245562791824,
-0.03956135734915733,
0.0050553553737699986,
0.003466786351054907,
0.005888972897082567,
-0.0015796886291354895,
0.048127371817827225,
-0.021986017003655434,
-0.005486189853399992,
-0.026069968938827515,
0.01007956825196743,
-0.010034892708063126,
0.005332171451300383,
0.02672826685011387,
-0.005790574476122856,
0.04204200953245163,
-0.009339666925370693,
-0.03925352543592453,
0.030670395120978355,
-0.01791124790906906,
-0.02399158850312233,
0.008171647787094116,
-0.03474528342485428,
0.047707680612802505,
0.022260548546910286,
-0.057272445410490036,
-0.00036341726081445813,
0.05119629204273224,
-0.03756890445947647,
-0.0019094255985692143,
0.03455032780766487,
-0.03341339901089668,
-0.04417281225323677,
-0.023315973579883575,
0.009674472734332085,
-0.039459653198719025,
-0.045399654656648636,
0.0036062237340956926,
0.030902352184057236,
-0.00837166141718626,
-0.011659177951514721,
-0.012973389588296413,
-0.006419534329324961,
-0.021223051473498344,
0.0042449431493878365,
0.0062395911663770676,
0.009458960965275764,
0.03538980707526207,
-0.05368966609239578,
0.026434022933244705,
0.024890705943107605,
0.02234911173582077,
-0.10031040757894516,
-0.00528399832546711,
0.00023749726824462414,
-0.010593130253255367,
0.03700277581810951,
-0.06626085937023163,
-0.006988408509641886,
0.03232763707637787,
-0.0776633471250534,
0.022860238328576088,
-0.0622590072453022,
0.007851586677134037,
-0.009659790433943272,
0.012645568698644638,
-0.0007922246004454792,
0.0003049427759833634,
0.008508666418492794,
0.022199463099241257,
0.028330059722065926,
0.049441300332546234,
-0.03056628815829754,
-0.01383210439234972,
0.005268019624054432,
0.038223229348659515,
-0.025809936225414276,
0.021591270342469215,
0.06430784612894058,
-0.015873534604907036,
-0.011715642176568508,
0.013426307588815689,
-0.032417070120573044,
-0.002084838692098856,
-0.006877104286104441,
-0.028295844793319702,
-0.010517452843487263,
0.05461328476667404,
0.010687334463000298,
0.005290255416184664,
0.007062243297696114,
0.0015035233227536082,
0.030094478279352188,
0.02997480519115925,
-0.00390473916195333,
0.001329778111539781,
0.002081136452034116,
-0.028616679832339287,
-0.009453186765313148,
0.03425492346286774,
-0.0235438235104084,
0.03053060732781887,
0.006034570746123791,
-0.006545931100845337,
0.02184288203716278,
0.011888690292835236,
-0.029545458033680916,
-0.02198043465614319,
0.00828517135232687,
0.02353089116513729,
-0.013916601426899433,
-0.006710977293550968,
0.02611619606614113,
-0.0006082102190703154,
-0.04325209930539131,
-0.010806054808199406,
0.0038307670038193464,
-0.02445444092154503,
-0.035245247185230255,
0.0055544874630868435,
0.01625974103808403,
-0.0238515455275774,
0.0052977208979427814,
-0.019892219454050064,
-0.04689784720540047,
0.02662433683872223,
0.025077305734157562,
0.07110462337732315,
0.014299669302999973,
-0.028710538521409035,
-0.01290964800864458,
-0.07744345813989639,
0.005518059246242046,
-0.0037608433049172163,
-0.008932983502745628,
0.011083192192018032,
-0.004614769946783781,
0.03207939490675926,
-0.016689985990524292,
0.03642364591360092,
-0.02084760181605816,
-0.013283542357385159,
0.04001826420426369,
-0.03950166329741478,
0.004142811521887779,
-0.020273203030228615,
-0.01735144853591919,
0.001624668133445084,
0.006724503356963396,
0.030333448201417923,
0.007040112279355526,
-0.007212938740849495,
-0.028254056349396706,
0.039728522300720215,
-0.00031394517282024026,
-0.005891675595194101,
0.016552848741412163,
-0.03184451162815094,
0.010168216191232204,
0.00179895362816751,
0.006695386487990618,
0.08557606488466263,
0.028841320425271988,
-0.01716502197086811,
-0.03146164491772652,
-0.04426981508731842,
-0.02067246474325657,
0.037202853709459305,
-0.069367915391922,
-0.012747533619403839,
-0.03277530521154404,
-0.023740379139780998,
0.013303712010383606,
-0.016485601663589478,
-0.017456959933042526,
0.06683383882045746,
-0.0086224265396595,
-0.022043928503990173,
0.024376921355724335,
0.004200808238238096,
0.027191050350666046,
-0.0013667966704815626,
0.0023887555580586195,
-0.006162412464618683,
0.01145112793892622,
0.0034581844229251146,
0.03829072415828705,
0.05275888741016388,
0.011212507262825966,
-0.037571512162685394,
0.029763000085949898,
0.003579293377697468,
0.011691151186823845,
0.02184203453361988,
0.042850568890571594,
-0.01936155930161476,
-0.04411814361810684,
0.0014483751729130745,
-0.020174888893961906,
-0.00693547073751688,
0.007330805994570255,
0.0023417274933308363,
0.06741363555192947,
0.024822648614645004,
-0.02297484688460827,
-0.057557813823223114,
0.02852344699203968,
0.022355331107974052,
0.008967247791588306,
0.019544295966625214,
0.011408912017941475,
-0.03812922537326813,
-0.028481272980570793,
-0.01450373139232397,
-0.0013579175574705005,
0.011112030595541,
-0.02817278541624546,
0.059029389172792435,
0.003986943047493696,
0.02253645285964012,
-0.020018966868519783,
-0.018971243873238564,
-0.019926706328988075,
-0.022496085613965988,
0.034071676433086395,
0.031230920925736427,
0.0028025435749441385,
-0.009881485253572464,
0.02490631863474846,
-0.01928132213652134,
0.07880965620279312,
-0.055018603801727295,
-0.03430791199207306,
-0.015565149486064911,
0.010792127810418606,
-0.03734610229730606,
-0.01171255111694336
] |
<p>Radiation is basically just particles flying around, right? Are free hydrogen atoms just typically not moving fast enough to be considered "radiation"?</p>
| 10,744 |
[
-0.028206512331962585,
-0.02577628754079342,
0.0066635264083743095,
-0.015169796533882618,
0.04017900303006172,
0.003680169116705656,
-0.041000284254550934,
-0.016777614131569862,
0.007144336123019457,
-0.032425858080387115,
0.03377658128738403,
0.04085010290145874,
0.046896792948246,
-0.006979644298553467,
0.011451979167759418,
0.009045515209436417,
-0.010738691315054893,
-0.01993429660797119,
-0.010618616826832294,
-0.016735047101974487,
0.0030390445608645678,
0.014026792719960213,
-0.0040345811285078526,
0.024147119373083115,
-0.0425674133002758,
0.009664581157267094,
0.0052696517668664455,
0.03168238699436188,
0.03362337499856949,
0.031338781118392944,
-0.00864392053335905,
-0.006400848738849163,
-0.0034058657474815845,
0.0211386289447546,
0.03550921007990837,
-0.014222236350178719,
-0.03376822918653488,
-0.03468085452914238,
-0.042538806796073914,
0.010956564918160439,
0.0009372933418489993,
-0.049617208540439606,
-0.005260232836008072,
0.04499628022313118,
-0.03876644745469093,
-0.005264977924525738,
-0.012042521499097347,
-0.0227311123162508,
0.03861580044031143,
-0.06041241064667702,
0.05458466708660126,
-0.02576560527086258,
0.030981799587607384,
-0.004144956823438406,
-0.020829007029533386,
0.034368328750133514,
0.10388906300067902,
0.06315556168556213,
-0.01845998503267765,
-0.021494021639227867,
-0.02684803493320942,
-0.04041318595409393,
-0.03287804499268532,
0.00954822450876236,
-0.01643630675971508,
0.025314198806881905,
-0.02815120480954647,
-0.05251806601881981,
0.04317168518900871,
0.03193327784538269,
0.01846322976052761,
0.0024218896869570017,
0.029891112819314003,
-0.025410404428839684,
0.021251825615763664,
-0.006267610006034374,
0.029737086966633797,
0.0014541205018758774,
0.03982720151543617,
0.045249197632074356,
-0.012136649340391159,
0.003380858339369297,
0.004036603029817343,
0.002808415563777089,
-0.0042664119973778725,
0.0009760063257999718,
0.0758497565984726,
0.00012859873822890222,
-0.0001888223778223619,
0.0280388742685318,
-0.009686789475381374,
0.002173878252506256,
0.04054518789052963,
0.02899942360818386,
-0.016008587554097176,
0.03268992900848389,
-0.004551054444164038,
0.06738129258155823,
0.019911406561732292,
-0.03913233056664467,
0.04750370234251022,
0.0026852991431951523,
0.05541772395372391,
0.07772868871688843,
-0.00977716688066721,
-0.041045986115932465,
-0.019959064200520515,
0.021546801552176476,
-0.0340268649160862,
-0.0168070737272501,
-0.043295226991176605,
0.007178781554102898,
-0.0013968746643513441,
-0.03185542672872543,
0.01009144727140665,
0.002849380951374769,
0.02437604032456875,
-0.003577933646738529,
0.04736353084445,
0.08222807943820953,
0.018093880265951157,
-0.02554973214864731,
0.044209521263837814,
0.018270211294293404,
-0.02689797431230545,
0.01667831838130951,
0.03635185956954956,
0.01591719500720501,
-0.07524361461400986,
0.009279918856918812,
-0.017119666561484337,
-0.00003670658406917937,
0.04500593990087509,
-0.03262302652001381,
0.03818568214774132,
-0.031352002173662186,
-0.08486322313547134,
-0.08135762065649033,
0.004706923849880695,
0.02625924162566662,
-0.05129566416144371,
-0.07674039155244827,
-0.01710747927427292,
0.03844379261136055,
0.06920120120048523,
-0.0009517394355498254,
-0.027309879660606384,
-0.022274348884820938,
0.04199104383587837,
-0.0016134920297190547,
-0.022449655458331108,
-0.006841330789029598,
0.009923460893332958,
-0.0462394654750824,
0.013698571361601353,
-0.05905056744813919,
0.004446617793291807,
0.03959997743368149,
0.006089494097977877,
-0.013196026906371117,
0.04967939108610153,
-0.0031718891113996506,
0.015308479778468609,
0.024902643635869026,
-0.008089202456176281,
-0.037065356969833374,
0.04980560019612312,
0.039333757013082504,
0.0017141852295026183,
0.0493055023252964,
0.03274908661842346,
0.07218094170093536,
-0.004023843910545111,
0.03784048929810524,
0.03945926949381828,
-0.05936736240983009,
-0.028147391974925995,
-0.03072471171617508,
0.0332220159471035,
0.009400254115462303,
-0.042272672057151794,
0.011186209507286549,
0.005234116222709417,
0.03763832151889801,
0.0030995956622064114,
0.04748240113258362,
0.0008030278841033578,
-0.0015165023505687714,
0.007615688256919384,
-0.04278164356946945,
0.007231824565678835,
-0.028083421289920807,
0.02209288254380226,
-0.0038235976826399565,
0.017176952213048935,
0.0060319737531244755,
0.0494515635073185,
0.00924097839742899,
-0.0383567288517952,
-0.03415071964263916,
0.004833292681723833,
0.04088791832327843,
0.0013380645541474223,
-0.005600574426352978,
0.04095277562737465,
0.08176667988300323,
0.016055826097726822,
0.030393360182642937,
-0.0012629209086298943,
-0.013567360118031502,
-0.03990839049220085,
-0.016787679865956306,
-0.018267536535859108,
-0.011678927578032017,
0.03283051401376724,
-0.005931825842708349,
0.02400784194469452,
-0.057734064757823944,
-0.031297773122787476,
0.03742797672748566,
-0.006798108108341694,
0.04910137876868248,
0.012234549038112164,
0.00588530208915472,
0.0021047014743089676,
0.0013053877046331763,
0.02190481871366501,
-0.006285891868174076,
-0.002663444261997938,
-0.03006930649280548,
-0.06900709122419357,
0.007644380442798138,
0.042666710913181305,
-0.01370676513761282,
-0.03729072958230972,
0.004922819323837757,
0.008519313298165798,
0.04007292911410332,
0.03696832433342934,
0.04507419094443321,
-0.03870868682861328,
-0.0315595418214798,
0.011630224995315075,
0.022311439737677574,
-0.006432492285966873,
-0.0074597857892513275,
0.025030791759490967,
0.01419749390333891,
0.0226484015583992,
0.0062994323670864105,
0.005375348962843418,
0.03645685687661171,
0.0008590901852585375,
-0.008510426618158817,
-0.0058988528326153755,
-0.052867911756038666,
0.0347488671541214,
-0.03778805583715439,
-0.0005290027474984527,
-0.01027880422770977,
-0.016677118837833405,
0.019258050248026848,
-0.010150398127734661,
-0.005695645231753588,
-0.002908845664933324,
-0.008497512899339199,
-0.024915767833590508,
0.0029615212697535753,
0.047584664076566696,
-0.026737116277217865,
0.04010066017508507,
-0.05343391373753548,
0.02128213830292225,
0.0036030656192451715,
-0.02462971769273281,
0.015917547047138214,
0.021107975393533707,
0.05334560573101044,
-0.04152238741517067,
-0.05333210900425911,
-0.012692159973084927,
-0.07629109174013138,
-0.026302212849259377,
0.022504210472106934,
-0.036223046481609344,
-0.002759147435426712,
-0.029745453968644142,
-0.060734156519174576,
0.04826142638921738,
-0.0438409186899662,
-0.005875495728105307,
0.02760216034948826,
-0.028704235330224037,
-0.038091178983449936,
-0.009871046058833599,
-0.027423318475484848,
-0.0030451237689703703,
-0.021286044269800186,
0.005247553810477257,
0.04886113852262497,
-0.04641115665435791,
-0.014569676481187344,
0.020173203200101852,
-0.019640371203422546,
-0.031117305159568787,
-0.00969344936311245,
-0.0012703891843557358,
0.036916930228471756,
-0.037785422056913376,
0.031180489808321,
0.03154952824115753,
-0.06661295890808105,
0.015102289617061615,
-0.016181517392396927,
-0.051214154809713364,
0.03925460949540138,
-0.00816666055470705,
0.023823294788599014,
-0.0025060696061700583,
-0.02752513252198696,
0.03859776258468628,
0.03445645049214363,
-0.01991160400211811,
-0.004114321433007717,
-0.022608904168009758,
-0.0544794499874115,
-0.03800084814429283,
-0.0055646151304244995,
0.036662034690380096,
0.036939505487680435,
-0.008709500543773174,
0.0008953158976510167,
0.014549790881574154,
0.011786026880145073,
0.012743073515594006,
-0.02235180139541626,
-0.012451736256480217,
0.0472852997481823,
0.013670222833752632,
0.036878760904073715,
0.016763905063271523,
-0.038407184183597565,
0.047262828797101974,
0.011095551773905754,
0.05891866981983185,
0.0021967031061649323,
-0.018145602196455002,
0.06223808601498604,
0.031564824283123016,
0.03154096007347107,
-0.020257845520973206,
0.02021094039082527,
0.00630598608404398,
-0.005700808949768543,
0.0029562213458120823,
0.008700432255864143,
0.036437954753637314,
0.02289510704576969,
-0.016229664906859398,
0.03806259110569954,
0.025797290727496147,
-0.013634895905852318,
-0.017285019159317017,
0.007356144487857819,
0.006061721593141556,
-0.02267175354063511,
0.01527902577072382,
-0.023881319910287857,
0.06962257623672485,
0.013147876597940922,
0.03208570182323456,
0.00789774302393198,
-0.04341784119606018,
-0.018720638006925583,
-0.051917705684900284,
0.015633607283234596,
-0.001377601409330964,
0.03050747513771057,
-0.011728301644325256,
0.05876385420560837,
0.02736496552824974,
0.015637695789337158,
0.005157123785465956,
-0.02622794173657894,
-0.042620737105607986,
0.011849128641188145,
-0.04922991991043091,
-0.02044743299484253,
-0.03917264565825462,
-0.005378254223614931,
-0.05216604471206665,
-0.021479614078998566,
-0.023973219096660614,
-0.03224610537290573,
-0.06109930947422981,
-0.028929688036441803,
0.007153604179620743,
-0.023187030106782913,
-0.04689442738890648,
-0.01642867550253868,
0.02036949433386326,
0.03125418722629547,
0.02419086918234825,
0.003531191498041153,
0.0634404867887497,
-0.016639329493045807,
0.003981973510235548,
0.008364379405975342,
0.007541864179074764,
-0.055807486176490784,
0.03645898401737213,
0.03312879428267479,
-0.00036958587588742375,
-0.0416371151804924,
-0.0131069365888834,
0.02181604877114296,
0.01955176703631878,
-0.0027429014444351196,
-0.0374152772128582,
-0.044942423701286316,
-0.0414443239569664,
-0.009855741634964943,
0.005141099449247122,
0.02621617540717125,
-0.01985272206366062,
0.03162247687578201,
0.021945223212242126,
-0.009955346584320068,
-0.013114528730511665,
0.013553419150412083,
0.03500101715326309,
-0.021511711180210114,
-0.014917262829840183,
-0.020319776609539986,
-0.014554030261933804,
-0.014399858191609383,
-0.018679756671190262,
0.007260384038090706,
-0.01208510622382164,
-0.030700791627168655,
0.007274025585502386,
-0.009933920577168465,
-0.008142846636474133,
-0.008671198971569538,
0.0064580258913338184,
-0.014665056951344013,
-0.004364711698144674,
-0.015672758221626282,
-0.0005527722532860935,
0.03055018000304699,
0.03467248007655144,
0.02851361222565174,
0.0031218277290463448,
-0.010047441348433495,
-0.09461328387260437,
0.01544563751667738,
0.028125669807195663,
0.04867525026202202,
0.0005962030263617635,
-0.029097268357872963,
-0.07274947315454483,
-0.031037406995892525,
0.03915303573012352,
-0.007839004509150982,
0.0052338759414851665,
-0.022445937618613243,
-0.019642848521471024,
0.0028203206602483988,
-0.03240346536040306,
0.0009187873802147806,
0.007983000949025154,
0.00331184477545321,
-0.006986598484218121,
-0.03438972681760788,
-0.018945664167404175,
-0.004408636596053839,
0.011138670146465302,
0.028677908703684807,
0.07204125821590424,
0.029124226421117783,
0.013225202448666096,
-0.009237420745193958,
0.047850560396909714,
-0.026253217831254005,
-0.08044616132974625,
-0.012362456880509853,
0.03825303167104721,
-0.04454396665096283,
0.0581401102244854,
-0.028444485738873482,
-0.0470275953412056,
0.026743358001112938,
0.011068410240113735,
0.018236199393868446,
-0.02265963703393936,
-0.053049635142087936,
0.03488576039671898,
0.03700309246778488,
0.015520508401095867,
0.030109845101833344,
0.052212003618478775,
-0.01675589010119438,
0.011491636745631695,
-0.02303062193095684,
0.0658312439918518,
-0.03326477110385895,
0.015443217940628529,
-0.017678847536444664,
-0.01884992979466915,
0.012350362725555897,
0.03963161259889603,
0.0118545638397336,
-0.004426215775310993,
0.02501569502055645,
-0.046243034303188324,
-0.005021208431571722,
0.012977936305105686,
-0.018013257533311844,
-0.03707997500896454,
-0.0520283468067646,
0.01694664917886257,
-0.05231718346476555,
-0.02938258647918701,
0.03160056844353676,
-0.022330138832330704,
-0.01237269677221775,
0.03371776267886162,
-0.017630457878112793,
0.020727451890707016,
-0.020542718470096588,
-0.007405680604279041,
0.026256820186972618,
-0.0371607206761837,
0.037919171154499054,
-0.010141766630113125,
-0.03143790736794472,
-0.0201717596501112,
-0.06366332620382309,
-0.008324142545461655,
0.025914866477251053,
-0.013084799982607365,
0.0520341619849205,
-0.025360913947224617,
0.04734345152974129,
-0.03634257987141609,
-0.0027382003609091043,
-0.07010907679796219,
-0.024600351229310036,
-0.005825333762913942,
0.0457938052713871,
-0.006064166780561209,
-0.05948225408792496,
0.04403417184948921,
-0.06667293608188629,
-0.027621114626526833,
-0.008141626603901386,
0.02665647119283676,
-0.03459715470671654,
-0.0027378469239920378,
0.03350537270307541,
0.00799220334738493,
0.06492027640342712,
-0.0236514899879694,
-0.07409792393445969,
0.02441501058638096,
0.03405587747693062,
-0.021690770983695984,
-0.0011150599457323551,
0.05512012541294098,
-0.0030526332557201385,
-0.01873547025024891,
-0.010534413158893585,
-0.02848443016409874,
0.020857298746705055,
-0.021088771522045135,
-0.02133505418896675,
0.07563340663909912,
0.020979030057787895,
-0.01809987612068653,
-0.004879621788859367,
0.04798956960439682,
-0.012973177246749401,
0.036950793117284775,
-0.014686386100947857,
-0.006216192618012428,
-0.03138994425535202,
-0.005892863031476736,
0.035500459372997284,
0.021854635328054428,
0.05312258005142212,
0.0007705967291258276,
0.03388896957039833,
-0.019098371267318726,
0.020054874941706657,
-0.0064019495621323586,
-0.00613624881953001,
0.028430482372641563,
-0.028255490586161613,
0.010212080553174019,
-0.0019104278180748224,
-0.006807500030845404,
0.00846001785248518,
-0.03272947296500206,
-0.048810023814439774,
-0.03651292994618416,
0.057474441826343536,
-0.04268182814121246,
0.05579144507646561,
-0.023246372118592262,
0.028418706730008125,
0.0022215843200683594,
-0.041279807686805725,
-0.025272855535149574,
0.013025177642703056,
-0.01924915239214897,
0.002549893455579877,
0.014053641818463802,
0.017620878294110298,
0.022301681339740753,
0.050966933369636536,
-0.00899055041372776,
0.030191276222467422,
0.026355797424912453,
0.029712889343500137,
-0.009916005656123161,
-0.006369882728904486,
-0.05308614671230316,
0.007110819220542908,
-0.04289386793971062,
0.03277123346924782,
0.00021756801288574934,
-0.036562517285346985,
0.04887088015675545,
-0.0013606720604002476,
-0.002902672393247485,
-0.042985428124666214,
-0.007093739230185747,
-0.04132745414972305,
0.024895720183849335,
-0.004436885938048363,
0.015204566530883312,
-0.03977416455745697,
-0.006308035459369421,
0.04574122279882431,
-0.0073579601012170315,
0.021075855940580368,
0.03874349966645241,
-0.0481598898768425,
-0.014829100109636784,
-0.03526530787348747,
-0.012569308280944824,
0.055088482797145844,
0.02027287147939205,
-0.02828204445540905,
-0.011289813555777073,
-0.008007366210222244,
-0.007391185499727726,
0.014788776636123657,
0.06910692155361176,
0.0038881234358996153,
0.03525190055370331,
-0.02181384153664112,
-0.008083527907729149,
-0.002037443220615387,
0.024787483736872673,
0.11771572381258011,
0.030992038547992706,
-0.016056062653660774,
-0.017287200316786766,
-0.011689259670674801,
-0.06298108398914337,
0.03007940948009491,
0.0005112214712426066,
0.00825947243720293,
-0.0227653831243515,
0.037808943539857864,
0.012972344644367695,
0.03725963830947876,
0.005217196419835091,
0.05912734195590019,
0.04658903181552887,
-0.0308090727776289,
-0.015703078359365463,
0.019656039774417877,
0.02289752848446369,
0.03869014233350754,
0.031486716121435165,
-0.04465240240097046,
0.00607671681791544,
-0.03819873183965683,
0.022848989814519882,
-0.023094279691576958,
-0.01893453858792782,
0.036401111632585526,
-0.01210571825504303,
-0.08411580324172974,
-0.01927480474114418,
0.0011247630463913083,
-0.006060780957341194,
-0.031963322311639786,
0.04158824309706688,
0.040123336017131805,
-0.00005597182462224737,
-0.020548107102513313,
-0.00637687835842371,
0.03219069167971611,
-0.004675453994423151,
-0.0064445193856954575,
-0.0015422350261360407,
-0.023364080116152763,
0.03841259703040123,
-0.013479727320373058,
0.02052352763712406,
-0.025583839043974876,
0.013815364800393581,
0.010514490306377411,
0.011367704719305038,
-0.040580980479717255,
-0.04352835193276405,
0.00378341949544847,
0.004832203965634108,
0.009692037478089333,
0.0008207046194002032,
-0.009215733036398888,
-0.042747002094984055,
0.03020450286567211,
-0.01765904389321804,
0.01896735653281212,
0.015873152762651443,
0.006558020133525133,
0.034237090498209,
0.00740643497556448,
0.0239701010286808,
-0.037575554102659225,
-0.0033967969939112663,
-0.0117128174751997,
-0.027780737727880478,
-0.046410735696554184,
-0.020168250426650047,
0.012645414099097252,
0.02546171098947525,
0.05511679872870445,
0.027107568457722664,
-0.00823734700679779,
-0.03134739398956299,
-0.07353676110506058,
0.06862097233533859,
-0.002566313138231635,
-0.02364310622215271,
-0.02329118736088276,
-0.01931023970246315,
0.028153758496046066,
0.036834243685007095,
-0.03086278773844242,
0.02277788333594799,
-0.013800603337585926,
0.027495495975017548,
0.017384516075253487,
-0.04855447635054588,
0.00994993094354868,
0.04756816476583481,
0.011338935233652592,
0.01946283131837845,
-0.013297520577907562,
0.03801168128848076,
0.03483671694993973,
0.012534829787909985,
-0.004830030724406242,
-0.01400719117373228,
-0.024385109543800354,
0.002691156230866909,
0.020735377445816994,
-0.0376758947968483,
0.0010539642535150051,
0.014274531975388527,
0.0020416860934346914,
-0.04115870222449303,
-0.02883370779454708,
-0.05304357409477234,
0.009761299937963486,
0.013016710989177227,
0.029264302924275398,
-0.005003036465495825,
0.04324445128440857,
-0.0004985393024981022,
0.043626777827739716,
-0.007534830830991268,
-0.006760639604181051,
-0.05766948685050011,
0.003347501391544938,
0.01597159542143345,
-0.018654869869351387,
-0.0014616224216297269,
0.02421402372419834,
-0.005421132780611515,
0.013259605504572392,
0.07117568701505661,
0.01806187815964222,
-0.01693093776702881,
0.037762027233839035,
0.008177612908184528,
-0.016492146998643875,
0.058014120906591415,
-0.03946029767394066,
0.005486752837896347,
0.028249269351363182,
-0.03881467878818512,
-0.03579890355467796,
0.015317118726670742,
-0.00587131641805172,
0.036726292222738266,
0.026239804923534393,
-0.032734885811805725,
0.02745204232633114,
0.07832878082990646,
-0.03096279874444008,
0.008524682372808456,
0.013353233225643635,
-0.014035187661647797,
-0.021375788375735283,
-0.029603904113173485,
0.026537423953413963,
0.006230821367353201,
-0.016927244141697884,
0.06715575605630875,
-0.0016243951395154,
-0.022648032754659653,
0.04647788405418396,
-0.03147490322589874,
-0.003462268505245447,
0.01580890081822872,
0.019868191331624985,
0.023577535524964333,
0.018123015761375427,
0.030612682923674583,
-0.04645806923508644,
0.03552033379673958,
0.0259645227342844,
0.023994386196136475,
-0.10576894134283066,
0.0009731513564474881,
-0.018725354224443436,
-0.008582081645727158,
0.0033786657731980085,
-0.030036944895982742,
-0.006727925501763821,
0.047138508409261703,
-0.08628769963979721,
0.017048293724656105,
0.010564139112830162,
-0.028804007917642593,
-0.03489447757601738,
0.018927454948425293,
-0.014110655523836613,
0.0341133177280426,
0.03505759313702583,
0.06304692476987839,
0.014618538320064545,
0.016055993735790253,
-0.028088975697755814,
-0.03463207185268402,
-0.0013288006884977221,
0.010301102884113789,
0.008195164613425732,
-0.012015041895210743,
0.027489034458994865,
-0.0297043789178133,
-0.0022833519615232944,
0.0049268994480371475,
0.0009153620339930058,
0.015553892590105534,
-0.023900995030999184,
-0.001586348284035921,
0.024827588349580765,
0.009934860281646252,
-0.008193322457373142,
-0.04321783408522606,
-0.033252209424972534,
0.04074931517243385,
0.014850913546979427,
0.041321609169244766,
-0.006356397643685341,
0.021355200558900833,
0.0340726338326931,
-0.0529487282037735,
-0.039626482874155045,
0.017870839685201645,
0.0029790387488901615,
-0.003901547519490123,
0.012778251431882381,
0.026935802772641182,
0.020237991586327553,
-0.014214131981134415,
-0.00001834408612921834,
-0.029318073764443398,
0.0011856666533276439,
0.014095456339418888,
0.006531838793307543,
0.007757688406854868,
-0.0002656303404364735,
-0.018883874639868736,
-0.015704849734902382,
-0.0013245927402749658,
0.020775435492396355,
-0.020731719210743904,
-0.039901889860630035,
0.018230309709906578,
0.017785344272851944,
-0.007878584787249565,
-0.030759433284401894,
-0.026362868025898933,
-0.06851980835199356,
0.023963192477822304,
0.006354143377393484,
0.012941538356244564,
0.030486881732940674,
-0.030605213716626167,
-0.04064580798149109,
-0.062409501522779465,
0.030367854982614517,
-0.005643805954605341,
0.02908881939947605,
-0.04583011567592621,
-0.05475141108036041,
-0.0449928380548954,
-0.003541558515280485,
0.06725797802209854,
-0.01774410903453827,
-0.002957973163574934,
0.004682824015617371,
-0.023803673684597015,
0.009982678107917309,
-0.03897034749388695,
0.009062114171683788,
-0.0320284329354763,
-0.03383653983473778,
-0.0058965012431144714,
-0.02774963155388832,
-0.04695054516196251,
-0.002006728667765856,
0.029001468792557716,
0.003010985441505909,
0.024872981011867523,
-0.020975979045033455,
-0.01745222508907318,
0.08737427741289139,
0.050192300230264664,
-0.03910699486732483,
0.028097696602344513,
-0.014635163359344006,
0.01436009630560875,
0.0789211243391037,
-0.0030733004678040743,
-0.04270903393626213,
0.026440320536494255,
-0.002502394374459982,
-0.010017392225563526,
0.015234153717756271,
0.002476271241903305,
-0.015901008620858192,
-0.020229628309607506,
0.0173533596098423,
0.04479358717799187,
-0.048228777945041656,
-0.0013579613296315074,
0.027049092575907707,
0.013407973572611809,
0.009105535224080086,
0.013148830272257328,
0.01521105132997036,
0.02875800058245659,
0.011432060971856117,
-0.03298059478402138,
0.07691490650177002,
0.021946942433714867,
0.0049263592809438705,
0.048922959715127945,
0.0036415026988834143,
0.0018380115507170558,
-0.018679533153772354,
0.027853503823280334,
0.03753628581762314,
-0.027512487024068832,
-0.012097257189452648,
-0.011844300664961338,
-0.005892033688724041,
-0.021311797201633453,
0.012914684601128101,
-0.014680439606308937,
0.07009580731391907,
-0.007015202194452286,
0.02094406448304653,
-0.0077660707756876945,
0.00510187353938818,
0.020209264010190964,
0.038367755711078644,
0.0003098787856288254,
0.04268636181950569,
-0.034943774342536926,
-0.020055510103702545,
-0.046317096799612045,
0.00020026172569487244,
0.05652270466089249,
-0.06125829741358757,
0.05066603422164917,
0.006232904270291328,
-0.016055503860116005,
-0.052410829812288284,
0.0017092066118493676,
0.0034481699112802744,
0.007197843864560127,
-0.0077145337127149105,
0.03403902426362038,
-0.018702998757362366,
-0.018038254231214523,
-0.024306708946824074,
-0.028530290350317955,
0.02155751921236515,
-0.06429079920053482,
0.02933952957391739,
-0.021121850237250328,
0.02917279116809368,
-0.008719328790903091,
-0.008064903318881989
] |
<p>This post is inspired by this <a href="http://math.stackexchange.com/questions/302023/best-sets-of-lecture-notes-and-articles">math.se post</a>.</p>
<p>Let me start by apologizing if there is another thread on phys.se that subsumes this.</p>
<p>I often find that I learn best from sets of lecture notes and short articles. There are three particular reasons that make me feel this way.</p>
<ol>
<li><p>Lecture notes and articles often times take on a very delightful informal approach. They generally take time to bring to the reader's attention some interesting side fact that would normally be left out of a standard textbook (lest it be too big). Lecture notes and articles are where one generally picks up on historical context, overarching themes (the "birds eye view"), and neat interrelations between subjects.</p></li>
<li><p>It is the informality that often allows writers of lecture notes or expository articles to mention some "trivial fact" that every textbook leaves out. Whenever I have one of those moments where a definition just doesn't make sense, or a theorem just doesn't seem right it's invariably a set of lecture notes that sets everything straight for me. People tend to be more honest in lecture notes, to admit that a certain definition or idea confused them when they first learned it, and to take the time to help you understand what finally enabled them to make the jump.</p></li>
<li><p>Often times books are very outdated. It takes a long time to write a book, to polish it to the point where it is ready for publication. Notes often times are closer to the heart of research, closer to how things are learned in the modern sense.</p></li>
</ol>
<p>It is because of reasons like this that I find myself more and more carrying around a big thick manila folder full of stapled together articles and why I keep making trips to Staples to get the latest set of notes bound.</p>
<p>So, if anyone knows of any set of lecture notes, or any expository articles that fit the above criteria, please do share!</p>
<p>I'll start:</p>
<p><strong>People/Places who have a huge array of fantastic notes:</strong></p>
<p><a href="http://www.staff.science.uu.nl/~hooft101/theorist.html">'t Hooft</a></p>
<p><a href="http://math.ucr.edu/home/baez/QG.html">John Baez</a></p>
<p><br />
<b>The <i>Feynman </i>lectures on Physics:</b><br /></p>
<li><a href="http://www.feynmanlectures.caltech.edu/I_toc.html">The Feynman Lectures on Physics, Volume I: mainly mechanics, radiation, and heat.</a> </li>
<li><a href="http://www.feynmanlectures.caltech.edu/II_toc.html">The Feynman Lectures on Physics, Volume II: mainly electromagnetism and matter.</a></li>
<li><a href="http://www.feynmanlectures.caltech.edu/III_toc.html">The Feynman Lectures on Physics, Volume III: quantum mechanics.</a></li>
<p>
<br />
<b>Introductory Courses</b><br />
<br /></p>
<ul>
<li><b>Introductory Classical Mechanics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/301/301.pdf</li>
<li>http://space.wccnet.edu/~gkapp/</li>
<li>http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/</li>
<li>http://academics.smcvt.edu/abrizard/Classical_Mechanics/Notes_070707.pdf</li>
<li>http://www.maths.tcd.ie/~dleen/mathsoc/pdf/Notes.pdf</li>
</ol>
<p><br /></p>
<ul>
<li><b>Optics and Thermodynamics & Electromagnetism</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/316/316.pdf</li>
<li>http://seagull.ukzn.ac.za/~mukaror/</li>
<li>http://www.sicyon.com/resources/library/pdf/optics.pdf</li>
</ol>
<p><br /></p>
<ul>
<li><b>Waves and Oscillations </b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/315/Waves.pdf</li>
<li>http://www.ma.hw.ac.uk/~bernd/F12MS3/</li>
<li>http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/OscWavesIndex.htm</li>
</ol>
<p><br /></p>
<ul>
<li><b>Statistical Mechanics and Thermodynamics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf</li>
<li>http://www.spms.ntu.edu.sg/PAP/courseware/statmech.pdf</li>
<li>http://www.physics.umd.edu/courses/Phys603/kelly/</li>
<li>http://stp.clarku.edu/notes/</li>
</ol>
<p><br /></p>
<ul>
<li><b>Electronics</b></li>
</ul>
<ol>
<li>http://openbookproject.net/electricCircuits/</li>
<li>http://ocw.mit.edu/courses/music-and-theater-arts/21m-380-music-and-technology-live-electronics-performance-practices-spring-2011/lecture-notes/</li>
<li>http://zebu.uoregon.edu/~rayfrey/432/DigitalNotes.pdf</li>
<li>http://courseware.ee.calpoly.edu/~jzhang/EE112/</li>
<li>http://www-inst.eecs.berkeley.edu/~ee130/sp07/lecture.html</li>
<li>http://www.engr.sjsu.edu/kghadiri/EE122/Class_notes.htm</li>
<li>http://www.cramster.com/course-introduction-lecture-note-r30-6638.aspx</li>
</ol>
<p><br /></p>
<ul>
<li><b>Computational Physics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/329/329.pdf</li>
<li>http://www.physics.umd.edu/courses/CourseWare/EssentialMathematica/</li>
<li>http://www.cmth.ph.ic.ac.uk/people/a.mackinnon/Lectures/compphys/</li>
<li>http://math.fullerton.edu/mathews/numerical.html</li>
</ol>
<p><br /></p>
<ul>
<li><b>Introductory Quantum Mechanics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/qmech/qmech.pdf</li>
<li>http://galileo.phys.virginia.edu/classes/252/home.html</li>
<li>http://walet.phy.umist.ac.uk/QM/QM.pdf</li>
<li>Video: http://physicsstream.ucsd.edu/courses/spring2003/physics130a/</li>
<li>http://quantummechanics.ucsd.edu/ph130a/130_notes.pdf</li>
<li>http://www.lecture-notes.co.uk/susskind/quantum-entanglements/</li>
</ol>
<p><br /></p>
<ul>
<li><b>Classical And Quantum Optics</b></li>
</ul>
<ol>
<li>http://people.seas.harvard.edu/~jones/ap216/lectures/lectures.html</li>
<li>http://atomoptics.uoregon.edu/~dsteck/teaching/optics/</li>
</ol>
<p><br />
<br />
<br /></p>
<p>(from my Blog <a href="http://quantizd.blogspot.com">http://quantizd.blogspot.com</a>)</p>
<p>So my goal is to ameliorate this list by adding more resources.</p>
<p>Thank you.</p>
| 10,745 |
[
-0.02878399007022381,
-0.031226083636283875,
0.031209463253617287,
-0.009307285770773888,
0.015250610187649727,
0.02101179026067257,
0.0041353353299200535,
0.01600886695086956,
-0.0044937822967767715,
-0.00833486020565033,
0.05078263208270073,
0.02943609468638897,
0.030376272276043892,
0.03311200439929962,
0.007562276441603899,
0.026718275621533394,
-0.0032229903154075146,
-0.021787570789456367,
-0.032556354999542236,
-0.03199823573231697,
0.03277914598584175,
0.0014750637346878648,
0.01908186450600624,
0.029460474848747253,
0.0009382586576975882,
-0.003090477781370282,
0.006776966154575348,
-0.002775544300675392,
0.011694968678057194,
0.03008502908051014,
-0.03772120177745819,
-0.006149256136268377,
-0.0038969768211245537,
0.019341131672263145,
0.009767202660441399,
0.03127524256706238,
0.03185296803712845,
0.006817512679845095,
0.024646466597914696,
0.020284539088606834,
-0.023527968674898148,
0.014619528315961361,
0.004779855255037546,
0.03596987575292587,
-0.03190097212791443,
0.0637483149766922,
-0.01847304031252861,
-0.002958474913612008,
0.03426020219922066,
-0.07123424857854843,
0.04106728732585907,
-0.010993553325533867,
0.003993109334260225,
0.02644238993525505,
0.011763792484998703,
-0.005330753978341818,
0.05460029095411301,
0.062496840953826904,
-0.0303689856082201,
-0.0519958958029747,
0.0030096371192485094,
-0.0246129147708416,
-0.003963681403547525,
-0.030042923986911774,
-0.012785576283931732,
0.02850579097867012,
0.013843042775988579,
0.004328782204538584,
0.0654294341802597,
-0.03617032244801521,
-0.03777150437235832,
0.019643055275082588,
0.054647840559482574,
-0.0002932575880549848,
0.035681966692209244,
-0.005861979443579912,
-0.016551440581679344,
-0.009359332732856274,
0.05168856680393219,
0.025437388569116592,
0.002019889187067747,
-0.004732346627861261,
0.06454886496067047,
0.014869029633700848,
0.023095782846212387,
-0.03881055861711502,
0.08186164498329163,
-0.005852325353771448,
-0.04197508096694946,
0.020995531231164932,
0.007094989065080881,
-0.009866615757346153,
0.023161930963397026,
-0.05179921165108681,
0.029381038621068,
0.030734380707144737,
-0.0022799631115049124,
-0.02102419175207615,
0.02372584119439125,
0.018772462382912636,
-0.021835114806890488,
-0.03300635889172554,
-0.007132450584322214,
0.07195135951042175,
0.026326552033424377,
-0.0575932115316391,
-0.03351855278015137,
0.022182345390319824,
-0.019628508016467094,
-0.025254227221012115,
0.00020870211301371455,
0.03684752807021141,
-0.011660734191536903,
0.014622616581618786,
-0.025340698659420013,
-0.012621797621250153,
0.030532019212841988,
-0.0219536405056715,
0.04922241345047951,
0.08201190084218979,
0.027934880927205086,
-0.052597835659980774,
-0.027104223147034645,
-0.04439830407500267,
-0.06431661546230316,
0.00006026388655300252,
0.05490593984723091,
-0.034862298518419266,
-0.04062508046627045,
0.007694749627262354,
0.0013870622497051954,
-0.0014717428712174296,
-0.0022318060509860516,
0.04493262991309166,
0.007000338286161423,
-0.006904055830091238,
-0.10603988170623779,
-0.0036872734781354666,
0.05272378772497177,
0.022028710693120956,
-0.05020459368824959,
-0.03991122171282768,
0.020148005336523056,
0.021410560235381126,
0.06793772429227829,
0.03233713656663895,
-0.01941714994609356,
0.0007871338748373091,
0.007708856835961342,
-0.006660348270088434,
-0.007959248498082161,
-0.007558580953627825,
-0.005952318198978901,
-0.029312580823898315,
0.016898207366466522,
-0.03675893321633339,
0.013377709314227104,
0.0373322032392025,
0.032866477966308594,
-0.02302607335150242,
0.0608065240085125,
-0.04662622511386871,
-0.0068664937280118465,
0.0020825848914682865,
-0.04297863692045212,
-0.04351399838924408,
0.06384405493736267,
-0.021376168355345726,
0.01817888207733631,
0.03527834638953209,
-0.01426912285387516,
0.03547872602939606,
-0.044530339539051056,
0.02667262963950634,
0.009781921282410622,
-0.04335172101855278,
0.00717654824256897,
0.02921735681593418,
-0.04237750917673111,
-0.003797102952376008,
-0.04787055030465126,
-0.05738982558250427,
0.02553497813642025,
0.03442051261663437,
-0.026307465508580208,
0.07113797217607498,
0.03132152184844017,
-0.0014723652275279164,
0.02624480240046978,
-0.06146697700023651,
-0.0373464971780777,
-0.02560390904545784,
0.024531785398721695,
-0.02844327501952648,
-0.0317336767911911,
0.040101658552885056,
-0.04092960059642792,
-0.047339145094156265,
-0.011759411543607712,
-0.005852310452610254,
0.0018306465353816748,
0.014736180193722248,
0.04259118437767029,
-0.03687344864010811,
0.006208517123013735,
0.03338959813117981,
0.035857077687978745,
-0.02034417726099491,
0.007931686006486416,
-0.0516231395304203,
-0.00929016899317503,
0.01775808073580265,
-0.054509904235601425,
0.05285632982850075,
-0.022938016802072525,
0.0024885504972189665,
0.00624972814694047,
0.00846376083791256,
-0.021058708429336548,
0.059843599796295166,
-0.02738115005195141,
0.02645503543317318,
0.05894600227475166,
0.03943957760930061,
-0.00571448216214776,
0.044010866433382034,
-0.01687452755868435,
0.006862394046038389,
0.01459276769310236,
-0.02440565824508667,
-0.08288506418466568,
-0.011995065025985241,
0.06042330712080002,
0.014865701086819172,
0.00503222830593586,
0.01825091429054737,
0.017649345099925995,
0.027418818324804306,
0.004110017791390419,
0.01109076477587223,
-0.05962739884853363,
-0.049368567764759064,
0.018147241324186325,
-0.033804621547460556,
0.010688412934541702,
0.021446244791150093,
0.027516713365912437,
0.0028711336199194193,
0.024460943415760994,
0.030477533116936684,
0.01060247141867876,
0.012291139923036098,
0.023962976410984993,
-0.015756649896502495,
0.013770511373877525,
0.005007866770029068,
0.028916537761688232,
-0.02440224401652813,
0.01888991892337799,
0.011505499482154846,
0.011223744601011276,
0.018498923629522324,
-0.02297472022473812,
-0.011188759468495846,
0.015277989208698273,
-0.01630919612944126,
-0.03198232874274254,
-0.006869075354188681,
0.05129280313849449,
-0.05557912960648537,
0.02911052480340004,
-0.015954134985804558,
-0.03804299607872963,
-0.011389280669391155,
-0.010573857463896275,
-0.025751469656825066,
0.01387636549770832,
0.02290455810725689,
-0.031216982752084732,
0.006729357410222292,
0.007012145593762398,
-0.02218717336654663,
0.033126018941402435,
0.010845192708075047,
0.01279478333890438,
0.0009178789332509041,
-0.030337655916810036,
-0.04592743515968323,
0.0218821931630373,
0.03610769659280777,
-0.0016480876365676522,
-0.007473781239241362,
0.018300971016287804,
-0.06018032133579254,
-0.02300211787223816,
0.008420784957706928,
-0.003356593195348978,
-0.015426844358444214,
-0.003419831395149231,
0.030937278643250465,
0.010427257046103477,
-0.05161445587873459,
-0.004812679253518581,
-0.007018726784735918,
-0.028065750375390053,
-0.02671818435192108,
-0.03768980875611305,
0.018284250050783157,
-0.036613866686820984,
-0.012636644765734673,
0.011299993842840195,
0.007697734050452709,
-0.02037247084081173,
-0.0609675869345665,
-0.04368700459599495,
-0.02476383186876774,
-0.014426630921661854,
0.030705993995070457,
-0.009593434631824493,
0.039835527539253235,
0.06895685940980911,
0.0042970008216798306,
-0.04910438507795334,
-0.023824190720915794,
0.0011290779802948236,
0.01702413521707058,
-0.008676145225763321,
0.037274591624736786,
0.024183839559555054,
-0.0028917447198182344,
0.0030465456657111645,
-0.0046115233562886715,
0.034958116710186005,
0.004226985387504101,
0.04078865423798561,
0.010851032100617886,
0.023056643083691597,
-0.02745259366929531,
-0.026269443333148956,
0.03136702626943588,
-0.012680086307227612,
-0.01523886900395155,
-0.016477428376674652,
-0.00434738676995039,
0.03467263653874397,
0.0452142134308815,
-0.03526689112186432,
0.06425634026527405,
0.01474553532898426,
-0.00760801974684,
-0.017333781346678734,
0.0392552874982357,
0.004512202460318804,
-0.05635816231369972,
-0.019495747983455658,
0.03716082498431206,
-0.004540326073765755,
-0.01477219257503748,
0.009490969590842724,
0.03912000730633736,
0.056194353848695755,
-0.047216784209012985,
-0.003260117955505848,
-0.025698138400912285,
0.03203100338578224,
0.033872928470373154,
-0.02766290120780468,
0.02270982228219509,
0.05982137471437454,
0.07427525520324707,
-0.015257110819220543,
0.01362109836190939,
-0.020090539008378983,
-0.027997516095638275,
-0.07846453040838242,
-0.035410474985837936,
-0.015717560425400734,
0.031780023127794266,
0.018694087862968445,
0.05466815456748009,
-0.028598692268133163,
0.041348159313201904,
-0.005976461339741945,
0.0079124104231596,
-0.09524334967136383,
-0.042109955102205276,
-0.022217968478798866,
-0.03848755359649658,
-0.0016186482971534133,
0.014422228559851646,
0.027138726785779,
-0.025906873866915703,
-0.06318391114473343,
-0.05478162690997124,
0.0014362041838467121,
-0.044526636600494385,
-0.010824588127434254,
-0.010528883896768093,
-0.04381069168448448,
-0.00603299168869853,
-0.009691368788480759,
0.08074542880058289,
-0.0037477894220501184,
0.0015562602784484625,
0.023482026532292366,
0.006855760235339403,
-0.029993025586009026,
-0.020772704854607582,
0.027001822367310524,
0.0010190500179305673,
0.009806012734770775,
-0.021608931943774223,
0.0068824803456664085,
-0.01038531307131052,
0.018803317099809647,
0.009247414767742157,
0.015007064677774906,
0.007970317266881466,
-0.017261415719985962,
-0.010149996727705002,
0.004466512706130743,
-0.004893137142062187,
0.03803521394729614,
0.05326858535408974,
-0.035801999270915985,
-0.023610783740878105,
0.05170578137040138,
0.01096434984356165,
0.014937947504222393,
0.01565561443567276,
0.008837740868330002,
-0.018191423267126083,
-0.025781340897083282,
-0.058471377938985825,
0.0024861362762749195,
-0.02866387367248535,
-0.00037641572998836637,
-0.019348839297890663,
0.02512490563094616,
0.032468851655721664,
-0.05444173142313957,
-0.003480194602161646,
0.01874655671417713,
-0.022342858836054802,
-0.003598221344873309,
0.010454123839735985,
-0.011786501854658127,
0.0005691645783372223,
-0.00858281645923853,
0.03060046210885048,
0.03949219733476639,
0.057207390666007996,
0.015423163771629333,
-0.02022257074713707,
-0.059789612889289856,
-0.05586402490735054,
0.04132954031229019,
0.019777754321694374,
0.010472704656422138,
0.030321087688207626,
-0.036871787160634995,
-0.02880413457751274,
0.02938777394592762,
0.0015567613299936056,
0.041043467819690704,
-0.06348872184753418,
-0.030310293659567833,
-0.053391337394714355,
-0.04412168264389038,
-0.042634133249521255,
0.01908048801124096,
0.010305655188858509,
0.04743528366088867,
-0.024886181578040123,
-0.023802893236279488,
-0.04789429157972336,
0.01270322035998106,
0.026112357154488564,
0.028566742315888405,
-0.035171639174222946,
-0.02138296328485012,
-0.011255791410803795,
0.01831625960767269,
-0.07229715585708618,
-0.07373995333909988,
0.016768721863627434,
0.00539409089833498,
-0.028641464188694954,
-0.004292687401175499,
0.019377803429961205,
-0.030375471338629723,
0.013830109499394894,
-0.017051830887794495,
-0.06251620501279831,
0.012516017071902752,
-0.028233574703335762,
0.007745124399662018,
0.020814068615436554,
0.03538651019334793,
0.02333781123161316,
0.04750588908791542,
-0.017479896545410156,
0.006835781969130039,
-0.03703685477375984,
0.008428884670138359,
-0.026199735701084137,
0.0009346029255539179,
0.000791139667853713,
-0.0013654280919581652,
-0.044878553599119186,
0.04638009890913963,
-0.019033722579479218,
-0.008272294886410236,
-0.002893774537369609,
-0.03368739038705826,
-0.03200743719935417,
-0.00402466207742691,
0.004316200502216816,
0.014298212714493275,
0.01641249470412731,
0.030305976048111916,
-0.0032172859646379948,
0.03519544005393982,
0.054700396955013275,
-0.005156371276825666,
0.002013763878494501,
0.0723358541727066,
0.020708486437797546,
0.020147457718849182,
-0.04188370332121849,
-0.010166460648179054,
-0.00378414336591959,
-0.027305440977215767,
0.05056297034025192,
0.012712732888758183,
0.034304067492485046,
0.02700846828520298,
-0.03715934976935387,
-0.047153543680906296,
-0.00021716712217312306,
-0.004196142312139273,
-0.02678103931248188,
-0.01799182780086994,
0.010617080144584179,
-0.002654501935467124,
0.013263457454741001,
-0.006640351377427578,
-0.029587864875793457,
0.04410683363676071,
0.010263933800160885,
-0.028257204219698906,
-0.026805954053997993,
0.029523100703954697,
-0.016574012115597725,
-0.018902959302067757,
-0.010573752224445343,
0.04105895012617111,
-0.0752011314034462,
-0.01285899244248867,
0.0008833958418108523,
0.033514004200696945,
0.042712487280368805,
-0.008393845520913601,
-0.021778523921966553,
-0.0010976844932883978,
0.004149578046053648,
0.008486460894346237,
0.014591746032238007,
0.05169037729501724,
-0.018732409924268723,
-0.03646180406212807,
-0.0023446371778845787,
0.0005664555937983096,
0.011419406160712242,
-0.05569174885749817,
-0.01181726809591055,
0.04837438836693764,
-0.009251625277101994,
0.00799149926751852,
-0.005123187322169542,
0.012546610087156296,
-0.00041485539986751974,
0.038221776485443115,
-0.011751647107303143,
0.010925471782684326,
0.03807011991739273,
-0.03387950360774994,
-0.0064817266538739204,
0.020204192027449608,
0.0006808107136748731,
-0.013225681148469448,
0.033980101346969604,
-0.04267020896077156,
0.004043879918754101,
0.05595686286687851,
-0.009588096290826797,
0.028392791748046875,
-0.006612520199269056,
0.031216274946928024,
-0.029427742585539818,
0.006943493150174618,
-0.016148462891578674,
-0.03263571485877037,
-0.04213565215468407,
-0.004470608662813902,
0.04987761750817299,
0.015844911336898804,
0.013327800668776035,
0.03307477757334709,
-0.02601955085992813,
0.017565753310918808,
0.011180287227034569,
-0.015433547087013721,
-0.034009821712970734,
0.027687406167387962,
0.02816384844481945,
-0.05598686262965202,
-0.009001378901302814,
0.04264376312494278,
0.045175619423389435,
-0.0818682387471199,
-0.010264668613672256,
0.000007553822797490284,
0.00394496088847518,
0.02593764290213585,
-0.013710541650652885,
-0.05244554951786995,
0.05369322746992111,
-0.0794915035367012,
-0.01073619443923235,
-0.036540549248456955,
-0.02382637746632099,
0.026789383962750435,
-0.012394891120493412,
0.038674160838127136,
-0.04944232106208801,
0.004908723756670952,
-0.043666791170835495,
-0.022634731605648994,
0.014435255900025368,
0.0045619565062224865,
0.009319502860307693,
-0.04094185307621956,
0.032505594193935394,
-0.02817818708717823,
0.008813529275357723,
-0.007338166236877441,
-0.024835705757141113,
-0.022044209763407707,
0.007904669269919395,
-0.030126534402370453,
0.04184538125991821,
0.007900233380496502,
-0.030527479946613312,
-0.008227385580539703,
-0.008711721748113632,
0.048425864428281784,
0.05560767650604248,
0.06569691002368927,
-0.017639270052313805,
0.05571696534752846,
-0.034435074776411057,
-0.024698885157704353,
-0.06011761724948883,
-0.022318949922919273,
0.15980517864227295,
0.030639508739113808,
0.033710356801748276,
-0.03902720659971237,
0.04994770139455795,
0.024782715365290642,
0.03118213638663292,
-0.029115622863173485,
-0.008158263750374317,
-0.02318083867430687,
0.03364274278283119,
-0.009532484225928783,
0.06130349636077881,
-0.03495898097753525,
-0.02286103554069996,
-0.016161935403943062,
-0.07001156359910965,
-0.030733028426766396,
-0.02953866310417652,
0.010840441100299358,
0.0031263858545571566,
0.059378042817115784,
-0.029009081423282623,
-0.013914036564528942,
0.02192719653248787,
0.007966136559844017,
-0.030918797478079796,
-0.020684683695435524,
0.029307367280125618,
-0.006827651523053646,
-0.017206743359565735,
0.019976932555437088,
0.07179044932126999,
0.0077408840879797935,
-0.020533915609121323,
0.05030090734362602,
0.0542442724108696,
0.015424052253365517,
0.017859449610114098,
0.012364820577204227,
0.0354880690574646,
0.013494315557181835,
0.040137115865945816,
0.01763162389397621,
-0.0686323344707489,
-0.02167602628469467,
-0.03741762414574623,
0.03945252671837807,
-0.04100140929222107,
-0.020106974989175797,
-0.035898905247449875,
-0.02471313811838627,
0.024806004017591476,
-0.026896324008703232,
-0.04416494444012642,
0.012782702222466469,
0.0047216941602528095,
-0.01295262761414051,
0.00751415453851223,
0.030246689915657043,
0.004499957896769047,
0.024859001860022545,
0.021316198632121086,
0.003494317876175046,
-0.006044343113899231,
-0.004368504974991083,
0.016971584409475327,
0.016284193843603134,
-0.011037907563149929,
0.0013305728789418936,
-0.026761705055832863,
0.004206527024507523,
-0.014323350042104721,
-0.02780897170305252,
-0.01943391002714634,
0.02784842625260353,
0.001714334124699235,
-0.008947550319135189,
-0.00549453217536211,
-0.027784571051597595,
-0.0580020509660244,
0.0279078371822834,
0.035471271723508835,
-0.046086445450782776,
-0.030866587534546852,
-0.022072700783610344,
-0.030206864699721336,
-0.0034840379375964403,
0.030759572982788086,
0.008164390921592712,
0.02216155268251896,
0.0867207944393158,
-0.0005611928063444793,
0.02256571315228939,
0.01001695729792118,
0.027743928134441376,
-0.025420984253287315,
0.0246933251619339,
0.022130243480205536,
0.04895723611116409,
0.05324489623308182,
0.0013095446629449725,
0.02368524670600891,
0.01729941926896572,
-0.008391602896153927,
0.0047269281931221485,
0.047966424375772476,
-0.025150461122393608,
-0.0018619225593283772,
0.037485793232917786,
0.01205653790384531,
-0.04000808298587799,
-0.03389933705329895,
0.01618918962776661,
-0.021462764590978622,
-0.02164899930357933,
-0.01940573751926422,
-0.023338910192251205,
0.04501963406801224,
-0.028732486069202423,
0.034488748759031296,
-0.045924749225378036,
-0.026244090870022774,
-0.04561395198106766,
-0.03706834465265274,
-0.023603862151503563,
-0.00795773509889841,
0.0034752697683870792,
0.0007219819817692041,
0.00015462790906894952,
0.018193375319242477,
0.0371764674782753,
0.028419319540262222,
-0.011908914893865585,
-0.03576141595840454,
-0.023087257519364357,
0.007051876746118069,
0.025877339765429497,
-0.0068777184933424,
-0.023798270151019096,
0.012615591287612915,
-0.0010430450784042478,
-0.05794060602784157,
0.0073323966935276985,
-0.007449008524417877,
0.01860545016825199,
0.03629399091005325,
-0.04143629968166351,
-0.025454366579651833,
0.03578267991542816,
-0.02596564218401909,
-0.012899506837129593,
-0.0006943292682990432,
0.005981956142932177,
0.028925495222210884,
0.004261342342942953,
-0.018953407183289528,
-0.011584238149225712,
-0.0010218097595497966,
-0.0016385382041335106,
-0.03467082977294922,
0.0057783545926213264,
-0.03900926932692528,
0.0009425547323189676,
-0.035923801362514496,
0.027916686609387398,
-0.015281242318451405,
0.021440155804157257,
0.029007866978645325,
0.027321387082338333,
-0.052034828811883926,
0.06025386601686478,
0.020139433443546295,
0.02096785232424736,
-0.07275285571813583,
-0.03614441305398941,
0.008698823861777782,
0.0005742143257521093,
-0.002265244023874402,
-0.020635981112718582,
-0.0077924602665007114,
0.016545984894037247,
-0.07391539961099625,
0.028328821063041687,
-0.029583008959889412,
0.007879167795181274,
-0.013225607573986053,
-0.0017304972279816866,
-0.022378623485565186,
0.06592216342687607,
0.02394874021410942,
0.023840870708227158,
-0.000930494221393019,
0.032664958387613297,
0.025511067360639572,
-0.03789040446281433,
-0.036757417023181915,
0.02106853574514389,
-0.03812946751713753,
-0.004422856494784355,
0.02725684829056263,
0.035832762718200684,
-0.028669286519289017,
0.008667184971272945,
0.02332359552383423,
-0.029057487845420837,
0.016721075400710106,
-0.0023156236857175827,
0.019842185080051422,
0.020835381001234055,
0.020761772990226746,
-0.007167889270931482,
-0.0383734256029129,
0.009165901690721512,
0.014916135929524899,
0.027739979326725006,
0.010974918492138386,
0.007858536206185818,
0.02176557295024395,
-0.026610378175973892,
-0.00598450843244791,
0.015159634873270988,
-0.01780005730688572,
-0.010622900910675526,
-0.005300430115312338,
0.013211067765951157,
-0.014786379411816597,
0.0009071357198990881,
0.004109170753508806,
-0.030119912698864937,
-0.02454853616654873,
0.04902874678373337,
0.0388263575732708,
0.002914273412898183,
0.0616324357688427,
-0.017357882112264633,
-0.027914833277463913,
0.025025876238942146,
0.02432960830628872,
0.031658466905355453,
-0.025871777907013893,
-0.016126476228237152,
0.025796303525567055,
0.009577741846442223,
-0.0011828236747533083,
-0.019813798367977142,
-0.05584171786904335,
0.004696476273238659,
0.02342315763235092,
0.01612740568816662,
-0.012163214385509491,
-0.02821292355656624,
-0.006872182246297598,
-0.054415956139564514,
0.038384754210710526,
-0.002186973812058568,
0.032665833830833435,
-0.048527345061302185,
-0.017903707921504974,
0.0030686799436807632,
0.04845466837286949,
0.06665374338626862,
0.008921739645302296,
0.00838437769562006,
-0.014269603416323662,
0.01953839138150215,
0.036609191447496414,
-0.01415962167084217,
0.032142408192157745,
0.004973890259861946,
0.03496251627802849,
0.006419519428163767,
0.001995016820728779,
0.012251321226358414,
-0.002379533601924777,
0.06822280585765839,
0.012252675369381905,
-0.010414930060505867,
-0.0017580909188836813,
-0.021217675879597664,
0.03727205842733383,
0.050059493631124496,
-0.029077541083097458,
0.031195176765322685,
0.0002985134779009968,
0.011242056265473366,
0.03837946057319641,
-0.036917801946401596,
-0.06026113033294678,
0.008146408945322037,
-0.07099929451942444,
-0.020481083542108536,
0.01661808229982853,
-0.037340883165597916,
0.008962556719779968,
-0.019203219562768936,
0.007989232428371906,
0.05529862269759178,
-0.02028665691614151,
-0.035984210669994354,
0.03441724181175232,
-0.004185715224593878,
0.03460949286818504,
0.004407728090882301,
-0.006644188426434994,
0.012218102812767029,
-0.06868117302656174,
0.0037291666958481073,
0.00843727495521307,
0.03620424494147301,
-0.0008794903988018632,
0.01051738578826189,
0.035493042320013046,
0.021673865616321564,
0.02416163496673107,
0.005969872232526541,
0.0455021858215332,
-0.02700134739279747,
-0.015150973573327065,
0.05063733085989952,
-0.03262261673808098,
-0.025822840631008148,
0.02928018756210804,
-0.0038917800411581993,
0.08358561992645264,
0.0026482760440558195,
0.02237652614712715,
-0.008098527789115906,
0.005026808939874172,
-0.013104244135320187,
-0.0008188667125068605,
-0.009047206491231918,
0.03320925310254097,
-0.0019219613168388605,
0.0035383757203817368,
-0.04028216749429703,
-0.02196470834314823,
-0.00017072746413759887,
0.001100590219721198,
0.002819324377924204,
0.034020524471998215,
-0.015661774203181267,
0.035793744027614594,
0.01180674321949482,
-0.019770270213484764,
-0.019871188327670097,
0.06759689003229141,
0.016198650002479553,
0.0138828344643116,
0.014785620383918285,
0.008862429298460484,
-0.038917966187000275,
0.08961917459964752,
-0.07821475714445114,
-0.0035849532578140497,
-0.029866041615605354,
0.04431777447462082,
-0.03383064642548561,
-0.007711580488830805
] |
<p>I'm having trouble understanding the surface used for <a href="http://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law" rel="nofollow">Ampere's Circuital Law</a>. In classes, we've been using simple circular or rectangular loops. Is the surface supposed to be area of the circle or the rectangle? Or is it a simple case of the law? </p>
<p>A example would be the surface used for displacement current. This one is just lost on me. The surface looks like a pot enclosing the wire and the capacitor. Does the law specify a closed loop of a surface? Is the line integral taken on the mouth of the pot-like surface or the bottom ($S_1$ below)? And is the enclosed current in the smaller mouth or the larger bottom surface ($S_2$)?</p>
<p><img src="http://i.stack.imgur.com/5Rlor.jpg" alt="enter image description here"></p>
| 10,746 |
[
-0.013763214461505413,
-0.0165764968842268,
0.01335192658007145,
0.017052985727787018,
0.03580590337514877,
-0.02551432140171528,
-0.008796420879662037,
-0.032941095530986786,
0.019136320799589157,
0.02986586093902588,
0.018083956092596054,
0.03496529906988144,
0.08357299119234085,
0.02180154249072075,
0.03844635188579559,
0.004183517303317785,
-0.005043680313974619,
-0.039159465581178665,
-0.0027494514361023903,
-0.05536497011780739,
-0.0006027249619364738,
0.010400762781500816,
-0.001389254815876484,
0.007501331623643637,
0.010435580275952816,
0.0367504321038723,
0.01840439811348915,
-0.002184846205636859,
0.025417055934667587,
0.04713279753923416,
-0.012114360928535461,
-0.061093054711818695,
-0.010604885406792164,
-0.010412869043648243,
0.018125055357813835,
-0.004116566851735115,
-0.022323263809084892,
-0.03877856582403183,
0.014167030341923237,
0.042368557304143906,
0.010675793513655663,
-0.006068613845854998,
-0.00009616243187338114,
0.024666495621204376,
-0.0072751897387206554,
0.01324338000267744,
-0.014069621451199055,
-0.015498187392950058,
0.021495958790183067,
-0.07269274443387985,
0.055604878813028336,
0.015234742313623428,
0.04388967156410217,
0.04044258967041969,
0.03893852233886719,
0.03132368251681328,
0.08897252380847931,
0.03718652203679085,
-0.03695977106690407,
-0.047282952815294266,
-0.011523446068167686,
-0.010231862775981426,
-0.030407970771193504,
-0.04621145874261856,
-0.004592571873217821,
0.00430102227255702,
-0.0060857608914375305,
-0.014570798724889755,
-0.004140890669077635,
0.006273780949413776,
0.014020079746842384,
0.04008374363183975,
0.0010564073454588652,
-0.013430004008114338,
0.039883751422166824,
-0.020948229357600212,
0.049493931233882904,
0.0032593305222690105,
0.021344227716326714,
0.030406270176172256,
-0.009796840138733387,
0.009837853722274303,
0.018608421087265015,
0.028476262465119362,
0.032580189406871796,
-0.018912438303232193,
0.06038790941238403,
0.010421263054013252,
0.014525203965604305,
0.020538726821541786,
-0.004337862133979797,
0.04360292851924896,
-0.009388781152665615,
-0.015822390094399452,
0.0015135123394429684,
0.001499368459917605,
0.018753694370388985,
0.028066951781511307,
-0.01606551557779312,
-0.03781052678823471,
-0.016544317826628685,
0.00045980329741723835,
0.008176257833838463,
0.07991266995668411,
0.023722229525446892,
-0.0002851970784831792,
-0.0015530961100012064,
0.03872261568903923,
0.025136278942227364,
-0.008603548631072044,
-0.059213172644376755,
0.04120834544301033,
-0.008806047029793262,
0.006827232427895069,
0.022184185683727264,
-0.03437592461705208,
-0.0036737534683197737,
0.030590174719691277,
0.016331572085618973,
0.025355447083711624,
0.03514314442873001,
-0.04205162823200226,
0.0086565762758255,
-0.02507854998111725,
-0.1077168732881546,
0.04515744000673294,
-0.012801920995116234,
-0.0007948914426378906,
-0.03279704973101616,
0.04046628624200821,
0.005920389201492071,
0.008941896259784698,
-0.017246685922145844,
0.017429733648896217,
0.020964646711945534,
-0.02975458838045597,
-0.05766486003994942,
-0.07553119957447052,
0.03537856787443161,
-0.012387593276798725,
0.008293055929243565,
-0.041501112282276154,
0.01610616035759449,
0.03422168642282486,
0.0682683065533638,
-0.022169476374983788,
-0.01722480170428753,
0.009410978294909,
0.06119164079427719,
0.0088069261983037,
-0.012543462216854095,
0.010329538024961948,
0.004812705330550671,
-0.011806025169789791,
0.006008134689182043,
-0.01883820816874504,
0.044642746448516846,
0.04874737560749054,
-0.005012482404708862,
-0.04242650419473648,
0.10616389662027359,
0.0027122783940285444,
-0.015882013365626335,
0.036805324256420135,
-0.013828786090016365,
-0.003843483282253146,
0.07822287082672119,
-0.0137634864076972,
-0.027507111430168152,
0.06599948555231094,
0.007981357164680958,
-0.03311415761709213,
-0.004940538201481104,
0.023107536137104034,
0.052094895392656326,
-0.020769542083144188,
-0.013993571512401104,
-0.03806569054722786,
0.02050354890525341,
0.020451998338103294,
-0.02326645329594612,
-0.012584011070430279,
-0.024663269519805908,
0.028639288619160652,
-0.009590753354132175,
0.03983231633901596,
-0.027249852195382118,
-0.052610572427511215,
0.008530083112418652,
-0.03286357969045639,
-0.020462363958358765,
-0.06037928909063339,
0.058098360896110535,
-0.003915582317858934,
-0.020601406693458557,
0.002112683141604066,
-0.03213704004883766,
0.019000690430402756,
-0.02401522547006607,
-0.015095348469913006,
0.03131314367055893,
0.04247741401195526,
-0.012333910912275314,
-0.031071599572896957,
0.011392970569431782,
0.039474550634622574,
0.010824255645275116,
0.007475952617824078,
0.0242496058344841,
-0.04512537643313408,
0.010333643294870853,
-0.007538262289017439,
-0.023913027718663216,
0.025900349020957947,
0.012853116728365421,
-0.027279235422611237,
-0.02788500301539898,
0.009192267432808876,
0.026795214042067528,
0.0467001311480999,
-0.01242178026586771,
0.06577940285205841,
0.053492531180381775,
0.041127678006887436,
0.013434158638119698,
0.00844326987862587,
0.010491029359400272,
-0.001292854780331254,
-0.021464534103870392,
-0.015664126724004745,
-0.07110752165317535,
-0.013909975066781044,
0.044824499636888504,
0.013356756418943405,
-0.0007632683264091611,
0.005374979693442583,
0.016383295878767967,
-0.006615496706217527,
0.01735108532011509,
0.014740057289600372,
-0.007010512053966522,
0.007890903390944004,
0.010231928899884224,
0.021672941744327545,
-0.013636014424264431,
-0.005301556549966335,
0.00010435120202600956,
0.04347144439816475,
0.028015535324811935,
0.03105330653488636,
-0.008943524211645126,
0.04680624604225159,
-0.02835342474281788,
0.05183561518788338,
0.0005911418120376766,
0.007368490565568209,
0.027090545743703842,
-0.03754305839538574,
-0.011014161631464958,
0.04092884063720703,
0.01759093813598156,
-0.005899082403630018,
-0.05201881378889084,
0.023399263620376587,
0.00555075891315937,
-0.020835045725107193,
-0.001553992973640561,
-0.029289165511727333,
0.0013655531220138073,
-0.046036262065172195,
0.012874782085418701,
-0.010802743956446648,
0.004056612960994244,
-0.017984837293624878,
0.01931835152208805,
0.03995382785797119,
-0.003708241507411003,
0.04237229377031326,
-0.034951623529195786,
-0.014931874349713326,
-0.02144906297326088,
0.0054581924341619015,
0.03873652219772339,
0.018266813829541206,
-0.03571861609816551,
0.02402624301612377,
-0.06655671447515488,
-0.02983660064637661,
0.06584790349006653,
0.008175413124263287,
-0.014559470117092133,
0.0023421109654009342,
-0.001055788598023355,
-0.05161125212907791,
-0.01623532362282276,
-0.0232868455350399,
0.046234842389822006,
-0.006774112582206726,
-0.02241656556725502,
0.05972021073102951,
-0.015800368040800095,
-0.01650189980864525,
0.0226002000272274,
-0.05417591333389282,
-0.037830132991075516,
-0.022120416164398193,
-0.010602760128676891,
0.015311718918383121,
0.01396782137453556,
0.002126122824847698,
0.03345704823732376,
-0.03619624301791191,
-0.023470452055335045,
-0.026311906054615974,
-0.030540307983756065,
-0.033364295959472656,
-0.038624659180641174,
0.04576929658651352,
-0.0028928150422871113,
-0.028608238324522972,
0.1072201058268547,
-0.002048745984211564,
-0.05098147317767143,
0.012261861003935337,
-0.03302110731601715,
-0.009467768482863903,
-0.04471105709671974,
0.00020689459051936865,
0.08397037535905838,
-0.030219919979572296,
0.010580859147012234,
0.012581268325448036,
0.049024101346731186,
0.025668475776910782,
0.033198319375514984,
-0.013335621915757656,
0.021313125267624855,
-0.031329717487096786,
-0.009562546387314796,
0.04895148053765297,
-0.012373633682727814,
-0.007037981413304806,
-0.018023665994405746,
-0.014704960398375988,
0.011506440117955208,
0.048572007566690445,
-0.03623557090759277,
0.010251643136143684,
-0.05530934035778046,
-0.01693352498114109,
-0.021057862788438797,
0.030070729553699493,
-0.005130062345415354,
-0.003294335212558508,
-0.004050152376294136,
0.030021417886018753,
0.046453509479761124,
-0.047138113528490067,
0.002839483320713043,
0.017404422163963318,
0.00031886325450614095,
-0.021760368719697,
-0.03611893579363823,
0.031643688678741455,
-0.02089613303542137,
0.006466418504714966,
-0.026151999831199646,
-0.048077862709760666,
0.0076684546656906605,
0.03921922668814659,
0.022186513990163803,
0.004328548908233643,
-0.034708213061094284,
0.029898323118686676,
-0.08643597364425659,
-0.020976591855287552,
0.014587366953492165,
0.06557461619377136,
-0.006411829497665167,
0.01750238426029682,
-0.0045949602499604225,
-0.006050058174878359,
-0.003636952256783843,
0.026100631803274155,
-0.06798920780420303,
0.0005822383100166917,
-0.03342772275209427,
-0.0078105805441737175,
-0.023965202271938324,
-0.010713442228734493,
-0.0021646067034453154,
0.013261492364108562,
-0.019355304539203644,
-0.02119036391377449,
0.01562286913394928,
-0.04285819083452225,
0.01054646447300911,
-0.016815245151519775,
-0.004141685552895069,
-0.047770485281944275,
0.04424150660634041,
0.017784005030989647,
-0.07196436822414398,
0.04253215715289116,
0.028644796460866928,
-0.016182497143745422,
0.0067643094807863235,
0.010825500823557377,
-0.012112419120967388,
0.028102820739150047,
0.03308543935418129,
0.04532121866941452,
0.013797998428344727,
-0.022652670741081238,
0.0059676868841052055,
0.001040777307935059,
0.0755053162574768,
0.008447696454823017,
-0.03153710812330246,
-0.024345682933926582,
-0.05106019228696823,
-0.028502468019723892,
-0.03508375585079193,
0.0685374066233635,
0.006585852243006229,
0.009334816597402096,
0.03294891119003296,
-0.03137011453509331,
-0.02121909148991108,
0.05477841570973396,
0.023735027760267258,
-0.01603914238512516,
-0.021539341658353806,
-0.07561896741390228,
-0.017849517986178398,
-0.06936163455247879,
-0.002979842247441411,
0.038799040019512177,
0.005764797329902649,
-0.04088698700070381,
-0.02885552868247032,
0.030750995501875877,
0.013952832669019699,
-0.002466078381985426,
0.0076169283129274845,
0.037663161754608154,
0.03529447317123413,
-0.011238083243370056,
-0.011278854683041573,
0.029274845495820045,
0.017920922487974167,
0.03419104963541031,
0.008141270838677883,
-0.030126681551337242,
-0.06717032194137573,
-0.04876929149031639,
0.06064748391509056,
0.00903974287211895,
0.02326531521975994,
-0.02766520529985428,
-0.08724345266819,
-0.021086184307932854,
0.04176652058959007,
-0.01681082881987095,
0.02294401079416275,
-0.045516159385442734,
0.02514578029513359,
-0.04429830610752106,
-0.03155382722616196,
0.0061777690425515175,
0.0009627139079384506,
-0.0013256407110020518,
0.017761070281267166,
-0.020786361768841743,
0.003648828249424696,
0.014164196327328682,
-0.009560609236359596,
0.01857331208884716,
0.023996777832508087,
-0.004966117907315493,
0.019011665135622025,
0.0251956507563591,
0.042606376111507416,
-0.01932918280363083,
-0.06319005787372589,
-0.0020684574265033007,
-0.021942351013422012,
0.0355965793132782,
0.030457723885774612,
-0.02527320198714733,
-0.02603592723608017,
-0.009410192258656025,
0.02088705264031887,
0.029072575271129608,
-0.006246453616768122,
0.018113169819116592,
0.058942195028066635,
0.03068467043340206,
-0.012060311622917652,
0.026328925043344498,
0.027898544445633888,
0.01594880037009716,
-0.02922912873327732,
0.013387804850935936,
0.010356014594435692,
-0.008035896345973015,
-0.03281693533062935,
-0.047567322850227356,
0.0006557570886798203,
-0.03435198590159416,
0.054626431316137314,
-0.01851177029311657,
0.017814917489886284,
-0.07808391004800797,
-0.038021866232156754,
-0.010355530306696892,
0.018893500789999962,
0.015150554478168488,
-0.026310525834560394,
0.012392772361636162,
0.02102617733180523,
0.015382003970444202,
-0.046099670231342316,
0.01426753681153059,
-0.039247021079063416,
0.03470368683338165,
0.0320003516972065,
0.015333513729274273,
0.013171655125916004,
-0.04576597362756729,
-0.04404548183083534,
0.004711572080850601,
-0.053804975003004074,
0.07374906539916992,
-0.03287077695131302,
0.01088796928524971,
0.00019347485795151442,
-0.03268611803650856,
-0.03476996719837189,
-0.007080550771206617,
0.009039883501827717,
0.04407788813114166,
-0.06166689842939377,
0.041368044912815094,
0.06499550491571426,
0.026012104004621506,
-0.0563151091337204,
-0.07486822456121445,
0.02301011234521866,
0.0233555156737566,
-0.024103360250592232,
-0.006506419740617275,
-0.014150717295706272,
-0.011557276360690594,
-0.02047049067914486,
0.009119201451539993,
0.016200482845306396,
-0.06436321139335632,
-0.02044663578271866,
0.025402363389730453,
0.007101740222424269,
0.07500596344470978,
0.025679314509034157,
0.03720312938094139,
0.004471121355891228,
-0.03612764924764633,
-0.017184415832161903,
-0.01848720572888851,
0.031129764392971992,
-0.041277118027210236,
-0.01681694947183132,
-0.04470909759402275,
0.01267749909311533,
0.051081232726573944,
-0.013808763585984707,
0.005613506771624088,
0.011713719926774502,
0.04508961737155914,
-0.03629831224679947,
-0.034772295504808426,
-0.014986247755587101,
0.0158796738833189,
0.00466832984238863,
-0.0016257743118330836,
-0.02859361469745636,
-0.04235214740037918,
0.014639242552220821,
-0.04399539902806282,
-0.016488997265696526,
-0.004894401412457228,
-0.021136585623025894,
0.049242157489061356,
-0.026480238884687424,
0.00946866162121296,
-0.0018651423742994666,
-0.03147977590560913,
0.04669661819934845,
0.0075622438453137875,
0.030071133747696877,
0.05866195261478424,
0.04201188310980797,
-0.009686755016446114,
-0.0001170555769931525,
-0.06469971686601639,
0.019679686054587364,
0.06681444495916367,
-0.01883525587618351,
0.03801397979259491,
0.03627198189496994,
-0.02967602014541626,
0.005591998342424631,
-0.025473110377788544,
-0.017543457448482513,
0.0035265376791357994,
-0.021106455475091934,
0.023163989186286926,
-0.027625123038887978,
0.015061728656291962,
0.00634651817381382,
-0.0012882159790024161,
-0.007894791662693024,
-0.011660563759505749,
0.03866824507713318,
0.019211236387491226,
0.00021264016686473042,
0.03859071806073189,
-0.05486702546477318,
0.0439596027135849,
0.00991775467991829,
0.02051113359630108,
0.008929316885769367,
0.006908809766173363,
0.041103631258010864,
0.0006087809451855719,
-0.015257135033607483,
-0.045349106192588806,
-0.00037327667814679444,
-0.02301466464996338,
0.017056500539183617,
-0.02094016969203949,
-0.006839612498879433,
-0.010108867660164833,
-0.014010569080710411,
0.015788448974490166,
0.001597380149178207,
0.025380028411746025,
-0.02300172671675682,
-0.05308268964290619,
0.0016439546598121524,
-0.04528891295194626,
-0.013865922577679157,
0.05623667687177658,
0.013499993830919266,
-0.030843690037727356,
0.03999738395214081,
-0.05290178209543228,
0.04475516453385353,
0.03171641379594803,
0.029984932392835617,
-0.017350034788250923,
0.08889346569776535,
-0.032337483018636703,
0.019661901518702507,
-0.036489203572273254,
-0.019076865166425705,
0.1138591468334198,
0.0315672867000103,
-0.029782304540276527,
-0.07840758562088013,
0.021838568150997162,
-0.04772081598639488,
0.009227165021002293,
-0.0062383003532886505,
0.010241111740469933,
-0.021173708140850067,
0.010378033854067326,
0.03831739351153374,
0.04374789074063301,
0.003865571226924658,
0.01757034659385681,
0.028695346787571907,
-0.023487737402319908,
0.000415607588365674,
0.03945497050881386,
0.01889338344335556,
-0.021390000358223915,
0.07663039118051529,
-0.08909381181001663,
-0.004563640803098679,
-0.04715736210346222,
-0.013164988718926907,
-0.022870736196637154,
-0.011968230828642845,
0.07343076914548874,
0.008492579683661461,
-0.06152862682938576,
0.036159612238407135,
-0.002947996836155653,
-0.01832638680934906,
-0.042926520109176636,
0.014850189909338951,
0.0038488467689603567,
0.014215474016964436,
0.018037501722574234,
0.01623663678765297,
0.015990693122148514,
-0.023614551872015,
0.0405239462852478,
0.021411199122667313,
-0.044230494648218155,
-0.008118236437439919,
-0.04999524727463722,
0.03658703714609146,
-0.009540720842778683,
-0.011750753037631512,
-0.015822211280465126,
-0.00037009938387200236,
0.015424581244587898,
-0.0819520652294159,
-0.05448315292596817,
-0.01792594976723194,
0.039273183792829514,
-0.017024820670485497,
0.00276098120957613,
-0.047629214823246,
0.02037583291530609,
-0.04594040289521217,
-0.01124133262783289,
0.010323481634259224,
0.016402220353484154,
0.021452583372592926,
0.012906752526760101,
0.034955646842718124,
0.018300408497452736,
-0.022048013284802437,
0.007554411888122559,
-0.012431211769580841,
-0.029325250536203384,
0.019674153998494148,
0.000054307980462908745,
0.024545352905988693,
0.00864836759865284,
0.014306040480732918,
-0.015373611822724342,
0.01965603046119213,
-0.04985291138291359,
0.050559937953948975,
0.004033374134451151,
-0.02270999550819397,
-0.03858335688710213,
-0.03685054928064346,
0.03062557429075241,
0.0223409291356802,
-0.014542006887495518,
-0.0018197556491941214,
0.016983695328235626,
-0.0064329407177865505,
0.024987436830997467,
0.002478271257132292,
-0.017628788948059082,
0.002896389691159129,
-0.02569233812391758,
-0.019837580621242523,
-0.009846297092735767,
0.026903482154011726,
0.03996998071670532,
0.005153623875230551,
-0.029362276196479797,
0.037602413445711136,
-0.02233912982046604,
-0.014181851409375668,
-0.009746579453349113,
-0.005598107818514109,
0.026850106194615364,
-0.006211054045706987,
0.027458973228931427,
-0.04247095435857773,
0.003737320192158222,
-0.034274425357580185,
-0.00342158367857337,
-0.001692596240900457,
0.03321169689297676,
-0.022097432985901833,
0.017659373581409454,
-0.009127719327807426,
-0.006694954354315996,
-0.029274428263306618,
-0.025437692180275917,
-0.06361215561628342,
-0.015967318788170815,
0.04484384134411812,
0.020943686366081238,
-0.04277196526527405,
0.04594294726848602,
-0.010526389814913273,
-0.0120310690253973,
0.015025673434138298,
0.015911158174276352,
-0.0028774491511285305,
-0.0021279500797390938,
0.001035174005664885,
-0.005341617856174707,
0.032166171818971634,
-0.03956104442477226,
-0.029276076704263687,
0.028370937332510948,
-0.030269170179963112,
0.001015913556329906,
-0.011024481616914272,
-0.0014358325861394405,
0.018844399601221085,
-0.006559042260050774,
-0.017434246838092804,
-0.005618146620690823,
0.004371511749923229,
-0.017065593972802162,
-0.006563258823007345,
-0.016032572835683823,
-0.029421936720609665,
0.016831956803798676,
-0.02307923696935177,
0.004304680973291397,
0.017344072461128235,
0.005130491219460964,
-0.0031188137363642454,
0.01884639449417591,
-0.0013364829355850816,
-0.00988016463816166,
-0.022067949175834656,
-0.010533671826124191,
0.021715018898248672,
0.024890772998332977,
0.00435994565486908,
0.023661278188228607,
0.02905013971030712,
-0.020358961075544357,
0.01402201782912016,
-0.008437382988631725,
0.01506042294204235,
-0.0586199089884758,
0.01244767289608717,
0.004490873776376247,
0.028091931715607643,
0.035240162163972855,
-0.07235711812973022,
-0.006546222139149904,
0.033866386860609055,
-0.021630994975566864,
-0.008061431348323822,
0.0024456996470689774,
-0.04885580390691757,
-0.003764381865039468,
-0.04035471752285957,
0.0060270377434790134,
0.04715343937277794,
0.010556130670011044,
0.025439688935875893,
0.010499171912670135,
-0.016278624534606934,
0.0005710546975024045,
-0.01758798584342003,
-0.021985085681080818,
0.039705947041511536,
-0.018877342343330383,
-0.06484631448984146,
0.03998100757598877,
-0.008909889496862888,
-0.030465807765722275,
0.04937030375003815,
0.005487984046339989,
-0.014005392789840698,
-0.04000689834356308,
0.0204362403601408,
-0.023281188681721687,
0.0502803735435009,
0.014552447944879532,
-0.02882002666592598,
-0.009209809824824333,
0.03794946148991585,
0.029345853254199028,
-0.016042442992329597,
0.026904184371232986,
-0.011898689903318882,
0.03708399087190628,
0.0011858645593747497,
-0.0161020215600729,
0.03270162642002106,
-0.016858648508787155,
-0.018998173996806145,
0.0022179707884788513,
-0.012554860673844814,
0.05431732162833214,
-0.027820995077490807,
0.004651915282011032,
-0.020664013922214508,
-0.008719438686966896,
0.04041605815291405,
-0.020047757774591446,
0.009241177700459957,
0.01466185413300991,
0.02418229915201664,
-0.023974208161234856,
0.04931555688381195,
0.03832501918077469,
-0.05365612730383873,
-0.052189867943525314,
0.0016284796874970198,
0.030576370656490326,
-0.043904125690460205,
0.027467574924230576,
-0.016756795346736908,
-0.021025702357292175,
0.008437065407633781,
-0.008958754129707813,
0.011092450469732285,
0.0028634786140173674,
-0.05538707599043846,
-0.018371649086475372,
-0.038825131952762604,
0.0384366549551487,
0.00472312280908227,
-0.033510465174913406,
-0.033454108983278275,
-0.02105368860065937,
0.035385821014642715,
0.016612963750958443,
0.03737569972872734,
0.02216891571879387,
-0.0007153935148380697,
-0.013023290783166885,
-0.015512901358306408,
0.028521297499537468,
-0.05356432497501373,
0.008168640546500683,
0.04154276102781296,
0.02055288478732109,
0.017458869144320488,
-0.003209079848602414,
-0.01577415131032467,
-0.0009181008790619671,
0.019471067935228348,
0.010951780714094639,
0.022548409178853035,
-0.03663753718137741,
-0.00730860373005271,
0.0008165473118424416,
0.021650344133377075,
-0.01162636000663042,
0.11803082376718521,
-0.014213536866009235,
-0.00666888989508152,
-0.0013868464156985283,
-0.027816737070679665,
-0.01838710531592369,
0.0012403210857883096,
-0.0015140800969675183,
0.016849910840392113,
-0.03035697713494301,
0.01002014335244894,
0.042622294276952744,
-0.0632740706205368,
-0.01793120615184307,
0.023936796933412552,
0.0017290881369262934,
-0.051803108304739,
0.07992642372846603,
-0.007335501257330179,
0.02611537277698517,
-0.032526202499866486,
0.02265702374279499,
0.014899459667503834,
-0.007418113760650158,
-0.03274879232048988,
0.018174391239881516,
0.06153762340545654,
-0.021087409928441048,
-0.03367295861244202,
0.0628746971487999,
-0.03622271865606308,
0.0020197622943669558,
-0.0025176017079502344,
-0.008540285751223564,
-0.004992769565433264,
-0.02484208531677723,
0.025700600817799568,
-0.03758777305483818,
0.0121436333283782,
0.013787558302283287,
-0.02208930440247059,
0.07523395866155624,
-0.029658114537596703,
0.03104431927204132,
0.007356142159551382,
-0.007463557180017233,
-0.01694478467106819,
0.015456653200089931,
0.023679595440626144,
0.02959319017827511,
-0.021674150601029396,
-0.040117789059877396,
-0.020855234935879707,
-0.0006438528653234243,
0.0427299328148365,
-0.018806438893079758,
0.0473468154668808,
0.015881270170211792,
0.004481118638068438,
-0.008789881132543087,
0.003580305026844144,
0.017909837886691093,
-0.007581330835819244,
0.07031714171171188,
0.03789493814110756,
0.004271017853170633,
0.003578017931431532,
-0.01607801951467991,
-0.011696423403918743,
0.04595812410116196,
-0.08520729094743729,
-0.025537336245179176,
-0.014270699582993984,
-0.0068428171798586845,
0.04970438405871391,
0.004010585602372885
] |
<p>The <a href="http://en.wikipedia.org/wiki/Random_phase_approximation" rel="nofollow">random phase approximation</a> (RPA) is an approximation method in condensed matter physics and in nuclear physics. </p>
<p>What is the difference between RPA and generalized RPA?</p>
| 10,747 |
[
0.0140079315751791,
-0.05186363309621811,
0.02025376632809639,
-0.05932547152042389,
0.03378475829958916,
0.01847599446773529,
-0.024069657549262047,
-0.041240498423576355,
-0.004228195641189814,
-0.05323852226138115,
0.044764161109924316,
0.029631225392222404,
0.03357507288455963,
0.012633527629077435,
-0.0021876429673284292,
0.036727238446474075,
-0.03116452693939209,
-0.0016602020477876067,
-0.023196378722786903,
-0.00715662119910121,
0.010010959580540657,
0.032778725028038025,
0.014620781876146793,
-0.01064782589673996,
0.008018231950700283,
0.0438363179564476,
-0.001584577257744968,
0.002267697360366583,
0.03243471309542656,
0.04914149269461632,
-0.010601699352264404,
-0.0254496019333601,
-0.0005896128714084625,
0.029585354030132294,
0.052150629460811615,
0.020404571667313576,
-0.03100065514445305,
-0.03071894682943821,
-0.03158194571733475,
0.006085237953811884,
-0.05226489529013634,
-0.03261382505297661,
-0.00879770889878273,
0.006823302246630192,
-0.002302751876413822,
0.03269190341234207,
0.00895004440099001,
-0.029559262096881866,
0.027450308203697205,
-0.04236305505037308,
0.039032064378261566,
-0.02488800324499607,
-0.0027322235982865095,
0.018396925181150436,
0.008732299320399761,
-0.023769842460751534,
0.04256480187177658,
0.09637732803821564,
-0.018649812787771225,
-0.03981196507811546,
0.01490623690187931,
0.015860291197896004,
-0.005417416803538799,
-0.012547703459858894,
0.01765533722937107,
0.04856330156326294,
0.022730732336640358,
-0.0328863300383091,
-0.0045461771078407764,
-0.009642399847507477,
0.030339717864990234,
0.005974142346531153,
0.03512481972575188,
-0.01786857657134533,
0.030775075778365135,
0.012269783765077591,
-0.008040993474423885,
0.02187396213412285,
0.036431461572647095,
0.02607298083603382,
0.005383800249546766,
0.04464951902627945,
0.02806522697210312,
-0.0213896706700325,
-0.03233473375439644,
-0.004596758168190718,
0.06755919754505157,
0.004839322995394468,
-0.002526944736018777,
0.05304330959916115,
-0.007859273813664913,
0.06472771614789963,
0.02837708592414856,
-0.0194152370095253,
-0.05996975302696228,
0.016213495284318924,
0.010275516659021378,
0.016508378088474274,
-0.009677083231508732,
-0.021146036684513092,
0.008835222572088242,
-0.054183099418878555,
-0.005200636573135853,
0.09142253547906876,
-0.0037738699465990067,
-0.03356952220201492,
-0.042247213423252106,
0.01916310377418995,
-0.007537506055086851,
0.000019635399439721368,
-0.017156872898340225,
0.013738381676375866,
0.008641093038022518,
0.021919146180152893,
0.0036484012380242348,
0.01779753714799881,
0.01198961678892374,
0.009030494838953018,
0.03908875212073326,
0.06871657073497772,
0.012532966211438179,
-0.0230704452842474,
0.02615044265985489,
-0.036666132509708405,
-0.05803852155804634,
0.0035224894527345896,
0.0315723642706871,
-0.017652511596679688,
-0.08785878866910934,
0.021004166454076767,
0.006575931794941425,
-0.0035163555294275284,
0.034796033054590225,
0.026217028498649597,
0.027905207127332687,
-0.03564657270908356,
-0.1297692358493805,
-0.04872795194387436,
0.048172611743211746,
-0.005519285798072815,
0.029186561703681946,
-0.07315415143966675,
0.018073417246341705,
0.012885970994830132,
0.06688898056745529,
0.011489572934806347,
0.017197582870721817,
0.007454715669155121,
0.041357044130563736,
0.003562884172424674,
-0.01962899975478649,
-0.012708480469882488,
0.01867426000535488,
-0.01518166158348322,
-0.01452863309532404,
-0.07698428630828857,
0.03412915766239166,
0.04360157251358032,
-0.010897376574575901,
0.01057054940611124,
0.05077754333615303,
-0.019789813086390495,
-0.010947096161544323,
-0.010574652813374996,
-0.022078776732087135,
-0.04369073361158371,
0.08621228486299515,
0.017087025567889214,
0.02906096540391445,
0.05979884788393974,
-0.02000023052096367,
0.0399361290037632,
0.0018423827132210135,
0.04118965566158295,
0.05910509452223778,
-0.0116111496463418,
-0.014331713318824768,
0.005735812708735466,
0.013013873249292374,
0.021162675693631172,
-0.061031442135572433,
0.003073069266974926,
0.020711736753582954,
0.008906500414013863,
-0.006888887379318476,
0.027836039662361145,
0.018457839265465736,
-0.012347593903541565,
0.007544347085058689,
-0.05057888105511665,
-0.018440572544932365,
-0.05353804677724838,
0.0013478314504027367,
-0.02407519891858101,
-0.0004670094349421561,
0.0427473820745945,
0.04239986464381218,
0.02552684396505356,
-0.010406496934592724,
-0.040091197937726974,
-0.019778843969106674,
0.0000845866888994351,
0.016186188906431198,
-0.03796226158738136,
0.021221214905381203,
0.060266587883234024,
-0.013439015485346317,
-0.04504549875855446,
0.04693485051393509,
-0.013330178335309029,
-0.029156412929296494,
-0.011041003279387951,
-0.022566333413124084,
0.02885327860713005,
0.018852028995752335,
-0.012937391176819801,
-0.02181342802941799,
0.013526055961847305,
-0.017655210569500923,
0.01103201974183321,
-0.03275374695658684,
0.03584694862365723,
0.06813889741897583,
0.02712479792535305,
-0.02379593811929226,
0.04706481844186783,
0.009159148670732975,
0.004781875293701887,
-0.00044765425263904035,
-0.013787479139864445,
-0.04737291857600212,
-0.02216501347720623,
0.06532255560159683,
0.04849999025464058,
-0.04218532145023346,
0.014729877933859825,
0.05355672538280487,
0.05618857219815254,
0.04476276412606239,
0.057540006935596466,
-0.013978194445371628,
-0.04541449248790741,
0.03782476484775543,
0.02583784982562065,
-0.03244306519627571,
0.006093584932386875,
0.0053188554011285305,
-0.02123669907450676,
0.003177048871293664,
-0.010364259593188763,
-0.04043285921216011,
0.004763027653098106,
-0.006216580513864756,
0.00044657569378614426,
-0.008366798050701618,
-0.06644773483276367,
0.0387609601020813,
-0.026248129084706306,
0.025360800325870514,
0.009939463809132576,
-0.004203856457024813,
-0.01677936315536499,
-0.051908228546381,
-0.04380050674080849,
0.006447278428822756,
-0.01959904469549656,
-0.035847537219524384,
-0.01876027137041092,
0.03053860552608967,
0.007836992852389812,
-0.02230706438422203,
-0.0448942556977272,
0.020547499880194664,
-0.05821646749973297,
-0.005768915172666311,
0.03246687352657318,
0.0039809877052903175,
0.03815224766731262,
-0.022399388253688812,
-0.02133318968117237,
0.027487723156809807,
-0.0052232928574085236,
-0.01578761637210846,
0.02009018138051033,
-0.0526796355843544,
0.039165232330560684,
0.032995522022247314,
0.007467149291187525,
0.008926323615014553,
-0.009727571159601212,
-0.018088622018694878,
0.00142737349960953,
-0.0031736167147755623,
-0.031403426080942154,
-0.007172485813498497,
0.026938948780298233,
0.009904444217681885,
-0.045166000723838806,
0.002766443882137537,
0.043491557240486145,
0.00006198705523274839,
-0.013775001280009747,
0.0013631513575091958,
-0.006969044450670481,
-0.018103547394275665,
-0.0031203965190798044,
0.002330196090042591,
0.031153813004493713,
-0.024691374972462654,
0.008199693635106087,
0.03206344693899155,
-0.05802424997091293,
-0.052445314824581146,
-0.05986475199460983,
-0.0244083721190691,
0.02919737622141838,
-0.034353964030742645,
0.016826624050736427,
0.019360635429620743,
-0.027577606961131096,
0.09804155677556992,
0.013854618184268475,
-0.020769650116562843,
0.01995709538459778,
0.024523572996258736,
-0.017977192997932434,
0.0024841742124408484,
0.025010110810399055,
0.026812072843313217,
0.015235944651067257,
0.016039155423641205,
0.0017374359304085374,
0.042117733508348465,
0.06271752715110779,
0.04710080474615097,
0.0016676833620294929,
-0.00877249613404274,
0.014919317327439785,
-0.03271941468119621,
0.029742959886789322,
-0.018364649266004562,
-0.014865981414914131,
0.0017492929473519325,
0.011961684562265873,
0.04706130549311638,
0.03475368022918701,
-0.04226302728056908,
0.011829343624413013,
-0.018360646441578865,
0.034615643322467804,
-0.03579217195510864,
0.07411165535449982,
-0.00982266291975975,
-0.024120859801769257,
-0.011440914124250412,
-0.012085449881851673,
0.07378268986940384,
-0.010527742095291615,
-0.004714269656687975,
0.03957827761769295,
0.06880763918161392,
-0.032652050256729126,
0.01309429295361042,
0.0005847670836374164,
-0.014163138344883919,
0.021093394607305527,
-0.027011971920728683,
-0.010316579602658749,
0.0546366348862648,
0.02236819453537464,
0.0014474086929112673,
-0.007422665134072304,
-0.009325571358203888,
-0.03687890246510506,
-0.06688082218170166,
0.03611456975340843,
-0.06509795784950256,
0.06803631037473679,
-0.00449763610959053,
0.07625439018011093,
0.028079446405172348,
-0.024589434266090393,
0.03372451290488243,
0.0036239868495613337,
-0.08576005697250366,
0.050397440791130066,
-0.004428305197507143,
-0.011943702585995197,
0.03382626548409462,
-0.020843714475631714,
-0.012621108442544937,
0.016936803236603737,
-0.03591122478246689,
-0.005743824876844883,
0.009200944565236568,
-0.02700059302151203,
0.032619789242744446,
-0.013785384595394135,
-0.04611127823591232,
-0.014243748039007187,
0.02163020148873329,
0.032351214438676834,
-0.059616897255182266,
0.022213809192180634,
0.028430109843611717,
-0.025188537314534187,
-0.024948181584477425,
-0.016588302329182625,
0.02877832017838955,
0.010937905870378017,
0.05924639478325844,
0.048587214201688766,
0.03881446272134781,
-0.035647835582494736,
0.0022293569054454565,
0.024136897176504135,
0.05147446319460869,
-0.011605161242187023,
-0.029989542439579964,
0.010091750882565975,
-0.07787548005580902,
0.0029789372347295284,
-0.009875140152871609,
0.013681530021131039,
-0.011062894947826862,
-0.013313916511833668,
-0.01620604656636715,
-0.0013232527999207377,
-0.017857607454061508,
0.011185575276613235,
0.044962383806705475,
-0.005699154920876026,
-0.016805022954940796,
-0.06652709096670151,
-0.016068393364548683,
0.0050179967656731606,
-0.01271512359380722,
0.05545838922262192,
-0.019491568207740784,
-0.022357290610671043,
0.01417778991162777,
-0.0003510418173391372,
0.0060060471296310425,
-0.04700038582086563,
-0.028678040951490402,
-0.0071673281490802765,
-0.01811063662171364,
0.00959488283842802,
-0.025416485965251923,
-0.017633995041251183,
0.017676474526524544,
0.030588490888476372,
0.019676849246025085,
0.015393991954624653,
-0.0625992864370346,
0.010489449836313725,
0.05703893303871155,
0.016710378229618073,
-0.037069033831357956,
-0.01844177395105362,
-0.059248186647892,
-0.02272743545472622,
0.04115104675292969,
-0.00824809167534113,
0.008729742839932442,
-0.020611237734556198,
-0.020182166248559952,
-0.011561346240341663,
-0.014582054689526558,
-0.01327862124890089,
0.005733435042202473,
-0.009780299849808216,
0.03184976056218147,
-0.02375956065952778,
-0.023593733087182045,
-0.019829601049423218,
-0.010218502022325993,
0.010690677911043167,
0.07330626994371414,
0.008359796367585659,
0.008143936283886433,
0.019451474770903587,
0.03571639955043793,
-0.013421894051134586,
-0.08345849066972733,
0.0022222413681447506,
0.008320867083966732,
-0.005109213292598724,
0.022367723286151886,
-0.03195956349372864,
-0.047790996730327606,
0.025134310126304626,
-0.020786046981811523,
-0.005723276175558567,
-0.02970697730779648,
-0.024734454229474068,
0.06747936457395554,
0.05058056861162186,
-0.016666287556290627,
0.058433037251234055,
0.03913527727127075,
0.007737808860838413,
-0.007040920201689005,
-0.01732032373547554,
0.04836820438504219,
-0.031246578320860863,
0.026925181970000267,
-0.0404961034655571,
0.03608129918575287,
-0.006391104776412249,
0.027854571118950844,
-0.018632259219884872,
0.032835494726896286,
0.028510162606835365,
-0.029290759935975075,
-0.03838861733675003,
0.041169099509716034,
-0.03195749595761299,
-0.0014562774449586868,
0.002559464192017913,
0.018090710043907166,
0.015000936575233936,
-0.010578357614576817,
0.012242946773767471,
0.012032978236675262,
-0.008374514058232307,
0.022512877359986305,
0.018388358876109123,
0.0026740911416709423,
-0.031333282589912415,
-0.040574412792921066,
0.03999566286802292,
-0.0527917705476284,
0.0564701110124588,
0.011216947808861732,
0.023697379976511,
-0.006161373108625412,
-0.07029075920581818,
0.002115586306899786,
-0.002363997045904398,
-0.02327870763838291,
0.06288528442382812,
-0.04017972573637962,
0.013968725688755512,
-0.011738782748579979,
-0.012908500619232655,
-0.06280232965946198,
-0.03850339353084564,
0.004461117088794708,
0.028877727687358856,
-0.02529088780283928,
-0.020529914647340775,
0.006774903740733862,
-0.011921999044716358,
0.020188376307487488,
-0.0014554585795849562,
0.023551370948553085,
-0.003560273675248027,
-0.029093246906995773,
0.023911532014608383,
0.02139829844236374,
0.08880575746297836,
0.024083077907562256,
-0.0014077809173613787,
0.024128014221787453,
-0.03702262043952942,
0.016940424218773842,
-0.005274241324514151,
0.04509459808468819,
-0.040923237800598145,
-0.012519722804427147,
-0.015759119763970375,
-0.00030921120196580887,
0.02775583416223526,
0.029133381322026253,
0.0445626899600029,
0.015992170199751854,
0.018354225903749466,
-0.014670468866825104,
-0.04165901616215706,
-0.049067847430706024,
0.006385379005223513,
0.03219740465283394,
0.0006291579338721931,
-0.0027712672017514706,
-0.03409632667899132,
-0.010388923808932304,
0.032953135669231415,
-0.0240215752273798,
-0.046340376138687134,
0.048096664249897,
0.04776184260845184,
-0.023535195738077164,
0.00624763173982501,
-0.005979275330901146,
-0.058782752603292465,
0.017213085666298866,
-0.036141443997621536,
0.05028427392244339,
0.042725831270217896,
-0.0010128994472324848,
-0.02630842663347721,
-0.026537461206316948,
-0.04993695765733719,
0.0007993433391675353,
0.06943819671869278,
0.00492869084700942,
0.050252482295036316,
0.01591510884463787,
-0.022982388734817505,
-0.009048852138221264,
-0.03967100754380226,
-0.010012281127274036,
0.020219750702381134,
-0.030794192105531693,
0.057337526232004166,
-0.03543366119265556,
-0.03777251020073891,
-0.01999574340879917,
0.004871531389653683,
0.004087470937520266,
0.020938731729984283,
0.009886972606182098,
0.03467000275850296,
0.013383542187511921,
-0.0036878150422126055,
-0.020888211205601692,
0.0436326302587986,
-0.013695478439331055,
0.027895290404558182,
0.0177215114235878,
-0.018505357205867767,
0.04805239289999008,
0.001240090117789805,
0.003637587884441018,
-0.0434352345764637,
0.00006660813960479572,
-0.017259232699871063,
0.03928913548588753,
0.01875295676290989,
0.009179709479212761,
0.010111510753631592,
-0.0004630651674233377,
-0.0018269133288413286,
0.008329056203365326,
0.014308133162558079,
0.0069897775538265705,
-0.09864433854818344,
-0.017934206873178482,
-0.0099854227155447,
-0.05721399188041687,
0.0016222601989284158,
-0.014886719174683094,
-0.05282267928123474,
0.01746421307325363,
-0.025803986936807632,
0.024914858862757683,
0.020470857620239258,
0.023473918437957764,
-0.006975844968110323,
0.04866848140954971,
0.005774973426014185,
0.03430987894535065,
0.03260953351855278,
0.00006841385766165331,
0.13811460137367249,
0.032923679798841476,
0.047447752207517624,
-0.050458021461963654,
0.008112248033285141,
-0.04327990859746933,
0.016111591830849648,
-0.009487143717706203,
-0.007748348172754049,
-0.0028441124595701694,
0.006871154997497797,
0.0051389518193900585,
0.010452879592776299,
0.003268518950790167,
0.01629824936389923,
0.06069629639387131,
-0.08007153123617172,
-0.0397295206785202,
-0.004657968413084745,
-0.021665500476956367,
-0.0023807459510862827,
0.01462878379970789,
-0.01407389435917139,
-0.003988473676145077,
-0.010047409683465958,
-0.003079091664403677,
-0.04804312437772751,
-0.021166183054447174,
0.057676803320646286,
0.025196528062224388,
-0.04153559356927872,
0.014564163982868195,
-0.023012742400169373,
0.019887838512659073,
0.009416892193257809,
0.013678180053830147,
0.02911013551056385,
-0.02377169579267502,
0.016243869438767433,
0.03512224927544594,
-0.0223158560693264,
-0.036780353635549545,
-0.005396836902946234,
0.00742925051599741,
-0.05147285386919975,
-0.014383799396455288,
-0.021738141775131226,
0.04188479855656624,
-0.0426982082426548,
-0.030057393014431,
0.013085396029055119,
-0.02104933373630047,
0.002093633869662881,
-0.043448664247989655,
0.010394773446023464,
0.02567501738667488,
0.012119447812438011,
0.0006682578823529184,
-0.04190308600664139,
-0.03527094051241875,
0.018831593915820122,
-0.028430018573999405,
0.004490762948989868,
0.013441951014101505,
0.008786669000983238,
0.04837033152580261,
-0.020306412130594254,
0.0075924452394247055,
-0.011955256573855877,
-0.010682507418096066,
-0.05377770960330963,
0.03593437746167183,
-0.047276295721530914,
-0.04624588415026665,
0.019807184115052223,
0.0037084361538290977,
0.0621829591691494,
0.016041576862335205,
0.00937481876462698,
-0.007658567279577255,
-0.04479881748557091,
0.05405345931649208,
-0.0035043428651988506,
-0.01966489851474762,
-0.00842549093067646,
-0.0040175518952310085,
0.0019479617476463318,
0.026774555444717407,
-0.019323941320180893,
-0.014114348217844963,
-0.02155306003987789,
0.0008720514015294611,
0.026125598698854446,
-0.00022446102229878306,
-0.024175383150577545,
-0.020094165578484535,
-0.012261301279067993,
0.010437377728521824,
0.009370876476168633,
0.0055101667530834675,
0.07717546820640564,
-0.012628022581338882,
-0.026503773406147957,
0.03338918834924698,
-0.025459570810198784,
-0.01013150904327631,
0.016666261479258537,
-0.02627561241388321,
-0.0013824424240738153,
0.016498558223247528,
-0.018738150596618652,
-0.04462733119726181,
0.018977535888552666,
-0.02851097844541073,
0.0008512773201800883,
0.007373160682618618,
0.03037109039723873,
-0.03458389639854431,
-0.03378469869494438,
-0.020798759534955025,
0.041326429694890976,
-0.029926946386694908,
-0.02210261858999729,
-0.02491580881178379,
0.030077550560235977,
0.009528242982923985,
0.0032084328122437,
0.0032180752605199814,
0.00659615034237504,
0.034143898636102676,
-0.008028942160308361,
0.07413293421268463,
-0.011984196491539478,
0.00027774463524110615,
0.027931585907936096,
0.034984637051820755,
-0.029054321348667145,
0.03597268462181091,
-0.023768533021211624,
-0.03120552748441696,
0.026306798681616783,
-0.05739623308181763,
-0.0490574911236763,
0.0045835175551474094,
0.007535250391811132,
0.040504805743694305,
0.034868743270635605,
-0.000969113374594599,
-0.007504042703658342,
0.06692124903202057,
-0.05417032912373543,
-0.04098205640912056,
-0.014182723127305508,
0.01374857872724533,
0.003355523804202676,
-0.02092478610575199,
0.0006521254545077682,
0.002843711758032441,
-0.0036844993010163307,
0.016840459778904915,
0.03311241418123245,
-0.02922414429485798,
-0.008281039074063301,
0.02250402607023716,
-0.01242397353053093,
0.0027044278103858232,
0.005470056086778641,
0.03367788344621658,
0.009134012274444103,
0.03144048526883125,
0.01630883850157261,
0.043842460960149765,
0.0163124967366457,
-0.014400335028767586,
-0.0787232369184494,
-0.011756076477468014,
-0.016436705365777016,
-0.03448616713285446,
0.024991350248456,
-0.02221689186990261,
0.02432216890156269,
0.012554955668747425,
-0.023268582299351692,
0.04197659716010094,
0.006970920599997044,
-0.021529268473386765,
-0.015545104630291462,
0.016486434265971184,
-0.02553197368979454,
0.03964969143271446,
0.011033640243113041,
0.03647806495428085,
0.019672051072120667,
-0.023189149796962738,
-0.01489769946783781,
-0.03221754729747772,
-0.004935092758387327,
0.017312780022621155,
-0.030428873375058174,
-0.037540752440690994,
0.021899843588471413,
-0.016954293474555016,
-0.02565750665962696,
0.015796713531017303,
-0.007673807442188263,
0.01463154423981905,
-0.02263486385345459,
0.0048420606181025505,
-0.037566401064395905,
0.011598705314099789,
0.015552711673080921,
-0.008478144183754921,
-0.004739317111670971,
-0.008948231115937233,
0.0027690213173627853,
0.016844671219587326,
0.023919155821204185,
0.031845059245824814,
0.012645088136196136,
-0.028140703216195107,
-0.008235976099967957,
0.024680031463503838,
0.0064079249277710915,
-0.04184989258646965,
-0.03142368793487549,
-0.022687677294015884,
-0.008021744899451733,
-0.006045606918632984,
0.011253607459366322,
-0.008072917349636555,
0.02825148217380047,
0.046107105910778046,
0.013873456045985222,
-0.013486332260072231,
0.01303553394973278,
0.014252590015530586,
-0.0384242907166481,
-0.01445087045431137,
0.020861824974417686,
-0.002400306286290288,
-0.04950714856386185,
-0.02186242863535881,
0.03413369879126549,
0.011766013689339161,
-0.022970857098698616,
-0.03543553128838539,
-0.03072930872440338,
0.005058655049651861,
-0.005013023503124714,
0.007315155118703842,
0.0009025250328704715,
-0.03593670204281807,
-0.0035987861920148134,
-0.08577726036310196,
0.06355065107345581,
-0.018270164728164673,
-0.03467626869678497,
-0.06234903261065483,
-0.005303922109305859,
-0.012301744893193245,
0.01129031740128994,
0.055517252534627914,
0.04894076660275459,
0.03129596635699272,
-0.017842285335063934,
0.03407920524477959,
0.015893930569291115,
-0.027977904304862022,
-0.016627086326479912,
-0.00020150322234258056,
-0.0180435199290514,
-0.004418733064085245,
-0.025017347186803818,
-0.03397895395755768,
0.016872957348823547,
-0.003941296599805355,
0.007678705267608166,
0.009226999245584011,
-0.00369925145059824,
-0.019630251452326775,
0.03191070258617401,
0.04381294921040535,
0.008109739981591702,
0.03480442985892296,
-0.03546914458274841,
0.045079417526721954,
0.007415676489472389,
-0.025019945576786995,
-0.02139792963862419,
0.001112275174818933,
-0.04999946430325508,
-0.05435941740870476,
-0.027188850566744804,
-0.003018124494701624,
-0.01261981949210167,
-0.04500671476125717,
-0.004098458215594292,
0.032828789204359055,
-0.0507751889526844,
-0.03198491781949997,
0.05809555575251579,
0.038778480142354965,
0.04026193544268608,
0.025014061480760574,
-0.0002054294163826853,
0.023673979565501213,
-0.001661350135691464,
0.014133270829916,
0.042118437588214874,
0.019481690600514412,
0.0013446989469230175,
0.025309517979621887,
-0.02211032249033451,
-0.02439967542886734,
-0.042586807161569595,
0.014220401644706726,
0.029743345454335213,
-0.05874965339899063,
-0.015099037438631058,
0.052316926419734955,
-0.0014689002418890595,
0.025764070451259613,
0.037676382809877396,
-0.021198922768235207,
0.08618104457855225,
-0.044500935822725296,
-0.005466917064040899,
-0.023844024166464806,
-0.028036998584866524,
-0.005532290320843458,
0.004139276221394539,
-0.007094125263392925,
0.00004927739792037755,
0.02389119751751423,
0.0240167286247015,
-0.020259927958250046,
-0.007696632761508226,
0.025752892717719078,
-0.06942907720804214,
-0.0006783786811865866,
0.016461458057165146,
0.011333977803587914,
-0.05241435393691063,
-0.03111349418759346,
-0.022273214533925056,
-0.008719325996935368,
0.031881820410490036,
0.01673942804336548,
0.00711904838681221,
0.018074214458465576,
-0.002926197834312916,
0.012251535430550575,
0.03990735113620758,
-0.06076917424798012,
-0.011049318127334118,
-0.03454478457570076,
0.030517401173710823,
-0.026251239702105522,
-0.0029245782643556595
] |
<p>I'm doing some homework in Classical Mechanics, and is about to write out the Lagrangian of a system. But, when I check the answer from my teacher, something is missing.</p>
<p>The kinetic energy I'm using is given by:</p>
<p>$$T =\frac{1}{2}m\dot{x_{m}}^{2},$$</p>
<p>where</p>
<p>$$\dot{x_{m}} = \dot{x}+L \cos(\phi)\dot{\phi}$$</p>
<p>Now, when I want to write out the entire Lagrangian I need to expand the squared $\dot{x_{m}}$, which in my calculations give me the following:</p>
<p>$$\frac{1}{2}m(\dot{x}^{2}+2\dot{x}L \cos(\phi)\dot{\phi}+L^{2} \cos^{2}(\phi)\dot{\phi}^{2})$$</p>
<p>But apparently, according to the solution, the $\cos^{2}(\phi)$ term becomes $1$, and only $L^{2}\dot{\phi}^{2}$ is left.</p>
<p>So my question is: Why is that? I've been checking around, but nothing I find makes it one. I know that $\cos^{2}(\phi) = \frac{1}{2}(1+\cos(2\phi))$, but that doesn't seem to help me either.</p>
| 10,748 |
[
-0.009809384122490883,
0.006808196660131216,
-0.01002059318125248,
-0.013776185922324657,
-0.006698159035295248,
-0.017939025536179543,
-0.031630709767341614,
-0.030922554433345795,
-0.004766101948916912,
-0.007864809595048428,
0.04388643056154251,
0.03276355564594269,
0.07388097047805786,
0.009092717431485653,
0.04444074630737305,
-0.005401145201176405,
0.00404881127178669,
-0.018288681283593178,
0.01383475586771965,
-0.010202798061072826,
-0.01808539591729641,
-0.007540496997535229,
0.018938345834612846,
-0.006117349956184626,
-0.025474725291132927,
0.059001535177230835,
-0.007899156771600246,
-0.03297681733965874,
0.05084711313247681,
0.03144241124391556,
-0.04143481329083443,
-0.01252321433275938,
0.046450063586235046,
-0.01277434267103672,
0.014988304115831852,
0.0031692078337073326,
-0.023474188521504402,
-0.0464986115694046,
0.026637813076376915,
0.01873800717294216,
-0.07663436233997345,
-0.007999631576240063,
0.005887972190976143,
0.058135755360126495,
-0.038034163415431976,
0.010201242752373219,
0.0218205526471138,
-0.023868000134825706,
0.07311791181564331,
-0.058546409010887146,
0.09989207983016968,
0.024528251960873604,
0.04911458119750023,
0.02159915305674076,
-0.0010131451999768615,
0.01571735180914402,
0.07514701783657074,
0.05465281754732132,
-0.0061951749958097935,
-0.05152545124292374,
-0.005657341796904802,
-0.03978152573108673,
-0.01673820987343788,
-0.0033822653349488974,
0.0064621008932590485,
0.03391340747475624,
-0.004147677216678858,
-0.022619856521487236,
0.040894921869039536,
-0.006560619454830885,
-0.0013628187589347363,
-0.019695058465003967,
0.05796287581324577,
-0.04081707075238228,
-0.0028767131734639406,
-0.030971527099609375,
0.030084703117609024,
0.01980762928724289,
0.0020231420639902353,
0.041221342980861664,
0.015099773183465004,
0.024625707417726517,
0.05878274142742157,
0.02880151942372322,
-0.05946740508079529,
-0.00898731965571642,
0.04488470032811165,
0.039424363523721695,
0.029860012233257294,
0.03216342628002167,
0.009988117031753063,
0.028255999088287354,
0.03022320568561554,
-0.027123210951685905,
0.008743287064135075,
0.05021021142601967,
0.0015935931587591767,
0.037628475576639175,
0.014153306372463703,
-0.0058663408271968365,
-0.04679699242115021,
-0.0017930474132299423,
0.02654309943318367,
0.043116919696331024,
0.006996003445237875,
-0.0055365548469126225,
-0.04427756741642952,
-0.010224111378192902,
-0.0026694326661527157,
-0.03758816048502922,
-0.026014234870672226,
0.012785539962351322,
0.005019009578973055,
0.02851463109254837,
-0.017666537314653397,
-0.05396438390016556,
-0.029408296570181847,
0.005612755659967661,
0.023943176493048668,
0.04957938194274902,
0.05029679462313652,
-0.0005558975390158594,
0.05058988928794861,
0.010981541126966476,
-0.03773364797234535,
0.016653763130307198,
0.04387056082487106,
-0.009141773916780949,
-0.012674963101744652,
0.002728099701926112,
0.021102724596858025,
-0.0107340719550848,
-0.044175196439027786,
0.017511937767267227,
0.02063480019569397,
-0.06695099920034409,
-0.07948171347379684,
-0.04961840808391571,
0.0021912804804742336,
0.015046190470457077,
-0.02564607746899128,
-0.05601769685745239,
0.016510581597685814,
0.021407900378108025,
0.10566370189189911,
0.008214275352656841,
0.004076851066201925,
0.024657635018229485,
0.016683561727404594,
-0.019170941784977913,
0.01043416652828455,
-0.0035358481109142303,
0.0046232761815190315,
-0.06267084181308746,
0.02833244577050209,
-0.05854320898652077,
0.004594310652464628,
0.03494129329919815,
0.03376550227403641,
0.005094488617032766,
0.061648812144994736,
-0.019948426634073257,
0.01958424039185047,
0.016219021752476692,
-0.009399834088981152,
-0.019892238080501556,
0.07893325388431549,
0.004822949878871441,
0.005795442033559084,
0.03509344160556793,
0.01567794382572174,
-0.007759867236018181,
-0.018648967146873474,
0.03773931413888931,
0.07033306360244751,
-0.007454593200236559,
-0.030809585005044937,
-0.030349085107445717,
0.012916399165987968,
-0.0007489054114557803,
-0.02138059213757515,
-0.0399610698223114,
0.009497945196926594,
0.026745103299617767,
-0.00932007934898138,
0.038477517664432526,
0.026884792372584343,
0.040671397000551224,
-0.03191005066037178,
-0.036965612322092056,
-0.012438880279660225,
-0.017412999644875526,
0.022037828341126442,
0.011599678546190262,
-0.013417494483292103,
0.038734372705221176,
0.0068709468469023705,
0.02814781293272972,
-0.008388303220272064,
-0.003712509525939822,
0.001556074246764183,
0.02369125559926033,
-0.0018578339368104935,
-0.033639099448919296,
0.035545364022254944,
0.038502078503370285,
0.017327314242720604,
0.040740951895713806,
0.01939191296696663,
-0.0015868371119722724,
0.016998428851366043,
-0.005090054124593735,
0.0044425479136407375,
0.031105440109968185,
-0.02243306115269661,
0.0059040929190814495,
0.00011233472469029948,
-0.01311464887112379,
-0.025171393528580666,
0.0485837422311306,
-0.04520859941840172,
0.035807400941848755,
0.06533167511224747,
0.00808388739824295,
-0.006593809463083744,
0.06613705307245255,
-0.011779922991991043,
0.009717360138893127,
0.01126632560044527,
-0.0381554439663887,
0.00670618237927556,
0.01311300229281187,
0.010204512625932693,
0.019707709550857544,
-0.0523005947470665,
-0.007053201086819172,
0.06626527011394501,
0.013718965463340282,
0.0295840073376894,
0.012064293958246708,
-0.03999289497733116,
-0.06672126799821854,
0.06426896899938583,
0.02739645726978779,
-0.025214405730366707,
0.007950563915073872,
0.05258125066757202,
0.009842387400567532,
-0.0006773757049813867,
0.043194014579057693,
-0.029555846005678177,
0.04548019915819168,
-0.039922621101140976,
-0.004760260693728924,
0.0021284427493810654,
0.017949499189853668,
0.059180017560720444,
-0.01802215538918972,
0.07645273208618164,
0.015187566168606281,
-0.01095065288245678,
-0.0269460529088974,
-0.027180563658475876,
-0.018191449344158173,
0.014372414909303188,
-0.020563364028930664,
-0.015848061069846153,
-0.002910442417487502,
0.0013285116292536259,
-0.07365864515304565,
0.0036879165563732386,
0.015046174637973309,
-0.046013254672288895,
-0.02895941212773323,
0.008839720860123634,
0.005176045466214418,
0.009192542172968388,
0.0037818122655153275,
-0.02321113646030426,
-0.025742722675204277,
-0.01535648200660944,
-0.009983930736780167,
0.027269627898931503,
0.03066410683095455,
-0.021423473954200745,
-0.03838266059756279,
-0.031086347997188568,
-0.005024478770792484,
0.05163438990712166,
-0.010987164452672005,
-0.002341339597478509,
-0.0005755575257353485,
-0.002969862427562475,
-0.061253949999809265,
-0.01658698357641697,
-0.010646781884133816,
0.012224314734339714,
-0.033151041716337204,
0.002387646120041609,
0.005187314935028553,
0.019199447706341743,
-0.03128477558493614,
0.003889362793415785,
-0.0609312579035759,
-0.021355310454964638,
-0.039893314242362976,
0.02039146237075329,
0.03974608704447746,
-0.029712436720728874,
0.0021095264237374067,
0.023584716022014618,
0.02550652250647545,
0.012616303749382496,
-0.0901605561375618,
-0.01841125451028347,
-0.004713886417448521,
0.03223530203104019,
0.006294697057455778,
0.004658774472773075,
-0.038694482296705246,
0.07734464108943939,
0.009388492442667484,
-0.00391569035127759,
-0.014757566154003143,
0.02589575946331024,
0.012983833439648151,
-0.07169101387262344,
-0.015384068712592125,
0.008257557637989521,
-0.03665517643094063,
0.023054206743836403,
-0.012068373151123524,
0.00720755523070693,
0.025844769552350044,
-0.020630482584238052,
-0.0029540874529629946,
0.025085510686039925,
-0.031550269573926926,
0.029439374804496765,
0.054799288511276245,
-0.0013513050507754087,
0.0003161394561175257,
-0.0026372536085546017,
-0.022465575486421585,
0.026088614016771317,
-0.004507387522608042,
-0.0673137679696083,
0.06406878679990768,
-0.006493858527392149,
0.013899064622819424,
0.01381751149892807,
0.02508692443370819,
0.009458832442760468,
-0.05350043997168541,
-0.002415001392364502,
0.015712041407823563,
0.024503355845808983,
-0.032385408878326416,
0.016208989545702934,
0.033429455012083054,
0.03242940455675125,
-0.006746997125446796,
-0.030639436095952988,
0.00208661169745028,
0.02768564037978649,
0.043129757046699524,
-0.0014710435643792152,
-0.002031358890235424,
0.004534485284239054,
0.018648888915777206,
0.006024607457220554,
-0.037484072148799896,
-0.021654216572642326,
0.038119301199913025,
-0.08037828654050827,
-0.017392536625266075,
0.001006284961476922,
0.056870441883802414,
-0.00047163013368844986,
0.05122847110033035,
0.03443727269768715,
0.017611991614103317,
0.0433591827750206,
0.03825598955154419,
-0.07497894763946533,
0.06540006399154663,
-0.021287083625793457,
-0.04191559553146362,
0.022583432495594025,
-0.005144091323018074,
0.027926968410611153,
-0.02651960588991642,
-0.01314485352486372,
0.002577940933406353,
-0.024762408807873726,
-0.05295494571328163,
0.020691389217972755,
-0.03208090737462044,
-0.027428055182099342,
-0.002763384021818638,
0.022288519889116287,
0.007324171718209982,
-0.03057290054857731,
-0.01738017238676548,
0.07826055586338043,
-0.02905370108783245,
0.02621917799115181,
-0.05705184116959572,
-0.005970949772745371,
0.017834635451436043,
0.01695171184837818,
0.024010710418224335,
0.03784972429275513,
0.023914247751235962,
0.011716498993337154,
0.0006392659270204604,
0.06782200932502747,
0.008893041871488094,
0.019997090101242065,
-0.00959286093711853,
-0.005242469254881144,
-0.005955841857939959,
0.033684708178043365,
0.057673051953315735,
0.005667186342179775,
0.002782409777864814,
0.042715247720479965,
0.01008729636669159,
0.029080692678689957,
0.033708393573760986,
0.009324519895017147,
-0.01447242870926857,
-0.03214575722813606,
-0.05677128955721855,
0.017798619344830513,
-0.029248347505927086,
-0.006732194684445858,
-0.006004351656883955,
-0.01333637535572052,
-0.001048418926075101,
-0.01076770480722189,
0.017079783603549004,
0.029628271237015724,
0.020491823554039,
0.0034919867757707834,
-0.001890835934318602,
0.0354715958237648,
0.0007567727006971836,
-0.007512567099183798,
0.006735204253345728,
0.011952003464102745,
0.018284065648913383,
0.007406662218272686,
0.01273559220135212,
-0.05332236737012863,
-0.018995709717273712,
-0.008244741708040237,
0.022032514214515686,
-0.0024611346889287233,
-0.013222719542682171,
-0.03124547190964222,
-0.007370262872427702,
0.03954029083251953,
-0.04060076177120209,
0.047206684947013855,
0.013364588841795921,
0.004041374661028385,
0.0011668320512399077,
-0.028853941708803177,
-0.057391468435525894,
-0.010280841961503029,
-0.003216625889763236,
0.028094854205846786,
-0.0370066799223423,
-0.001957911066710949,
-0.004205139819532633,
0.013748746365308762,
0.014728903770446777,
0.06319056451320648,
-0.006826626602560282,
-0.04625225067138672,
-0.02023906446993351,
0.023627255111932755,
-0.02221304550766945,
-0.08853327482938766,
-0.010745502077043056,
-0.0051056272350251675,
-0.022332217544317245,
-0.007715072017163038,
-0.03979529067873955,
-0.07832590490579605,
0.03379369154572487,
0.020204011350870132,
-0.005488892085850239,
0.02155299112200737,
-0.058482881635427475,
0.007298300974071026,
0.017913594841957092,
0.009763240814208984,
0.040793031454086304,
0.05041193217039108,
-0.019339222460985184,
-0.012636504136025906,
-0.038220688700675964,
0.01808229647576809,
-0.003885096637532115,
-0.0068417200818657875,
-0.030017638579010963,
0.011707784608006477,
-0.03188128396868706,
0.017389999702572823,
-0.025394894182682037,
0.022014662623405457,
-0.025053130462765694,
0.0023649604991078377,
0.015299676917493343,
0.02440224215388298,
-0.010117446072399616,
0.0036909969057887793,
0.0054824091494083405,
0.0360613688826561,
-0.00020342905190773308,
-0.011908805929124355,
0.002887197770178318,
-0.02344932034611702,
-0.030920183286070824,
0.05093434825539589,
0.0037522923666983843,
0.01659601740539074,
-0.016720231622457504,
-0.011218170635402203,
0.011450059711933136,
-0.06844883412122726,
0.048068705946207047,
0.00670322822406888,
0.0024072162341326475,
0.0230609942227602,
-0.04810816049575806,
-0.05989205464720726,
-0.003986070863902569,
-0.008710970170795918,
0.039356645196676254,
-0.05312477797269821,
-0.03611148148775101,
0.014647689647972584,
-0.013872276060283184,
-0.06180917099118233,
-0.061589840799570084,
-0.004207405727356672,
-0.008247590623795986,
-0.019383691251277924,
0.005479632411152124,
-0.006403950974345207,
-0.034687601029872894,
-0.03136752173304558,
0.015365933068096638,
0.0178400706499815,
-0.000732496555428952,
0.01321388129144907,
0.01147068478167057,
0.0164333526045084,
-0.004850159864872694,
-0.0240761861205101,
0.0023879159707576036,
0.030222555622458458,
-0.01356629841029644,
-0.05456969514489174,
-0.002669215900823474,
0.06297130137681961,
-0.0009173496509902179,
-0.020702198147773743,
-0.027395907789468765,
0.0011892085894942284,
0.012037237174808979,
-0.0020677943248301744,
-0.037956684827804565,
0.029403673484921455,
0.024392440915107727,
0.021178849041461945,
-0.02804785966873169,
-0.005883523263037205,
0.020367341116070747,
0.04405157268047333,
-0.023562895134091377,
0.005421565379947424,
-0.011577975936233997,
-0.03355245292186737,
0.0077095795422792435,
0.0151092279702425,
0.020140256732702255,
-0.010346448048949242,
0.05756433680653572,
0.003775497432798147,
-0.012324258685112,
0.05780976638197899,
0.012981723994016647,
0.006035200320184231,
0.03367527201771736,
0.005841152276843786,
-0.0015363225247710943,
0.008867204189300537,
-0.032279860228300095,
0.0011342403013259172,
0.00461984146386385,
0.009061417542397976,
0.09335535019636154,
-0.039710767567157745,
0.02307923138141632,
-0.010086911730468273,
-0.004434189293533564,
0.026788031682372093,
0.003854650305584073,
-0.03729806840419769,
-0.008334477432072163,
-0.006882279645651579,
0.04851488023996353,
-0.06196483224630356,
0.012761049903929234,
0.023929616436362267,
0.02228759042918682,
-0.03661615401506424,
-0.003212723648175597,
-0.004510856233537197,
-0.001749388757161796,
-0.024985965341329575,
0.01838514395058155,
-0.0425223670899868,
0.03461843356490135,
0.017867842689156532,
0.05148319900035858,
-0.017490366473793983,
-0.037199921905994415,
0.08207300305366516,
0.0035784931387752295,
0.021110527217388153,
-0.03185530751943588,
0.008496561087667942,
-0.008737883530557156,
0.011286545544862747,
-0.01409595925360918,
-0.02147480845451355,
-0.008769741281867027,
0.003552010515704751,
0.0481552854180336,
0.011797764338552952,
0.025192778557538986,
-0.022166959941387177,
-0.045246340334415436,
-0.030919954180717468,
-0.05816815420985222,
-0.07019330561161041,
0.047900550067424774,
0.014822037890553474,
-0.00440552644431591,
0.034176040440797806,
-0.010348125360906124,
0.030376169830560684,
-0.02095336653292179,
0.024002300575375557,
-0.01663970574736595,
0.048509858548641205,
0.00885615311563015,
0.011534444987773895,
-0.039542317390441895,
0.015305940993130207,
0.1014314815402031,
0.05491003021597862,
0.03345798701047897,
-0.06584322452545166,
0.0008615211700089276,
-0.05133150890469551,
-0.0017812951700761914,
-0.06338077038526535,
0.022892236709594727,
-0.020639672875404358,
-0.0114636505022645,
-0.03161391243338585,
0.07575832307338715,
-0.02629302814602852,
-0.005447161849588156,
0.01787589304149151,
-0.013885206542909145,
-0.047331392765045166,
0.02109568752348423,
0.009977895766496658,
0.013096459209918976,
0.026802750304341316,
-0.01786036789417267,
0.044014886021614075,
-0.04549797251820564,
0.012510418891906738,
-0.039428871124982834,
-0.04787896201014519,
-0.0059946514666080475,
0.0108450036495924,
-0.05357768386602402,
-0.011964680626988411,
0.02801787294447422,
-0.007861773483455181,
-0.015443653799593449,
0.028415687382221222,
0.03729002922773361,
0.035729218274354935,
0.024666085839271545,
0.01860504224896431,
0.006199419964104891,
0.07018572837114334,
0.05017884075641632,
-0.012582285329699516,
-0.037631019949913025,
0.0014353303704410791,
-0.005765924230217934,
0.10443621873855591,
-0.007187522482126951,
0.04872589930891991,
-0.008703446947038174,
0.005428178235888481,
-0.02059333771467209,
-0.037924427539110184,
-0.015379644930362701,
0.0263874102383852,
0.0290587916970253,
0.0038665011525154114,
-0.019342023879289627,
-0.04088309779763222,
-0.01725587248802185,
0.004263715352863073,
0.00714320270344615,
-0.015295998193323612,
-0.0004036304890178144,
0.010905140079557896,
0.005820146761834621,
0.03012024238705635,
-0.00674115214496851,
-0.02815016359090805,
-0.004902367480099201,
-0.014595183543860912,
-0.043816328048706055,
-0.020574161782860756,
-0.0037786157336086035,
-0.0076636397279798985,
0.02792811021208763,
-0.03198914974927902,
-0.012884506024420261,
-0.04735039174556732,
-0.08499544113874435,
0.003521823789924383,
0.016542816534638405,
-0.037187252193689346,
-0.0043012346141040325,
-0.03627790883183479,
-0.025763055309653282,
0.03476710245013237,
-0.05092129111289978,
-0.0122040631249547,
0.016176985576748848,
0.008266755379736423,
0.03533603623509407,
-0.021553555503487587,
-0.038971077650785446,
0.014658923260867596,
-0.013703370466828346,
-0.017052989453077316,
-0.008141920901834965,
0.005506205838173628,
-0.0005150923389010131,
0.054694537073373795,
-0.00506243109703064,
0.019382981583476067,
-0.008834543637931347,
-0.012875928543508053,
0.019683297723531723,
-0.0033278698101639748,
-0.011707902885973454,
0.04557730630040169,
0.01891542598605156,
-0.020596766844391823,
-0.016082733869552612,
-0.011774334125220776,
-0.03610386326909065,
-0.03393864259123802,
0.02548515796661377,
-0.04124877229332924,
0.0068509867414832115,
-0.055486783385276794,
0.009545106440782547,
0.012958860956132412,
0.004724693018943071,
-0.08246131986379623,
0.01478512305766344,
-0.008895913138985634,
-0.03978317603468895,
-0.010382091626524925,
0.06534962356090546,
-0.052768073976039886,
0.009570915251970291,
0.023854199796915054,
0.04049433767795563,
-0.019435137510299683,
-0.028691846877336502,
0.002461099298670888,
0.005116143263876438,
0.0625855103135109,
-0.01580551639199257,
-0.02966739796102047,
0.023110033944249153,
-0.013887857086956501,
-0.005032393150031567,
0.02548048458993435,
0.00927592720836401,
0.04534231871366501,
0.03722784295678139,
-0.020331326872110367,
-0.025951551273465157,
0.056757956743240356,
-0.04534072056412697,
0.017007052898406982,
-0.010407310910522938,
-0.024631822481751442,
0.014819235540926456,
-0.02896541729569435,
-0.021733827888965607,
-0.008567053824663162,
0.015317392535507679,
0.003648576559498906,
0.03086286410689354,
0.0017317096935585141,
-0.0006444501923397183,
-0.022060133516788483,
0.007415530271828175,
0.03519640117883682,
0.04591359198093414,
0.01914333552122116,
0.009434984996914864,
0.05431787669658661,
-0.006899774074554443,
-0.016710802912712097,
0.03723179176449776,
0.019384710118174553,
-0.0932549312710762,
-0.004982330836355686,
-0.02699134312570095,
0.030919864773750305,
0.04625818878412247,
-0.03997180983424187,
0.010761149227619171,
0.03310256823897362,
-0.08151736110448837,
-0.014244201593101025,
-0.041429247707128525,
-0.011158211156725883,
0.0003457826387602836,
-0.043640147894620895,
-0.020350633189082146,
0.06345953792333603,
0.05063663050532341,
0.01735926978290081,
0.028890907764434814,
-0.011419872753322124,
-0.020809734240174294,
-0.026408836245536804,
0.019739530980587006,
0.03238169848918915,
-0.017752617597579956,
-0.01678919419646263,
0.03387635201215744,
0.0014221329474821687,
-0.017090406268835068,
0.015169281512498856,
-0.04333812743425369,
-0.0053062704391777515,
0.009616448543965816,
0.021061846986413002,
0.020948970690369606,
0.0005846449639648199,
0.015022002160549164,
-0.013016577810049057,
0.002553661586716771,
0.009895434603095055,
0.05716300755739212,
0.022203832864761353,
-0.04489213600754738,
-0.01351908128708601,
0.033036425709724426,
-0.03836333751678467,
-0.046428557485342026,
0.04284196346998215,
-0.013953148387372494,
0.01628124713897705,
0.014390973374247551,
0.009201236069202423,
-0.0016449401155114174,
-0.04980574548244476,
0.026137547567486763,
-0.03155605122447014,
-0.006029799114912748,
0.03319928050041199,
0.0020125119481235743,
0.002770403167232871,
0.026966266334056854,
-0.014039874076843262,
-0.01517434511333704,
0.020826516672968864,
-0.003863308811560273,
0.006667529232800007,
-0.06415745615959167,
-0.01025063544511795,
0.009260264225304127,
0.007560023106634617,
-0.007452209945768118,
-0.016014911234378815,
-0.06964035332202911,
0.04436631128191948,
0.016284635290503502,
0.009684688411653042,
-0.018757879734039307,
-0.014015412889420986,
-0.028297536075115204,
-0.09345071762800217,
-0.0013227281160652637,
0.007935800589621067,
-0.03529169410467148,
-0.022853637114167213,
-0.03333599865436554,
-0.004394116345793009,
0.0314556322991848,
0.05720042064785957,
-0.00021949439542368054,
0.005118822678923607,
0.03180258721113205,
0.007060406729578972,
-0.003929921425879002,
-0.013289317488670349,
-0.005984145682305098,
-0.007302863523364067,
0.00004490147330216132,
0.00905078835785389,
0.013018897734582424,
-0.007753855083137751,
0.049035072326660156,
0.04070242866873741,
-0.02148827165365219,
0.019739046692848206,
-0.01119266264140606,
-0.03799935057759285,
-0.0035873681772500277,
-0.036987241357564926,
-0.008087558671832085,
0.06683562695980072,
0.01094744447618723,
0.009175300598144531,
0.03453869745135307,
-0.04607366770505905,
-0.046736784279346466,
0.01587384194135666,
-0.06123661249876022,
-0.033663369715213776,
-0.014671714045107365,
0.0033380119130015373,
0.027832644060254097,
-0.0496811605989933,
0.01699422486126423,
0.04247165098786354,
-0.017085794359445572,
-0.04482119530439377,
0.022013043984770775,
0.021328378468751907,
0.017033429816365242,
0.025488361716270447,
0.026845328509807587,
0.0062927259132266045,
-0.0027776688802987337,
0.0448511466383934,
0.053790077567100525,
0.03432203829288483,
0.017515305429697037,
-0.006569867022335529,
-0.012247389182448387,
-0.05005576089024544,
0.020001376047730446,
-0.007312670350074768,
0.0318436324596405,
-0.038311030715703964,
-0.002358172321692109,
-0.019113311544060707,
-0.008615978062152863,
0.025951771065592766,
-0.03206537663936615,
-0.018191896378993988,
0.042808160185813904,
-0.0428374819457531,
0.02198060229420662,
-0.02859802544116974,
0.019876327365636826,
0.013589679263532162,
0.013230299577116966,
0.007342291530221701,
0.049747154116630554,
-0.004150196444243193,
-0.008373684249818325,
-0.06758531183004379,
-0.010977302677929401,
0.003775497432798147,
-0.047059401869773865,
-0.034931864589452744,
0.015347586013376713,
0.004560693167150021,
-0.012554642744362354,
-0.024188434705138206,
0.005266952328383923,
-0.04326365143060684,
-0.003230964532122016,
0.04080004245042801,
0.030705640092492104,
-0.04062464088201523,
-0.016880111768841743,
-0.021652577444911003,
0.056025419384241104,
-0.07370620965957642,
-0.016131950542330742,
0.0041331639513373375,
0.008423078805208206,
-0.03401976823806763,
0.011662852950394154
] |
<p>The Beer-Lambert law is: $ I=I_{0}e^{-n\sigma(\lambda) x} $,
where $ n $ is the volume concentration and $ \sigma $ the "efficient" cross-section.</p>
<p>For interaction with F-centers (kind of crystal defects: electrons trapped in negative ions lakes), what is the boundary effect on the exponential parameter: $ n\sigma(\lambda) $ ?</p>
<p>Thank you.</p>
| 10,749 |
[
-0.002431992208585143,
-0.03432230278849602,
0.008413158357143402,
-0.009762020781636238,
0.025390835478901863,
0.007128188386559486,
-0.023928945884108543,
-0.002289853524416685,
-0.00357435061596334,
0.0019692489877343178,
0.08602139353752136,
0.018460161983966827,
0.07971753180027008,
-0.001049115788191557,
-0.0006425154278986156,
0.016277676448225975,
-0.025534670799970627,
-0.0070442636497318745,
-0.020812027156352997,
-0.023550793528556824,
0.011315388604998589,
0.049198511987924576,
-0.003660001326352358,
0.012625428847968578,
-0.07281086593866348,
0.04930480942130089,
-0.005023215431720018,
-0.02571449801325798,
-0.008060888387262821,
0.07764775305986404,
-0.011409986764192581,
-0.009964083321392536,
0.035588767379522324,
0.0379507914185524,
-0.008339847438037395,
0.022674309089779854,
-0.02556597627699375,
-0.050525031983852386,
-0.037703417241573334,
0.028567450121045113,
-0.039199937134981155,
-0.02577010914683342,
0.027605092152953148,
0.0168939046561718,
0.03115137666463852,
-0.02187355048954487,
-0.03665369004011154,
-0.037392355501651764,
0.04907175898551941,
-0.0523814782500267,
0.03661253675818443,
-0.03142179921269417,
0.04349822923541069,
0.01896078884601593,
0.0019439742900431156,
-0.006025318056344986,
0.05331509932875633,
0.06085360422730446,
0.037792857736349106,
-0.021416334435343742,
0.0017885798588395119,
-0.00043116341112181544,
-0.02037052996456623,
-0.017767006531357765,
-0.0015624063089489937,
0.002629472641274333,
0.004931478761136532,
-0.04201981797814369,
0.010994454845786095,
0.02276318147778511,
-0.014844933524727821,
0.02161053754389286,
0.046239860355854034,
-0.036061253398656845,
0.06749986112117767,
-0.0050599658861756325,
0.06206484138965607,
0.02077610231935978,
0.025119822472333908,
0.037495050579309464,
-0.05028088390827179,
0.02397117018699646,
0.045686449855566025,
0.021963929757475853,
-0.017907017841935158,
-0.028815647587180138,
0.06453095376491547,
-0.04058957099914551,
0.03248780593276024,
0.006143296603113413,
-0.01708388514816761,
0.015664510428905487,
0.0626986101269722,
0.015213760547339916,
-0.06841156631708145,
0.013974360190331936,
0.009303836151957512,
0.05695214867591858,
0.024423450231552124,
0.005659474525600672,
-0.027678318321704865,
-0.010915513150393963,
0.0008362114895135164,
0.09392976015806198,
-0.023763254284858704,
-0.01378040760755539,
-0.06137452647089958,
-0.024284234270453453,
-0.02343033440411091,
-0.02522655762732029,
-0.051863908767700195,
0.00521791260689497,
0.01490803249180317,
-0.0015297598438337445,
0.05060247331857681,
-0.04206206649541855,
0.00726282736286521,
-0.02020210027694702,
0.046183452010154724,
0.02211582474410534,
0.029718298465013504,
0.0012482308084145188,
0.043288327753543854,
0.005500403232872486,
-0.04184391349554062,
0.0028727888129651546,
0.03244371339678764,
-0.02218289114534855,
-0.015292768366634846,
0.01700711064040661,
0.01765180006623268,
-0.015844767913222313,
0.01788642443716526,
0.0001743564789649099,
0.03589003533124924,
0.014255538582801819,
-0.012603037990629673,
-0.051538556814193726,
0.027129467576742172,
-0.021486321464180946,
-0.0015235485043376684,
-0.06928637623786926,
-0.026301531121134758,
0.0671771913766861,
0.07930202037096024,
0.023083599284291267,
-0.025707058608531952,
-0.033864252269268036,
0.06331709027290344,
0.002010325901210308,
-0.027053674682974815,
-0.013678856194019318,
0.006254505831748247,
-0.0062346369959414005,
0.005049447063356638,
-0.06953342258930206,
0.0324779748916626,
0.0341079980134964,
-0.004363127052783966,
-0.013466550968587399,
0.06627848744392395,
0.002871923381462693,
0.01676154136657715,
-0.016024339944124222,
-9.373307534588093e-7,
-0.017993997782468796,
0.06916672736406326,
0.030066736042499542,
0.039539020508527756,
0.035816602408885956,
-0.002492664149031043,
0.007102001458406448,
-0.011716977693140507,
0.015622874721884727,
0.03994035720825195,
-0.046727776527404785,
-0.016627177596092224,
-0.07403386384248734,
-0.002230292186141014,
0.014820880256593227,
-0.03468300402164459,
-0.02488735504448414,
-0.031227311119437218,
-0.012520168907940388,
-0.019863568246364594,
0.037937603890895844,
0.0046701738610863686,
-0.005620267242193222,
-0.012679523788392544,
-0.03079698048532009,
-0.015212992206215858,
-0.03151334449648857,
0.03589681535959244,
0.012906271032989025,
-0.05427153781056404,
0.020642712712287903,
-0.017289545387029648,
0.01645125076174736,
-0.0011999194975942373,
-0.03282715007662773,
-0.0030407565645873547,
0.02721002697944641,
-0.007097010966390371,
-0.00836648978292942,
0.05152410268783569,
0.07798419147729874,
0.05131274834275246,
-0.006509041879326105,
0.055331841111183167,
-0.05220775678753853,
-0.031159784644842148,
0.0014525774167850614,
-0.02263999544084072,
0.048448346555233,
0.034864697605371475,
-0.033790428191423416,
-0.0045227110385894775,
0.021641096100211143,
0.01688457280397415,
0.011439817026257515,
-0.01714649796485901,
0.047651875764131546,
0.023607036098837852,
0.03911783918738365,
0.048031724989414215,
0.02920394577085972,
0.0071067060343921185,
0.015131582506000996,
-0.000532415637280792,
-0.04561285302042961,
-0.02106597274541855,
-0.03437327221035957,
0.017411425709724426,
0.0001575673813931644,
-0.03493158519268036,
0.00746317021548748,
0.03976443037390709,
-0.01325927022844553,
0.043017707765102386,
0.01282394491136074,
-0.05967110022902489,
-0.006693593226373196,
0.04421568661928177,
0.039990250021219254,
0.0004204284923616797,
-0.008169006556272507,
0.022127922624349594,
-0.018328776583075523,
0.03999970853328705,
-0.04977347329258919,
0.00019638675439637154,
-0.011609327048063278,
-0.009622563607990742,
0.01534153614193201,
0.00472678616642952,
0.001504214946180582,
0.03551628813147545,
-0.027763869613409042,
-0.013239688239991665,
0.012863096781075,
-0.014977815560996532,
0.0609387643635273,
-0.04323909804224968,
-0.0027438406832516193,
0.03347388654947281,
-0.019327446818351746,
-0.000625799351837486,
0.021885909140110016,
0.01881299540400505,
-0.028253570199012756,
0.04679424315690994,
0.009760113433003426,
0.009748064912855625,
-0.008084149099886417,
0.01555047370493412,
-0.01500115729868412,
0.020122360438108444,
0.0007488245028071105,
-0.030539248138666153,
-0.046026505529880524,
-0.03613946586847305,
-0.009099633432924747,
0.033347975462675095,
0.012070325203239918,
-0.0006767527665942907,
-0.023585056886076927,
-0.053812429308891296,
-0.028201691806316376,
0.03629576787352562,
-0.004627171903848648,
-0.03557967767119408,
-0.021154120564460754,
-0.0016096148174256086,
-0.019983557984232903,
-0.004518498200923204,
0.012052453123033047,
-0.04025933891534805,
-0.02212420105934143,
0.029253391548991203,
0.03638078644871712,
-0.033077072352170944,
-0.04611549153923988,
0.025798797607421875,
-0.023916641250252724,
-0.02000405639410019,
-0.024610700085759163,
-0.012553209438920021,
0.011060903780162334,
-0.046453528106212616,
-0.001615382730960846,
0.034164294600486755,
-0.014171015471220016,
0.0025001985486596823,
-0.04425658658146858,
-0.041629813611507416,
0.023032527416944504,
-0.013020851649343967,
0.017902912572026253,
-0.06800724565982819,
-0.03942872956395149,
0.05697306618094444,
0.0038694862741976976,
-0.028779126703739166,
-0.0269765742123127,
-0.045735977590084076,
-0.02616451121866703,
-0.029309462755918503,
0.015065961517393589,
0.04959634318947792,
-0.030152177438139915,
0.0378679521381855,
-0.019443942233920097,
0.046317342668771744,
0.011117939837276936,
0.03482776880264282,
-0.012593298219144344,
0.031234098598361015,
0.007241228129714727,
-0.004036860540509224,
0.05940242484211922,
0.011443342082202435,
-0.01122586615383625,
0.04407146945595741,
-0.024193113669753075,
0.012071684934198856,
0.08334077149629593,
-0.045640699565410614,
0.017609545961022377,
-0.041213907301425934,
0.013022584840655327,
0.0028434477280825377,
0.012436311691999435,
0.014493168331682682,
0.005328443367034197,
-0.00913611426949501,
0.024578969925642014,
0.05709642544388771,
-0.007557350676506758,
-0.01591905951499939,
0.0043899063020944595,
0.06317935138940811,
-0.0092655960470438,
-0.06949018687009811,
0.005084340926259756,
-0.044207099825143814,
-0.00374995986931026,
-0.017749741673469543,
-0.011073569767177105,
0.013751529157161713,
0.05330576002597809,
-0.030653787776827812,
-0.026406360790133476,
0.014942537993192673,
-0.0325433686375618,
-0.03206019103527069,
-0.04489774629473686,
-0.02873845398426056,
0.04234835505485535,
0.00825672410428524,
0.042862776666879654,
0.022545164451003075,
0.014272733591496944,
0.022517669945955276,
0.006396540906280279,
-0.09077462553977966,
-0.01910126581788063,
0.01963379979133606,
0.0072029693983495235,
0.005623396020382643,
0.013795156031847,
0.008897149935364723,
0.0052348957397043705,
-0.027281809598207474,
0.010153849609196186,
0.017677273601293564,
-0.04689761623740196,
0.008827338926494122,
-0.01475544087588787,
-0.014409784227609634,
-0.06484098732471466,
0.03441423177719116,
-0.00889174360781908,
-0.003196198493242264,
-0.0008354223100468516,
-0.001453713746741414,
-0.031099729239940643,
-0.008928807452321053,
-0.025816861540079117,
0.007493523880839348,
0.01250176690518856,
0.03528153523802757,
0.05254024639725685,
0.014142329804599285,
-0.02448844164609909,
0.02046993374824524,
-0.0038423279765993357,
0.027587560936808586,
0.013838552869856358,
-0.020739054307341576,
0.031018296256661415,
-0.06301004439592361,
-0.018540410324931145,
-0.019613925367593765,
0.0852280855178833,
-0.0333373099565506,
0.016737915575504303,
0.04784705489873886,
-0.016839679330587387,
-0.016328275203704834,
0.02180732786655426,
0.012229044921696186,
0.05038854479789734,
-0.03441677615046501,
-0.027080517262220383,
-0.038756873458623886,
-0.01072093565016985,
0.018153071403503418,
-0.011689641512930393,
-0.0006961098406463861,
-0.019905898720026016,
0.0046746027655899525,
0.023924676701426506,
-0.008013344369828701,
0.014699811115860939,
-0.03481891378760338,
-0.013440823182463646,
-0.008602594025433064,
-0.04140189662575722,
-0.012288942001760006,
0.0023233797401189804,
-0.01511119119822979,
0.03205493465065956,
0.024282408878207207,
0.022496439516544342,
-0.06452056020498276,
-0.04616592079401016,
0.051480893045663834,
0.027468454092741013,
-0.005024312064051628,
-0.01066468097269535,
-0.045688170939683914,
0.012587074190378189,
-0.0033245389349758625,
-0.03610720485448837,
0.027279943227767944,
-0.023737747222185135,
0.0015949596418067813,
0.007917639799416065,
-0.006453376729041338,
-0.023617984727025032,
0.020969189703464508,
0.03218056634068489,
0.02484910748898983,
-0.04276062920689583,
0.004326075781136751,
0.016365831717848778,
0.015903834253549576,
0.0016805358463898301,
0.07681949436664581,
0.00678247818723321,
-0.02314475178718567,
0.024057697504758835,
0.03560878336429596,
-0.0008815599721856415,
-0.06796826422214508,
0.044237904250621796,
0.009117062203586102,
0.04270434007048607,
0.052007243037223816,
-0.013839703984558582,
-0.02138579823076725,
-0.007068794220685959,
0.07009082287549973,
-0.007555362302809954,
-0.028432123363018036,
0.005373800173401833,
0.06614773720502853,
0.03314513340592384,
-0.044871699064970016,
0.1020982638001442,
0.045395150780677795,
-0.03216680884361267,
-0.00721532991155982,
-0.04610288515686989,
0.054738178849220276,
0.006191958673298359,
0.029980838298797607,
-0.02472054772078991,
0.032365553081035614,
-0.003817993914708495,
0.05799175798892975,
-0.03354755416512489,
0.013658384792506695,
0.004875066224485636,
-0.029482411220669746,
0.02707734704017639,
-0.003185341600328684,
-0.03156854957342148,
-0.012335292994976044,
0.0014226081548258662,
0.032476846128702164,
-0.001801611972041428,
-0.008867572993040085,
-0.02013521082699299,
-0.04358915984630585,
0.044088173657655716,
-0.019334321841597557,
0.003601876785978675,
0.0073873186483979225,
-0.031308937817811966,
-0.01132515724748373,
0.01176496036350727,
-0.02296821027994156,
0.06455668061971664,
0.00007651072519365698,
-0.009800955653190613,
0.03823046013712883,
0.021013321354985237,
0.008742094039916992,
0.02334253489971161,
-0.03467736765742302,
0.029344698414206505,
-0.0686178132891655,
0.006407028064131737,
0.01088686566799879,
0.02584277093410492,
-0.09625859558582306,
-0.03939078375697136,
0.012257330119609833,
-0.04662499576807022,
-0.02599661611020565,
-0.03156496211886406,
-0.03896588459610939,
-0.020465577021241188,
-0.0609268955886364,
0.009352408349514008,
0.060644861310720444,
-0.02194567397236824,
-0.035878993570804596,
0.021375279873609543,
0.02140185609459877,
0.034981176257133484,
0.017700746655464172,
-0.026356102898716927,
0.025025254115462303,
0.004271830897778273,
-0.03468706086277962,
0.02588220313191414,
0.016387533396482468,
-0.009991631843149662,
-0.027600344270467758,
0.011442641727626324,
0.01529922429472208,
0.025504296645522118,
-0.00951655488461256,
-0.03668507561087608,
0.036447495222091675,
0.020547213032841682,
0.023730477318167686,
0.023946058005094528,
0.0035278990399092436,
0.01892557367682457,
0.03618071600794792,
-0.004703623242676258,
-0.022407280281186104,
-0.041017986834049225,
-0.007151242811232805,
0.018858961760997772,
0.0008054141071625054,
0.0014193928800523281,
-0.009865257889032364,
0.10557126998901367,
0.012810377404093742,
-0.019098058342933655,
0.02717897854745388,
-0.011403992772102356,
0.03891216218471527,
-0.04165303334593773,
-0.027079928666353226,
0.015238522551953793,
0.03206974267959595,
-0.03823086991906166,
-0.03320064768195152,
-0.04899471998214722,
0.041315820068120956,
0.013527827337384224,
-0.018752388656139374,
0.012458661571145058,
-0.01276610977947712,
0.044143129140138626,
-0.02486591413617134,
-0.07195716351270676,
0.0043503036722540855,
0.01614430360496044,
-0.025607477873563766,
0.0258623156696558,
-0.020852558314800262,
0.02505664713680744,
0.03978700563311577,
0.061064958572387695,
-0.04314795881509781,
0.02070971019566059,
0.012077055871486664,
-0.014653264544904232,
0.03846972808241844,
-0.05785442888736725,
0.00407000444829464,
0.049550388008356094,
-0.042081400752067566,
0.0255456380546093,
0.03421147167682648,
-0.013399547897279263,
0.0645165741443634,
0.01737530343234539,
0.03852178901433945,
-0.038769178092479706,
0.0009413480875082314,
-0.023384636268019676,
-0.0031227627769112587,
-0.0020630364306271076,
0.00669819163158536,
0.00433553708717227,
-0.0011420551454648376,
0.016888530924916267,
0.00463767210021615,
-0.011787992902100086,
-0.012587681412696838,
-0.03956913948059082,
-0.018078280612826347,
-0.06400421261787415,
-0.06509582698345184,
0.05122183635830879,
-0.029290297999978065,
-0.056637756526470184,
0.033379361033439636,
-0.03554162755608559,
0.03256623446941376,
0.013660113327205181,
0.01845920830965042,
0.032820481806993484,
0.04423610493540764,
-0.028140097856521606,
0.02188301272690296,
0.014931993559002876,
0.030377309769392014,
0.11834532767534256,
0.030968083068728447,
-0.012292396277189255,
-0.04943409189581871,
-0.010811710730195045,
0.0007092771120369434,
0.012425599619746208,
-0.03373480588197708,
-0.028847936540842056,
-0.019103894010186195,
-0.007329877931624651,
0.0233614519238472,
0.054072730243206024,
0.003715556813403964,
0.002474024426192045,
0.014362776651978493,
-0.03229970484972,
-0.015303400345146656,
0.043382640928030014,
-0.0008375591714866459,
-0.027454018592834473,
0.02040882036089897,
-0.030472971498966217,
0.032010503113269806,
-0.015379372052848339,
0.015544540248811245,
-0.05038142204284668,
-0.0049532512202858925,
0.022263163700699806,
-0.003307906910777092,
-0.01268348004668951,
-0.010674876160919666,
0.011409006081521511,
-0.015875061973929405,
0.01135218609124422,
-0.02105448767542839,
-0.011504498310387135,
-0.009509957395493984,
0.007974796928465366,
0.024043796584010124,
-0.012600656598806381,
-0.03330807760357857,
0.024207526817917824,
0.005468927323818207,
-0.04452335834503174,
-0.026966622099280357,
-0.007797298952937126,
0.04736237972974777,
0.0024395380169153214,
-0.00818441342562437,
-0.0054662893526256084,
-0.017346929758787155,
0.006081703118979931,
-0.023134414106607437,
-0.02638639137148857,
-0.004372695926576853,
0.024649865925312042,
-0.025028783828020096,
-0.01293860748410225,
0.015837853774428368,
0.03971840441226959,
-0.0035419666673988104,
-0.03152138367295265,
0.0059664687141776085,
-0.0318807028234005,
0.016755221411585808,
-0.023755993694067,
0.013363330624997616,
0.01077839732170105,
-0.018829135224223137,
-0.03651614859700203,
-0.00936004240065813,
-0.02989606186747551,
-0.037684351205825806,
-0.019328204914927483,
0.008159295655786991,
0.030568258836865425,
0.0003666736010927707,
0.0043904646299779415,
-0.0011750896228477359,
-0.06948427855968475,
-0.009949722327291965,
-0.04475955665111542,
-0.02279820293188095,
-0.023240141570568085,
0.002365810563787818,
0.014594707638025284,
-0.014127693139016628,
-0.012275059707462788,
0.015898482874035835,
0.029222272336483,
0.07669136673212051,
0.03359713777899742,
-0.04627801850438118,
-0.05471721664071083,
0.008005091920495033,
-0.014988240785896778,
0.030765298753976822,
-0.012794476002454758,
0.010282703675329685,
-0.039018984884023666,
0.006295903120189905,
0.04913819953799248,
0.019686805084347725,
-0.028053248301148415,
-0.029287103563547134,
0.004529356956481934,
-0.020441515371203423,
0.0027738676872104406,
0.01681653782725334,
-0.012408854439854622,
-0.033878277987241745,
-0.03077121451497078,
-0.03551829606294632,
-0.03394211083650589,
0.029353491961956024,
0.02959580346941948,
-0.04316212609410286,
0.0122480858117342,
-0.03547889366745949,
0.014607452787458897,
0.01139803696423769,
-0.012338968925178051,
-0.012331732548773289,
0.011866712011396885,
-0.029887497425079346,
0.017095139250159264,
0.007170942611992359,
-0.00630307849496603,
-0.0220633614808321,
0.011551251634955406,
0.029086841270327568,
0.05130114033818245,
0.0075836763717234135,
-0.008151672780513763,
0.009650561958551407,
0.011160872876644135,
0.026216423138976097,
-0.03673909232020378,
-0.003152808640152216,
0.04675393924117088,
-0.030352992936968803,
-0.04028168320655823,
-0.013180083595216274,
-0.006921903230249882,
0.0064494120888412,
0.018807407468557358,
0.024768799543380737,
0.0033691541757434607,
0.02595667913556099,
-0.0227230004966259,
0.015768814831972122,
-0.027229227125644684,
-0.032281920313835144,
0.005159022286534309,
-0.018368655815720558,
0.029585979878902435,
-0.01773662306368351,
0.023568546399474144,
-0.017417369410395622,
0.03443845361471176,
-0.06160586327314377,
-0.007012398447841406,
0.02481769025325775,
-0.029586104676127434,
0.0033607122022658587,
-0.005620304960757494,
-0.010807878337800503,
0.006230618804693222,
0.018220985308289528,
0.0015545424539595842,
0.018639035522937775,
-0.006862200330942869,
-0.008343609049916267,
-0.08076257258653641,
-0.015505279414355755,
0.0036417788360267878,
0.03454093262553215,
0.009875253774225712,
-0.03369166702032089,
0.00047220615670084953,
0.0004929223214276135,
-0.0776679590344429,
0.016402242705225945,
-0.012795438058674335,
-0.038289379328489304,
-0.058567970991134644,
-0.02589796856045723,
-0.0446498729288578,
0.021717464551329613,
0.014474274590611458,
0.061840254813432693,
-0.005211640149354935,
0.05715275928378105,
0.001488064881414175,
-0.016897229477763176,
0.011321443133056164,
0.008367815054953098,
0.01184921432286501,
-0.003911694511771202,
0.048412878066301346,
-0.004278527107089758,
0.014363804832100868,
0.008664905093610287,
0.00486226798966527,
-0.011817366816103458,
0.018350902944803238,
0.017387675121426582,
-0.018420621752738953,
0.08520574867725372,
0.015638340264558792,
-0.000857381266541779,
0.009852622635662556,
0.04777674749493599,
0.007868683896958828,
0.022955046966671944,
-0.011421347968280315,
0.003657921915873885,
0.005097104236483574,
-0.021507229655981064,
-0.026322461664676666,
0.023891456425189972,
0.009041612036526203,
0.0037841820158064365,
0.011511909775435925,
-0.004292376805096865,
0.028862038627266884,
-0.018933262676000595,
0.03058983013033867,
-0.027043400332331657,
-0.020351706072688103,
0.02653692662715912,
0.013470890000462532,
0.02733621373772621,
0.02732628583908081,
-0.013601339422166348,
-0.039737518876791,
-0.011325686238706112,
0.03368840366601944,
-0.027034824714064598,
-0.03610744699835777,
-0.017128605395555496,
-0.006994591094553471,
-0.01095072366297245,
-0.019276242703199387,
-0.009019865654408932,
-0.0743289366364479,
0.03452177718281746,
-0.014197371900081635,
0.03942224010825157,
0.008710169233381748,
-0.033771663904190063,
0.027108287438750267,
-0.07783955335617065,
-0.0013296471443027258,
0.010765522718429565,
0.04990754276514053,
-0.017949756234884262,
-0.031158598139882088,
-0.00730916578322649,
0.010926512070000172,
0.07274868339300156,
0.008461355231702328,
-0.06758075207471848,
0.003975781612098217,
-0.026451149955391884,
-0.012765608727931976,
-0.05899611860513687,
0.01936510019004345,
-0.014093703590333462,
-0.014370131306350231,
-0.030889611691236496,
0.021551169455051422,
-0.016862649470567703,
0.02478817105293274,
0.01261379849165678,
-0.002655134303495288,
-0.018585490062832832,
-0.043666813522577286,
-0.021275930106639862,
0.04451609402894974,
0.029368219897150993,
-0.0011541849235072732,
0.0717923492193222,
0.0335966981947422,
0.019931450486183167,
0.009582915343344212,
-0.033171627670526505,
-0.08041001856327057,
0.012891516089439392,
-0.018750902265310287,
-0.014168080873787403,
-0.029467837885022163,
0.0008964254520833492,
0.004598774015903473,
-0.04448032006621361,
-0.017409782856702805,
0.04564017802476883,
-0.07217748463153839,
-0.02138179913163185,
0.03889627754688263,
0.013301104307174683,
0.044171445071697235,
-0.010117665864527225,
0.017279472202062607,
-0.0033942388836294413,
-0.004352211486548185,
-0.024271955713629723,
0.03249887004494667,
0.0232547577470541,
0.025787316262722015,
0.048693519085645676,
0.013645751401782036,
-0.031181467697024345,
0.032392699271440506,
0.018522614613175392,
0.015440761111676693,
-0.01202147826552391,
-0.0028908278327435255,
0.05100575089454651,
0.04116099700331688,
0.018671084195375443,
0.026074757799506187,
0.01179592963308096,
0.06898891180753708,
-0.029922515153884888,
0.036593809723854065,
-0.02902507223188877,
-0.02863757498562336,
0.02781026065349579,
0.005628963932394981,
0.04625020548701286,
0.06136999651789665,
-0.030246630311012268,
-0.02580004371702671,
-0.010962531901896,
-0.011441848240792751,
0.0009297881624661386,
-0.06337279826402664,
0.03140559792518616,
-0.01594635285437107,
-0.014079715125262737,
-0.005028956104069948,
-0.004422293044626713,
-0.006083483342081308,
-0.05509266257286072,
-0.00031886290526017547,
0.04063289240002632,
0.012626518495380878,
0.041877057403326035,
-0.006680257618427277,
0.028516128659248352,
0.04366649314761162,
-0.047861386090517044,
-0.015663599595427513,
0.015292695723474026,
0.024706462398171425,
-0.01607707142829895,
0.0038023588713258505
] |
<p>It has been stated <a href="http://physics.stackexchange.com/a/100719">here</a> that:
<blockquote>we can say, without introducing a coordinate system, that the interval associated with two events is <em>timelike</em>, <em>lightlike</em>, or <em>spacelike</em></blockquote>.</p>
<p>This assertion appears at variance with </p>
<ul>
<li><p>the definition of "<i>time-like (or light-like, or space-like) intervals</i>" as defined here: <a href="http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals" rel="nofollow">http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals</a> explicitly in terms of "<i>differences of the space and time coordinates</i>", and</p></li>
<li><p>the definition of "<i>curves</i>" as "<i>chronological (or timelike)</i>", "<i>null</i>" (or "lightlike"), or "<i>spacelike</i>", and thus correspondingly of pairs of "<i>points</i>" of any such "<i>curve</i>" as "<i>timelike (or lightlike, or spacelike)</i> related to each other" of <a href="http://en.wikipedia.org/wiki/Causal_structure#Curves" rel="nofollow">http://en.wikipedia.org/wiki/Causal_structure#Curves</a> which explicitly requires the notion of <a href="http://en.wikipedia.org/wiki/Lorentzian_manifold#Lorentzian_manifold" rel="nofollow">Lorentzian manifold</a> and thus according to <a href="http://en.wikipedia.org/wiki/Manifold#Mathematical_definition" rel="nofollow">http://en.wikipedia.org/wiki/Manifold#Mathematical_definition</a> uses coordinates as subsets of $\mathbb R^n$ and their topological relations (as "<i>coordinate system</i>"). </p></li>
</ul>
<p>Therefore I'd like to know:<br>
How can be determined whether the interval associated with two events (which are given or characterized and distinguished by naming, for either event, the distinct individual participants which had been coincident at that event) is for instance "<i>timelike</i>", <b>without</b> using any coordinates and coordinate system?</p>
<p>Is it correct that the interval associated with two events (given as described above) is "<i>timelike</i>" if and only if there exists at least one participant who took part in both of these events?</p>
| 10,750 |
[
-0.011741585098206997,
-0.04866522550582886,
0.004830989986658096,
-0.03394471853971481,
0.03135992959141731,
0.010640840046107769,
-0.026577336713671684,
-0.049922071397304535,
-0.008104439824819565,
-0.02157384715974331,
0.046770427376031876,
0.019808370620012283,
0.0367644727230072,
0.04516344889998436,
0.014269820414483547,
0.004678448662161827,
0.02271275967359543,
0.04297087714076042,
-0.00866870116442442,
-0.06300872564315796,
0.03947430104017258,
-0.003753763623535633,
-0.0032216606196016073,
-0.006239915266633034,
-0.032789889723062515,
0.02279040776193142,
0.04413037374615669,
-0.008519467897713184,
-0.03415084630250931,
0.06505776196718216,
-0.06408488750457764,
-0.019241584464907646,
-0.025893285870552063,
0.02794765681028366,
0.009451033547520638,
0.0017047806177288294,
-0.04177112504839897,
-0.03421137109398842,
0.02935774251818657,
0.00024407314776908606,
-0.014135612174868584,
-0.0018884304445236921,
-0.038021523505449295,
0.058850523084402084,
-0.051563560962677,
0.03593822568655014,
0.0198972225189209,
0.002182983560487628,
0.03772317245602608,
-0.009756394661962986,
0.036599595099687576,
-0.03729432821273804,
0.02960876002907753,
-0.012585081160068512,
-0.019983163103461266,
0.014178157784044743,
0.061743710190057755,
0.05178005248308182,
-0.018187934532761574,
-0.07310541719198227,
-0.02774779498577118,
-0.003132325131446123,
0.02751149982213974,
-0.005878159776329994,
0.008898070082068443,
0.049318958073854446,
-0.0327080674469471,
0.004165145102888346,
0.000029752492991974577,
-0.04560069367289543,
-0.004944009240716696,
-0.001814673887565732,
0.016365379095077515,
-0.018282810226082802,
-0.0011702008778229356,
-0.03375295549631119,
0.024371890351176262,
-0.0028213774785399437,
0.03367438167333603,
0.04130590334534645,
-0.01003300677984953,
0.015660008415579796,
0.02411363646388054,
-0.02596638724207878,
0.05489487573504448,
-0.010212196037173271,
0.0466906763613224,
-0.01021987572312355,
-0.019986798986792564,
0.02556631900370121,
-0.013509254902601242,
-0.0025298180989921093,
0.011231626383960247,
-0.010595690459012985,
0.002808081451803446,
0.05376763269305229,
0.020442070439457893,
0.02596483752131462,
-0.021610895171761513,
-0.03293021395802498,
-0.03436814993619919,
-0.027300525456666946,
0.012699137441813946,
0.06847528368234634,
0.010002020746469498,
-0.021694501861929893,
-0.0322149358689785,
0.039265502244234085,
-0.022228257730603218,
0.006858213804662228,
-0.008973338641226292,
0.021204065531492233,
0.017458559945225716,
0.022492611780762672,
0.013121900148689747,
-0.03444613516330719,
-0.009898245334625244,
0.009913560003042221,
0.047989316284656525,
0.06983254849910736,
0.029582777991890907,
-0.053569208830595016,
-0.015880178660154343,
-0.01623406819999218,
-0.07683718204498291,
-0.017401058226823807,
0.04619992896914482,
0.0038502688985317945,
0.010662900283932686,
-0.0019294493831694126,
-0.00929914228618145,
-0.016084615141153336,
0.027052011340856552,
0.03491997718811035,
0.053710080683231354,
-0.0031753238290548325,
-0.09837844967842102,
-0.052887968719005585,
0.017736712470650673,
0.025117482990026474,
-0.006926210131496191,
-0.04547465965151787,
0.035080596804618835,
0.013147239573299885,
0.08007588237524033,
0.0055035497061908245,
0.014400885440409184,
0.032704051584005356,
0.04378841072320938,
-0.004144976381212473,
-0.0252205953001976,
0.0013789244694635272,
0.018209585919976234,
-0.05076004937291145,
-0.023952988907694817,
-0.0618865080177784,
0.024886639788746834,
0.028251800686120987,
-0.0072914655320346355,
0.004381000995635986,
0.053480446338653564,
-0.01165343914180994,
0.016188595443964005,
0.01608537696301937,
0.0011674308916553855,
-0.02445494942367077,
0.0770387277007103,
-0.00621411856263876,
-0.00748196616768837,
0.05917356163263321,
0.010426224209368229,
0.03181212767958641,
-0.011788159608840942,
0.043200962245464325,
0.03695850819349289,
-0.017071859911084175,
-0.03520726040005684,
0.041647713631391525,
-0.01160338893532753,
-0.012203454971313477,
-0.07329338788986206,
-0.010504052974283695,
-0.03761503845453262,
-0.021745575591921806,
0.02075699158012867,
0.050284601747989655,
0.010876539163291454,
0.012851307168602943,
0.02902369759976864,
-0.036525651812553406,
0.021663835272192955,
-0.05528401955962181,
-0.017899425700306892,
0.002496433909982443,
-0.04829976707696915,
0.008705288171768188,
-0.036790523678064346,
-0.01525540929287672,
-0.04548180475831032,
-0.03719957172870636,
-0.02474721521139145,
0.04211181774735451,
0.016088223084807396,
-0.03132501617074013,
-0.01739569567143917,
0.050721678882837296,
0.056994590908288956,
-0.005335028748959303,
-0.00861746072769165,
-0.0005881295073777437,
-0.04214020445942879,
0.03053523227572441,
-0.012725656852126122,
0.031124437227845192,
-0.0038358785677701235,
-0.00010274447413394228,
0.0067235976457595825,
0.04723193123936653,
-0.04313167929649353,
0.03434453904628754,
-0.04794769361615181,
0.0526348315179348,
0.038735490292310715,
0.024813521653413773,
-0.01907571591436863,
0.05009511485695839,
0.022695165127515793,
0.021665088832378387,
0.007855456322431564,
-0.0412517711520195,
-0.028992772102355957,
-0.02042531594634056,
0.04200497269630432,
0.03177108243107796,
-0.028967123478651047,
0.004539153538644314,
0.007187656592577696,
0.07518837600946426,
-0.02876374125480652,
0.018693285062909126,
-0.0044327182695269585,
-0.05276976898312569,
-0.01566903293132782,
-0.025827564299106598,
0.04124574363231659,
-0.0161181278526783,
0.019562100991606712,
-0.015569056384265423,
0.021866533905267715,
-0.02933824248611927,
0.002382083563134074,
0.03107784129679203,
-0.03256111964583397,
-0.03487062081694603,
0.031360119581222534,
-0.007614199072122574,
0.02690068818628788,
0.00600545946508646,
0.021104862913489342,
0.041116997599601746,
-0.023502850905060768,
-0.03467376530170441,
-0.021437643095850945,
-0.004569443874061108,
-0.03706973418593407,
0.009049329906702042,
-0.02790253795683384,
-0.020160196349024773,
0.011359441094100475,
-0.02182801067829132,
-0.01885366253554821,
-0.014762266539037228,
-0.038898956030607224,
-0.02150685340166092,
-0.02426970936357975,
0.030806779861450195,
0.03452198952436447,
0.009639129973948002,
-0.03070908784866333,
-0.01531886775046587,
0.020869171246886253,
0.01605195924639702,
0.0006026832270435989,
0.011776551604270935,
-0.027547061443328857,
0.028567558154463768,
-0.018862511962652206,
-0.015095033682882786,
0.03486168384552002,
-0.024525387212634087,
0.015175102278590202,
0.018215510994195938,
-0.007438647095113993,
-0.062463466078042984,
-0.00909060426056385,
-0.01642843894660473,
0.014895816333591938,
-0.021407175809144974,
-0.02823668159544468,
0.07998619973659515,
0.012399183586239815,
-0.09030549973249435,
0.03661166504025459,
-0.021298125386238098,
-0.02351383864879608,
-0.051449038088321686,
0.000586886890232563,
0.015398970805108547,
-0.026416806504130363,
0.017720229923725128,
0.05016692727804184,
-0.036139748990535736,
0.001986732007935643,
-0.05432950705289841,
-0.07183840870857239,
0.014713980257511139,
-0.017969781532883644,
0.0631825253367424,
0.005927772261202335,
-0.017847562208771706,
0.05617046356201172,
0.014782089740037918,
-0.0009685123804956675,
-0.0754791870713234,
0.02553250640630722,
0.0048342300578951836,
-0.0038595569785684347,
0.010101481340825558,
0.016621632501482964,
0.028551043942570686,
0.004655380267649889,
0.03937501087784767,
0.030820071697235107,
0.04015379026532173,
0.025461943820118904,
0.04014407470822334,
-0.01912478357553482,
0.015189766883850098,
-0.02592284046113491,
0.0152787109836936,
0.02506178431212902,
-0.025896893814206123,
0.000011229206393181812,
-0.018582098186016083,
0.02514735795557499,
0.048868320882320404,
-0.06505046784877777,
0.022922663018107414,
0.012027531862258911,
0.016666986048221588,
0.004073249641805887,
0.024714676663279533,
-0.0024387696757912636,
0.0012551330728456378,
-0.024282153695821762,
0.0177588053047657,
0.029658032581210136,
-0.018818654119968414,
-0.013409106060862541,
0.027549562975764275,
0.03277096897363663,
-0.028601080179214478,
-0.0037429400254040956,
-0.01655874401330948,
-0.026969732716679573,
0.05127789452672005,
-0.036722585558891296,
-0.014633974060416222,
0.053017761558294296,
0.023497123271226883,
-0.0018396873492747545,
0.025558751076459885,
-0.022001119330525398,
-0.02862953580915928,
-0.07066581398248672,
0.025740690529346466,
-0.014938805252313614,
0.01883188635110855,
0.0015042219310998917,
0.03137008473277092,
-0.0019880752079188824,
-0.010131556540727615,
-0.002073560608550906,
-0.00764040183275938,
-0.08028928190469742,
0.013048979453742504,
-0.04241866245865822,
-0.03267936781048775,
0.0008783547673374414,
-0.003619543742388487,
-0.006356329657137394,
0.005638724658638239,
-0.0090565150603652,
-0.011646068654954433,
0.009187228977680206,
-0.07533209025859833,
0.04926719889044762,
-0.03643802925944328,
-0.04671994596719742,
-0.0015042031882330775,
0.016567058861255646,
0.06023455411195755,
-0.00414499593898654,
0.04131219908595085,
0.008228410966694355,
-0.006110357586294413,
0.001393767073750496,
0.03389347344636917,
0.01955215074121952,
0.04456339403986931,
0.01381353847682476,
0.00687694177031517,
0.011194264516234398,
-0.0026830972637981176,
0.033976051956415176,
0.0002923494903370738,
0.048264920711517334,
0.027658136561512947,
-0.046459682285785675,
-0.03689532354474068,
-0.028605706989765167,
-0.013175519183278084,
0.009894396178424358,
0.0787656381726265,
-0.0017102882266044617,
-0.0004899260820820928,
0.004023615270853043,
0.015291576273739338,
0.031703151762485504,
0.020561309531331062,
0.029597405344247818,
-0.012660501524806023,
-0.040581874549388885,
-0.06920377910137177,
-0.02011982724070549,
0.0015153837157413363,
-0.03067256510257721,
0.015009259805083275,
0.04216616228222847,
-0.003430741373449564,
0.01003742404282093,
-0.006155418697744608,
0.005326620768755674,
-0.005446577910333872,
-0.00864754430949688,
-0.013260823674499989,
0.008473672904074192,
0.0088467663154006,
-0.0036916020326316357,
0.00126373500097543,
0.040516048669815063,
0.050601210445165634,
0.03949563205242157,
0.0012849790509790182,
-0.08036509156227112,
-0.030912764370441437,
0.045386649668216705,
0.04091523215174675,
-0.008775479160249233,
-0.03003009408712387,
-0.06055158004164696,
0.01309119164943695,
0.03767866641283035,
-0.032475054264068604,
0.02145528979599476,
-0.012788418680429459,
0.010682942345738411,
-0.04176798462867737,
-0.022728612646460533,
0.02517625316977501,
0.04616149887442589,
0.007187963463366032,
0.013012989424169064,
-0.010918271727859974,
0.010564826428890228,
0.0012493653921410441,
0.022679191082715988,
0.008669909089803696,
0.04520538076758385,
0.02808212861418724,
-0.008026505820453167,
-0.015420198440551758,
-0.0035641768481582403,
-0.017828786745667458,
-0.0682380199432373,
0.00012795100337825716,
0.04958014190196991,
-0.02031262032687664,
0.0413006953895092,
-0.018436811864376068,
0.013567566871643066,
0.010271001607179642,
0.003672483144327998,
-0.0059485966339707375,
0.05455818027257919,
-0.03773363679647446,
0.04941315948963165,
0.03256089240312576,
-0.007267257198691368,
0.02042749524116516,
0.051137205213308334,
-0.03470238298177719,
-0.023868152871727943,
-0.017796944826841354,
0.0169509444385767,
-0.029477376490831375,
0.018465552479028702,
-0.02652587927877903,
-0.006920136045664549,
-0.0508103184401989,
0.022818153724074364,
-0.03672076389193535,
-0.050639837980270386,
0.01300816796720028,
0.010228899307549,
-0.00567195750772953,
0.016131259500980377,
0.014930050820112228,
0.012569381855428219,
-0.045802515000104904,
0.016152558848261833,
0.008924195542931557,
0.002603428438305855,
0.03797386214137077,
-0.009448224678635597,
-0.015835966914892197,
0.05022368207573891,
0.01508567575365305,
0.004981484729796648,
-0.03197893872857094,
0.0036601105239242315,
-0.004333180375397205,
-0.04827529191970825,
0.015243658795952797,
-0.03173983469605446,
-0.026446692645549774,
0.03816438838839531,
-0.012286335229873657,
-0.0349418930709362,
-0.0016265450976788998,
-0.023791691288352013,
0.02274877391755581,
-0.06944289058446884,
0.026650188490748405,
0.02625438943505287,
-0.009949916042387486,
-0.08880560845136642,
-0.04776225611567497,
0.06308300048112869,
-0.01975805126130581,
-0.052366387099027634,
0.001469218754209578,
0.013350166380405426,
-0.03837781026959419,
-0.007659056223928928,
-0.019345717504620552,
0.043764032423496246,
-0.03907575085759163,
-0.06419356912374496,
-0.01627413183450699,
0.018005747348070145,
0.03652697801589966,
0.0162593312561512,
-0.0012636353494599462,
0.01641278713941574,
0.015335236676037312,
-0.0011722499039024115,
-0.012295449152588844,
0.06166611239314079,
-0.026995312422513962,
-0.035233210772275925,
-0.038978468626737595,
0.0008944653673097491,
-0.010315440595149994,
-0.02371416799724102,
-0.04060064256191254,
0.022009454667568207,
0.021385392174124718,
-0.005768494214862585,
-0.06884036213159561,
0.02344672568142414,
0.009183205664157867,
-0.01184405293315649,
-0.02416067197918892,
0.00510372593998909,
0.01371387392282486,
-0.024128185585141182,
0.014133372344076633,
-0.0288691446185112,
-0.011856235563755035,
-0.00412743492051959,
0.024331679567694664,
0.010343767702579498,
-0.004682636354118586,
0.009300187230110168,
0.003319335402920842,
0.009126522578299046,
-0.045006297528743744,
0.005283134523779154,
0.0005635262932628393,
-0.0031215099152177572,
-0.02655935473740101,
0.018643731251358986,
-0.03672831133008003,
0.014592296443879604,
0.07046166062355042,
0.002795280423015356,
0.04511300101876259,
0.045835185796022415,
-0.01720152609050274,
0.0058546825312078,
-0.03694704547524452,
0.03192441910505295,
-0.02944733388721943,
0.028376029804348946,
0.055251725018024445,
-0.058387886732816696,
-0.03941437602043152,
0.053564365953207016,
0.031894441694021225,
-0.04349755495786667,
0.008017733693122864,
-0.014830180443823338,
0.00006344660505419597,
0.01865650713443756,
0.013413624837994576,
-0.03565547615289688,
0.03938283771276474,
-0.01792093552649021,
0.019666554406285286,
0.04159963130950928,
0.0008946767775341868,
0.03706546500325203,
0.001853121560998261,
0.022855792194604874,
-0.009360364638268948,
0.007792602758854628,
-0.04205770418047905,
0.014096269384026527,
0.010403532534837723,
0.02664337120950222,
0.0014093252830207348,
-0.012280306778848171,
0.04792289435863495,
0.002356079639866948,
-0.01858268491923809,
-0.012411724776029587,
-0.05358095467090607,
-0.014004775322973728,
-0.07223664969205856,
-0.03676651418209076,
0.05130917951464653,
-0.004274482373148203,
-0.029660940170288086,
-0.01848178170621395,
-0.02528337948024273,
-0.013927137479186058,
0.025738578289747238,
0.024733101949095726,
-0.01659632846713066,
0.05387027934193611,
-0.008502479642629623,
-0.011460634879767895,
-0.06722770631313324,
-0.03872411698102951,
0.12191817164421082,
0.05011193826794624,
-0.0029405546374619007,
-0.06356924772262573,
0.04287680611014366,
0.019943861290812492,
0.007280317135155201,
-0.03742992877960205,
0.027187274768948555,
-0.015533278696238995,
-0.015165891498327255,
0.0491287000477314,
0.031848713755607605,
-0.005324443802237511,
-0.03186363726854324,
0.0449497252702713,
-0.03603605926036835,
-0.009939772076904774,
-0.030459444969892502,
0.008147153072059155,
0.016216890886425972,
0.03581630066037178,
-0.02079683355987072,
0.02195432037115097,
-0.01725790835916996,
0.04041832685470581,
-0.023606907576322556,
-0.025180963799357414,
0.01956556737422943,
0.014407023787498474,
-0.04997370019555092,
0.002795554231852293,
0.04017946869134903,
0.013736019842326641,
-0.009314673021435738,
-0.01859254017472267,
0.01846727356314659,
-0.012111295945942402,
0.033310823142528534,
0.060632891952991486,
0.017973564565181732,
0.0025198087096214294,
0.02955353446304798,
0.0381639190018177,
-0.06242116168141365,
-0.02517472766339779,
-0.047614965587854385,
0.011545108631253242,
0.002933681942522526,
0.00013895079609937966,
-0.009773739613592625,
0.0008904553833417594,
0.02295561134815216,
-0.056050192564725876,
-0.006636058446019888,
-0.025933384895324707,
0.002045954344794154,
0.0273439921438694,
0.015067041851580143,
0.0077251894399523735,
0.019747741520404816,
-0.01507145818322897,
0.03212693706154823,
-0.03286204859614372,
0.013459318317472935,
0.001996302744373679,
0.004990001674741507,
0.029137812554836273,
-0.007368496619164944,
0.023480124771595,
-0.03442912921309471,
-0.008820618502795696,
-0.04234712943434715,
-0.0024542545434087515,
0.013290703296661377,
0.03629768267273903,
0.039940912276506424,
0.013634604401886463,
0.01412039902061224,
0.01973276026546955,
-0.041336510330438614,
0.020257579162716866,
0.017941975966095924,
-0.0580248199403286,
0.005223565269261599,
0.041848890483379364,
0.03215160220861435,
0.039042048156261444,
-0.019362378865480423,
0.02290445566177368,
-0.019343065097928047,
0.03580205515027046,
0.011121993884444237,
-0.03801557794213295,
-0.00728065287694335,
0.011849719099700451,
0.01800752431154251,
0.008005904033780098,
-0.029849058017134666,
0.015780339017510414,
0.027074212208390236,
0.02536400780081749,
0.009212207049131393,
0.023808414116501808,
0.001478352234698832,
-0.03182392194867134,
0.020194239914417267,
-0.005231496877968311,
-0.0023271518293768167,
0.011389914900064468,
0.056342124938964844,
-0.06697924435138702,
-0.010368945077061653,
0.013168198987841606,
-0.014712042175233364,
-0.0023951975163072348,
-0.01115962490439415,
-0.0368279367685318,
0.0009196108439937234,
0.019160974770784378,
-0.017520936205983162,
-0.024754734709858894,
0.01380284782499075,
-0.05111168324947357,
0.010801118798553944,
-0.018257420510053635,
-0.0075235506519675255,
-0.008060485124588013,
0.02883286587893963,
-0.014651242643594742,
-0.022126324474811554,
0.024691028520464897,
0.027262773364782333,
-0.015352197922766209,
0.011922657489776611,
0.0314251147210598,
0.011606874875724316,
0.003860753495246172,
-0.008734846487641335,
-0.05977265164256096,
-0.029451090842485428,
-0.033631399273872375,
-0.04846952483057976,
0.04184773936867714,
-0.00005350634455680847,
-0.00708982115611434,
0.014705119654536247,
-0.017168134450912476,
0.012257153168320656,
0.05684420093894005,
-0.015164192765951157,
-0.01525806076824665,
0.014330890960991383,
-0.035985786467790604,
-0.018154053017497063,
0.002421871991828084,
0.0032057214993983507,
0.019632890820503235,
-0.009939806535840034,
-0.006731762085109949,
0.02785431034862995,
-0.016761956736445427,
-0.04668537899851799,
-0.008179731667041779,
-0.012029827572405338,
0.0054312581196427345,
-0.006518226116895676,
-0.008597342297434807,
0.06048145890235901,
0.033859092742204666,
-0.03720523789525032,
0.0348612442612648,
0.035502634942531586,
0.01512053981423378,
-0.10746998339891434,
0.02524668723344803,
0.03211236372590065,
0.040350355207920074,
0.04704229161143303,
-0.013397549279034138,
0.005440386012196541,
0.018057435750961304,
-0.05552506446838379,
0.03337633237242699,
-0.0023817962501198053,
-0.010553509928286076,
-0.016255898401141167,
0.011263457126915455,
-0.020109662786126137,
0.03743753582239151,
0.08300524204969406,
0.03532037511467934,
0.0018687621923163533,
0.006757672410458326,
-0.03576705604791641,
-0.03787447139620781,
-0.05208582803606987,
0.016033699735999107,
-0.022250885143876076,
-0.0527307502925396,
0.06726484000682831,
-0.004149782005697489,
-0.0037416834384202957,
0.03957057371735573,
0.014282949268817902,
0.024615677073597908,
-0.005179608706384897,
0.00599358044564724,
0.007768036797642708,
-0.0008039685199037194,
0.029462074860930443,
0.0006769232568331063,
-0.01705242693424225,
-0.023001257330179214,
0.001999747008085251,
0.01790032908320427,
-0.009106801822781563,
-0.04735584184527397,
0.007977114990353584,
-0.05699234828352928,
-0.0247845146805048,
0.042121607810258865,
-0.02408086135983467,
-0.01913142018020153,
-0.020694782957434654,
0.04252799600362778,
0.011656560935080051,
-0.012242692522704601,
-0.0003733646881300956,
-0.02287365309894085,
0.0019637062214314938,
0.07697808742523193,
-0.02129480056464672,
-0.023769089952111244,
0.013286149129271507,
-0.04272104427218437,
-0.020620739087462425,
0.010323666967451572,
-0.020418519154191017,
-0.00717991404235363,
-0.06566713750362396,
0.02127467654645443,
-0.028367841616272926,
-0.009842250496149063,
-0.01041781809180975,
-0.021345531567931175,
-0.014881898649036884,
0.05040790140628815,
0.016844475641846657,
0.003498783567920327,
-0.007289862725883722,
-0.015840401872992516,
-0.024300923570990562,
-0.0772022008895874,
0.03628947585821152,
-0.001802130718715489,
-0.013008490204811096,
-0.07092448323965073,
-0.016542598605155945,
-0.004181142896413803,
0.04586847499012947,
0.06477698683738708,
-0.0017518106615170836,
-0.02279564179480076,
0.009450898505747318,
0.02779286727309227,
0.05410308018326759,
-0.025123663246631622,
0.00835892278701067,
0.012565022334456444,
-0.013593737967312336,
0.03891107067465782,
-0.027692362666130066,
-0.03971921280026436,
0.043684761971235275,
0.031887199729681015,
-0.02091572992503643,
0.07768934220075607,
0.024536196142435074,
-0.03631235659122467,
0.02385668270289898,
0.01868780329823494,
-0.02440020442008972,
0.0555274523794651,
0.002464143792167306,
0.012989455834031105,
0.03672100231051445,
-0.010954104363918304,
-0.03695555403828621,
-0.012949572876095772,
-0.02018476463854313,
-0.025426361709833145,
0.00263723311945796,
-0.039496611803770065,
0.016922088339924812,
-0.045827582478523254,
-0.008420715108513832,
0.04469244182109833,
0.005989076104015112,
-0.021273920312523842,
0.05277855321764946,
0.017891276627779007,
0.026616524904966354,
0.005882840603590012,
-0.0029588043689727783,
-0.010421174578368664,
-0.010491782799363136,
0.028543241322040558,
0.014879942871630192,
0.050877172499895096,
0.001276989933103323,
-0.00974564254283905,
0.01747315563261509,
0.0017562606371939182,
0.00989585742354393,
-0.0027683039661496878,
0.06669796258211136,
0.015766140073537827,
0.012401148676872253,
0.014792978763580322,
0.0008866079151630402,
0.004745463375002146,
0.05885287746787071,
-0.0014912906335666776,
0.060898520052433014,
-0.004933502990752459,
0.016339341178536415,
-0.03574008494615555,
-0.03283195197582245,
-0.05006013438105583,
0.042840857058763504,
0.04213568568229675,
0.01755298487842083,
0.008103564381599426,
-0.009161285124719143,
0.0011375361355021596,
-0.018531639128923416,
0.014632930979132652,
-0.05108846351504326,
0.01399875059723854,
-0.009668532758951187,
0.011388590559363365,
0.01953628472983837,
-0.017576662823557854,
0.010628592222929,
-0.018731923773884773,
0.02011902816593647,
0.0053907413966953754,
0.05368896573781967,
-0.039528410881757736,
0.01917998306453228,
-0.0694759264588356,
0.02794911339879036,
-0.10333326458930969,
0.005949856713414192,
-0.012034544721245766,
0.05257229506969452,
-0.034242868423461914,
-0.012598038651049137
] |
<p>I've been reading a lot but cannot find an example of 2D Gaussian wave packet moving in a particular direction. I've done some of the math myself, in a 1D case, and then kind of guessed the generalization to 2D. I'd be thrilled if someone could confirm or correct the expression. This is supposed to model a free particle moving in the x axis with a fairly definite momentum:</p>
<p>$\Psi (x,y,t) = \frac{1}{\sqrt{\alpha + i\beta t}} \exp \left[-\dfrac{(x-vt)^2+y^2}{4(\alpha + i\beta t)} + i(kx-\omega t) \right] $</p>
<p>The wave function is not normalized and the constants $\alpha$ and $\beta$ are not relevant in my opinion, I could add how they relate with mass and $\hbar$ if someone thinks they're necessary. </p>
<p>Also I would like to add to the question what's the relation between $k$, $\omega$ and $v$ and what does each one represent. My guess is that $v$ is the group velocity, and you'd get the average momentum from the fourier transform of that wave function, but I'm not sure what's $k$ then. Is there any need at all to add the phasor $e^{i(kx-wt)}$, does it change anything?? The packet is going to move anyway and the amplitude is not going to change unless you add other wave functions. </p>
<p>Thank you very much!</p>
| 10,751 |
[
0.022356916218996048,
-0.008126913569867611,
0.021197251975536346,
-0.022057201713323593,
0.049775123596191406,
-0.03229769691824913,
-0.05313411355018616,
-0.06444098055362701,
0.01432971004396677,
-0.04021158069372177,
0.025594238191843033,
0.046344093978405,
0.05877789109945297,
0.007986268028616905,
-0.02587110549211502,
0.048121627420186996,
-0.013034084811806679,
-0.039091069251298904,
-0.005523406434804201,
-0.06686205416917801,
-0.023456064984202385,
0.01976197212934494,
-0.00051291030831635,
0.00019396876450628042,
-0.0166409220546484,
0.04719933867454529,
0.01165856048464775,
-0.005655338056385517,
0.032904159277677536,
0.03153735026717186,
-0.003316191490739584,
-0.01294312346726656,
0.006299009080976248,
0.042846955358982086,
-0.013276191428303719,
-0.008724509738385677,
-0.06113915517926216,
-0.06370957940816879,
0.012492693029344082,
0.04260833188891411,
-0.033571068197488785,
0.00202958844602108,
-0.008852077648043633,
0.015742093324661255,
-0.0031257462687790394,
0.03317524492740631,
0.04823954030871391,
-0.0029395839665085077,
0.057196442037820816,
-0.06138725206255913,
0.05751633271574974,
-0.02359333261847496,
0.02506999298930168,
-0.01765337958931923,
0.007396699395030737,
0.00015851351781748235,
0.05941585823893547,
0.06151443347334862,
0.021738840267062187,
-0.050170738250017166,
-0.010712266899645329,
-0.007624262943863869,
-0.012745212763547897,
-0.016553711146116257,
-0.015055366791784763,
-0.03241262957453728,
0.011409120634198189,
-0.01625845953822136,
-0.010964560322463512,
-0.0033131998497992754,
0.056827154010534286,
0.029099024832248688,
0.0218768659979105,
-0.031178543344140053,
-0.008217713795602322,
0.018339581787586212,
-0.011423032730817795,
0.052176494151353836,
-0.0008075617370195687,
-0.007312789559364319,
-0.003846389940008521,
-0.023359326645731926,
-0.0012128660455346107,
0.006690911948680878,
-0.02704797498881817,
0.018172195181250572,
0.07672671228647232,
-0.012835396453738213,
-0.0010060090571641922,
0.05069614574313164,
-0.02916242927312851,
0.04143908619880676,
0.02509455941617489,
0.003160499967634678,
-0.008548246696591377,
0.014740269631147385,
0.01940007507801056,
0.05430656298995018,
0.003936318680644035,
0.0025667590089142323,
0.012716179713606834,
-0.047284167259931564,
0.021447602659463882,
0.09083805233240128,
-0.0263771153986454,
0.014771997928619385,
-0.02477297931909561,
-0.007807111833244562,
-0.007355856243520975,
-0.05463653430342674,
-0.07085701078176498,
0.007703036535531282,
0.00705410772934556,
0.01875140331685543,
-0.0074547636322677135,
-0.02763468585908413,
-0.008539536967873573,
-0.0029832185246050358,
0.02905271202325821,
0.08796942234039307,
0.06201232969760895,
-0.03369547426700592,
0.034545253962278366,
-0.0041816383600234985,
-0.06050186976790428,
0.030873918905854225,
-0.0056260921992361546,
-0.013383348472416401,
-0.04862777888774872,
0.025463439524173737,
0.02125459536910057,
-0.012074247933924198,
0.04632669314742088,
-0.02086573652923107,
0.023847363889217377,
-0.03521816432476044,
-0.08772623538970947,
-0.04603949189186096,
0.04575776681303978,
-0.016563212499022484,
-0.0027455436065793037,
-0.09685294330120087,
-0.02612939476966858,
0.03166816011071205,
0.09544110298156738,
-0.03862372040748596,
0.021997081115841866,
-0.012717196717858315,
0.031363971531391144,
0.008550439961254597,
-0.028969286009669304,
-0.04095994681119919,
-0.02858581207692623,
-0.03723147138953209,
-0.014336914755403996,
-0.041415318846702576,
0.009842673316597939,
0.04425135627388954,
-0.025287877768278122,
0.03656982630491257,
0.06613241136074066,
-0.011154841631650925,
-0.008084319531917572,
0.014209882356226444,
0.001626108307391405,
-0.052866388112306595,
0.06729176640510559,
0.04686298221349716,
0.009351575747132301,
-0.014065141789615154,
-0.01123922411352396,
0.014800159260630608,
-0.01622752659022808,
0.001668210607022047,
0.019952617585659027,
-0.006364071276038885,
-0.02604389563202858,
-0.034631602466106415,
0.016723008826375008,
-0.03338894248008728,
-0.006841444876044989,
-0.05538315325975418,
-0.020103495568037033,
0.01878235675394535,
0.0059583755210042,
0.017350252717733383,
-0.0025591831654310226,
0.0031832309905439615,
0.000780772534199059,
-0.04406680911779404,
-0.02080305851995945,
-0.040723178535699844,
0.04042482748627663,
-0.014663591049611568,
0.0027331230230629444,
0.023840991780161858,
0.004450981970876455,
0.04815066233277321,
0.024553731083869934,
-0.03369705006480217,
0.008027918636798859,
0.013167822733521461,
0.011836227029561996,
-0.042962994426488876,
0.003016326343640685,
0.03720400854945183,
-0.005812272895127535,
-0.00011557977268239483,
0.02804052270948887,
-0.037588056176900864,
0.007110509555786848,
-0.012139204889535904,
-0.007393172476440668,
0.006809660699218512,
0.0032811062410473824,
0.0014549073530361056,
0.01216372475028038,
-0.013494756072759628,
-0.00005965953096165322,
-0.0246694665402174,
-0.058142393827438354,
0.06068269535899162,
0.07719633728265762,
0.013017400167882442,
-0.012303818948566914,
0.053406741470098495,
-0.002219313057139516,
0.0218106210231781,
-0.0009330544271506369,
-0.04496997594833374,
-0.030618442222476006,
-0.0029558709356933832,
0.02057267539203167,
0.027904901653528214,
-0.03888148069381714,
-0.006615562830120325,
0.02304268069565296,
0.016911474987864494,
0.031058913096785545,
-0.0051960088312625885,
0.01659313216805458,
-0.019918862730264664,
0.006014925893396139,
-0.02225124090909958,
0.0020839034114032984,
-0.01581679843366146,
0.0455348901450634,
0.005658433772623539,
0.02107052132487297,
0.019859330728650093,
-0.06338194012641907,
0.011694918386638165,
-0.014045804738998413,
0.008368300274014473,
-0.02950584888458252,
-0.04522773623466492,
0.0330689400434494,
-0.013560263440012932,
0.03529513254761696,
0.04825645685195923,
-0.012756701558828354,
-0.003002897137776017,
-0.04325185343623161,
-0.02962755225598812,
0.008784121833741665,
-0.01147651020437479,
-0.0025345038156956434,
-0.013639621436595917,
0.01360961701720953,
-0.030995391309261322,
0.012059411033987999,
-0.010908394120633602,
0.008147821761667728,
-0.012927762232720852,
0.007564426399767399,
0.028064420446753502,
0.01986122317612171,
0.04938438907265663,
-0.032094188034534454,
-0.052582185715436935,
0.026129288598895073,
0.011620956473052502,
0.031963977962732315,
0.021488385275006294,
-0.04745073243975639,
0.018252583220601082,
-0.045918773859739304,
-0.01497474405914545,
0.041896719485521317,
-0.03417866304516792,
-0.03546777740120888,
0.001617877627722919,
-0.014477016404271126,
-0.07740114629268646,
0.006824582815170288,
-0.00988577026873827,
0.022305350750684738,
-0.0556652806699276,
-0.0005892409244552255,
0.012666835449635983,
0.0004284060560166836,
-0.010732380673289299,
0.04308900609612465,
-0.013232249766588211,
-0.03427021577954292,
-0.022297844290733337,
-0.0030421153642237186,
-0.0007947661215439439,
-0.017060406506061554,
0.027069436386227608,
0.007147750351577997,
-0.018230924382805824,
-0.01388324424624443,
-0.024416575208306313,
-0.038056958466768265,
0.04638035222887993,
-0.002590722870081663,
0.038876552134752274,
0.012252427637577057,
-0.018552104011178017,
0.07676635682582855,
0.029097044840455055,
-0.0059526339173316956,
0.002711634850129485,
0.004208562429994345,
-0.006952866446226835,
-0.04259113594889641,
0.019935494288802147,
0.0387641005218029,
0.02224777452647686,
0.0543087013065815,
0.009344004094600677,
0.00225382880307734,
0.04490334540605545,
-0.041613444685935974,
-0.0335322767496109,
0.04300167039036751,
-0.007687550038099289,
0.026104291900992393,
0.05146220698952675,
0.009707832708954811,
-0.017008354887366295,
0.013330954127013683,
0.008144811727106571,
-0.018961317837238312,
0.03343278169631958,
-0.05215629190206528,
0.05330107361078262,
0.018506016582250595,
-0.010840406641364098,
-0.0013438875321298838,
0.03972075134515762,
0.0013080732896924019,
-0.02554307132959366,
-0.03329763934016228,
0.026833824813365936,
0.036515165120363235,
0.01640939526259899,
0.032940573990345,
0.01999848149716854,
0.0036139548756182194,
-0.008995246142148972,
-0.03029479831457138,
0.009113281033933163,
0.02332768402993679,
0.030039284378290176,
0.021850189194083214,
-0.07110661268234253,
0.02800736203789711,
0.01890510506927967,
0.00683621084317565,
-0.007278382778167725,
-0.0388764925301075,
-0.02895052544772625,
-0.03998809680342674,
-0.02995350770652294,
-0.028464434668421745,
0.021840088069438934,
0.025474222376942635,
0.052455250173807144,
0.04971163719892502,
0.003940743859857321,
0.01698550023138523,
0.021152274683117867,
-0.08143751323223114,
-0.019898546859622,
-0.03374180942773819,
-0.010307656601071358,
0.006878804415464401,
-0.007700471207499504,
0.00347209838218987,
-0.012850630097091198,
-0.03707161173224449,
-0.021661745384335518,
-0.030883939936757088,
-0.061891037970781326,
0.020594777539372444,
-0.017782410606741905,
-0.01654905080795288,
-0.010601061396300793,
0.029088234528899193,
0.05221102014183998,
0.004424424842000008,
-0.0316857174038887,
0.03368094563484192,
-0.038470037281513214,
0.01636265590786934,
-0.01589602418243885,
-0.0014280955074355006,
0.008938011713325977,
0.009878832846879959,
0.0472111813724041,
-0.0020051307510584593,
0.006472783163189888,
-0.0005335422465577722,
-0.007971840910613537,
0.06513988971710205,
0.0018349135061725974,
-0.020845284685492516,
0.02644156478345394,
-0.036329712718725204,
0.01675003580749035,
0.0016470382688567042,
0.06273210793733597,
0.01664414070546627,
-0.006302290596067905,
0.03347330912947655,
0.007398822344839573,
-0.019158942624926567,
0.012555764988064766,
0.025737717747688293,
-0.007603789214044809,
0.019352227449417114,
-0.06216123700141907,
-0.00851491466164589,
0.010176045820116997,
-0.030081668868660927,
0.00939573161303997,
-0.03928331658244133,
-0.022985225543379784,
0.03026166744530201,
0.012227404862642288,
0.018204690888524055,
0.0018874730449169874,
-0.014895305968821049,
-0.030789421871304512,
0.005321927834302187,
0.0030087106861174107,
-0.0073902602307498455,
0.00652715191245079,
0.028476716950535774,
-0.0077223507687449455,
-0.0002450787869747728,
0.034526705741882324,
-0.05331452563405037,
-0.007337603252381086,
0.028807390481233597,
0.05267688259482384,
0.03769047558307648,
-0.014773627743124962,
-0.023006949573755264,
-0.036126311868429184,
0.06284155696630478,
-0.0059675006195902824,
0.03444167226552963,
0.018088435754179955,
-0.014591271057724953,
-0.011356858536601067,
-0.025817666202783585,
-0.04305087402462959,
-0.020817792043089867,
-0.0018737526843324304,
-0.010951435193419456,
-0.028756530955433846,
-0.033331967890262604,
-0.020399481058120728,
0.0061083221808075905,
0.020146990194916725,
0.04513300955295563,
-0.007857457734644413,
-0.03630848601460457,
-0.024103576317429543,
0.03239540755748749,
-0.027646290138363838,
-0.08743765950202942,
-0.03591807931661606,
0.024438856169581413,
0.0006089442176744342,
0.04444718360900879,
-0.02852959744632244,
-0.029973993077874184,
0.006451485678553581,
0.01690024323761463,
-0.029148515313863754,
0.017520295456051826,
0.00676365289837122,
0.06890833377838135,
0.04110000655055046,
-0.0046523744240403175,
0.06295152753591537,
0.052309852093458176,
-0.051224611699581146,
-0.0011053136549890041,
-0.012306908145546913,
0.06925573945045471,
-0.014348339289426804,
0.03505134955048561,
-0.05244402587413788,
-0.006550486199557781,
-0.038388196378946304,
0.04371834546327591,
0.00745459645986557,
0.03297082707285881,
-0.011187044903635979,
-0.02587255649268627,
0.006601586937904358,
0.044983334839344025,
-0.043492451310157776,
0.0002098508266499266,
-0.02898867055773735,
0.03142119199037552,
0.004268335178494453,
-0.04787295684218407,
-0.0008887246949598193,
-0.0008307662792503834,
0.02302929386496544,
0.046129535883665085,
0.013701572082936764,
-0.016897350549697876,
-0.04302966594696045,
0.0019553254824131727,
0.014354725368320942,
-0.07905373722314835,
0.04309532046318054,
-0.010804956778883934,
-0.003311903215944767,
-0.010464035905897617,
-0.028696728870272636,
-0.034125640988349915,
-0.0009681079536676407,
-0.011464527808129787,
0.015745878219604492,
-0.0059333061799407005,
-0.010287517681717873,
0.0033653464633971453,
0.04080256074666977,
-0.08731198310852051,
-0.05640925467014313,
0.021103372797369957,
-0.034790996462106705,
0.003914029337465763,
-0.03458799794316292,
0.0012686632107943296,
-0.038296107202768326,
-0.02714233286678791,
0.019863858819007874,
0.049426011741161346,
0.009238442406058311,
-0.01895817741751671,
0.016237430274486542,
0.008426242507994175,
0.04945226013660431,
0.035407308489084244,
-0.026588965207338333,
0.020671052858233452,
-0.03383913263678551,
0.00011014012125087902,
-0.011632837355136871,
0.06640101969242096,
-0.030739575624465942,
-0.009497060440480709,
-0.04830625280737877,
-0.015185816213488579,
0.034473568201065063,
-0.03821716457605362,
-0.056607529520988464,
0.017750747501850128,
0.03188508376479149,
0.012877780944108963,
-0.03807589039206505,
-0.01911100745201111,
-0.026249468326568604,
0.00800376757979393,
0.017814619466662407,
-0.011226484552025795,
-0.04337397590279579,
-0.035369399935007095,
0.007025854662060738,
0.00572178652510047,
-0.023465197533369064,
0.014814616180956364,
0.02873987704515457,
0.002714390167966485,
0.015284087508916855,
0.011686905287206173,
-0.007455800194293261,
-0.007921956479549408,
0.005686456337571144,
-0.019236113876104355,
0.03511436656117439,
0.01220797374844551,
-0.02073352411389351,
-0.027561133727431297,
-0.07360254973173141,
0.000864204834215343,
0.09010354429483414,
-0.033177319914102554,
0.0603051483631134,
0.002232968807220459,
0.02181202545762062,
-0.01073811948299408,
0.025464681908488274,
0.019984109327197075,
0.010385501198470592,
-0.049558643251657486,
0.015482919290661812,
-0.009378361515700817,
-0.003210625611245632,
-0.008232229389250278,
0.03365103900432587,
-0.011307992041110992,
-0.027910752221941948,
0.04785813391208649,
0.022423671558499336,
-0.009130612947046757,
-0.012391636148095131,
-0.033389732241630554,
0.04584138095378876,
-0.002401972422376275,
0.03446659818291664,
-0.024926861748099327,
-0.011622456833720207,
0.04319673776626587,
0.03621378540992737,
-0.01853422075510025,
-0.051793795078992844,
0.014639195054769516,
-0.04054481163620949,
0.005238846875727177,
0.047178417444229126,
-0.0086788609623909,
0.013192800804972649,
0.0038166381418704987,
0.029777629300951958,
0.033550433814525604,
0.011156301014125347,
-0.016422078013420105,
-0.0508275181055069,
0.005661871284246445,
-0.028539301827549934,
-0.03719296306371689,
0.026262376457452774,
0.00922724325209856,
-0.0217656921595335,
0.012253171764314175,
-0.03803524747490883,
0.05498575046658516,
0.02808050811290741,
0.018636927008628845,
0.005752053577452898,
0.08262158930301666,
-0.010875830426812172,
-0.0011438876390457153,
-0.02585841529071331,
-0.010200691409409046,
0.12148843705654144,
0.0632973164319992,
0.06058837100863457,
-0.03910587355494499,
0.01688348315656185,
-0.015655240043997765,
0.001766679808497429,
-0.03284784406423569,
0.011010388843715191,
-0.009138702414929867,
-0.010676901787519455,
-0.015822377055883408,
0.08363939076662064,
0.011272218078374863,
-0.0014850454172119498,
0.05073090270161629,
-0.04208699241280556,
-0.03229744732379913,
0.0241398923099041,
-0.037102434784173965,
0.014981199987232685,
0.02749735862016678,
-0.03510772064328194,
0.03024539165198803,
-0.036586638540029526,
-0.01783263497054577,
-0.03876982256770134,
-0.0331430584192276,
0.049731217324733734,
0.0075202095322310925,
-0.040312666445970535,
0.010278018191456795,
0.020188042894005775,
-0.01592809148132801,
0.009962941519916058,
0.03932228311896324,
0.0031883143819868565,
-0.019061924889683723,
0.037694040685892105,
0.01258879154920578,
0.009346949867904186,
-0.008064089342951775,
0.050561100244522095,
-0.011020610108971596,
-0.004688641522079706,
-0.02753789909183979,
-0.03352023661136627,
0.08367698639631271,
-0.006897593382745981,
-0.00431597838178277,
0.03198368102312088,
-0.015042644925415516,
0.007667784113436937,
-0.08952376246452332,
0.006395077332854271,
-0.008988268673419952,
0.09142275154590607,
0.0029669497162103653,
0.02996322326362133,
-0.022731563076376915,
0.027771154418587685,
0.007318662013858557,
0.025361239910125732,
-0.010419275611639023,
-0.019947227090597153,
-0.0033468278124928474,
0.007335139438509941,
0.04956245422363281,
-0.0029872520826756954,
-0.025237496942281723,
0.001707479590550065,
-0.0006801750278100371,
-0.077753946185112,
-0.02852964773774147,
0.004217888228595257,
0.001978748245164752,
0.027649182826280594,
-0.0206246729940176,
-0.01755927875638008,
-0.026962047442793846,
-0.08967038244009018,
-0.018716733902692795,
0.0027385384310036898,
-0.0013915677554905415,
0.024260355159640312,
-0.005890204571187496,
0.03093835338950157,
0.03075147420167923,
-0.04707486182451248,
0.015470298007130623,
0.002596780890598893,
0.04625526815652847,
0.01882837899029255,
-0.04145007207989693,
-0.04040073603391647,
0.0326571986079216,
-0.025619354099035263,
0.0006998083554208279,
-0.010441153310239315,
0.00788381788879633,
0.00432546203956008,
-0.014482023194432259,
-0.0010680684354156256,
0.03757414594292641,
-0.043515004217624664,
-0.0075148907490074635,
-0.005704027600586414,
-0.05269794166088104,
0.005870636086910963,
0.030474694445729256,
0.025261634960770607,
-0.022801745682954788,
-0.006722312420606613,
-0.014831433072686195,
-0.0021076281554996967,
-0.010170194320380688,
-0.015416857786476612,
-0.037783846259117126,
-0.0017163539305329323,
-0.038959115743637085,
0.02606823854148388,
-0.007318499498069286,
0.006220641080290079,
0.0022665192373096943,
0.027422990649938583,
-0.012109475210309029,
0.00025606362032704055,
-0.0005164226749911904,
0.00930454395711422,
-0.016689438372850418,
0.00482331495732069,
0.041907522827386856,
0.03595665842294693,
0.014943396672606468,
0.03291556239128113,
-0.019719872623682022,
-0.018656490370631218,
0.003498158184811473,
0.0022860546596348286,
-0.008938463404774666,
0.022957272827625275,
-0.026006322354078293,
-0.009100738912820816,
0.05085168778896332,
0.006483170669525862,
0.014665259048342705,
0.028495008125901222,
-0.008054829202592373,
-0.022198302671313286,
0.04957675561308861,
-0.01582980901002884,
-0.010352875106036663,
0.013265370391309261,
-0.07111280411481857,
-0.013747276738286018,
-0.048748236149549484,
0.0048068128526210785,
0.026671461760997772,
0.0018923226743936539,
0.036161478608846664,
-0.001412181300111115,
-0.028165725991129875,
0.011424969881772995,
0.0028718840330839157,
-0.009293477982282639,
0.017178958281874657,
0.051596950739622116,
-0.018615644425153732,
0.04928828775882721,
0.03741907328367233,
-0.022777313366532326,
0.017700307071208954,
-0.0012189502594992518,
0.010237528011202812,
-0.07942499965429306,
0.013411377556622028,
0.021291153505444527,
0.03780577704310417,
0.0859706848859787,
-0.05400974303483963,
0.019046448171138763,
0.02396380715072155,
-0.06834359467029572,
0.03716340661048889,
-0.019647149369120598,
0.00040406337939202785,
-0.0439370833337307,
0.013309888541698456,
-0.0326019823551178,
0.033721618354320526,
0.0036977811250835657,
0.04646456241607666,
0.031002921983599663,
0.00860088225454092,
0.016401641070842743,
-0.04961464926600456,
0.028629200533032417,
0.022738512605428696,
0.022110771387815475,
-0.003956245724111795,
0.04221482202410698,
-0.013298570178449154,
-0.04367370903491974,
0.014842207543551922,
-0.01666640117764473,
0.02444993332028389,
-0.03695058822631836,
0.03758031874895096,
-0.011148901656270027,
0.05897154659032822,
0.009163226932287216,
0.00323898415081203,
0.021584689617156982,
-0.011994775384664536,
0.02116379514336586,
0.007766883820295334,
0.027211368083953857,
-0.0009473275858908892,
-0.009692700579762459,
-0.05010472983121872,
0.008342677727341652,
0.05153927952051163,
-0.007132770027965307,
-0.007892818190157413,
-0.017274636775255203,
-0.018418753519654274,
0.011296266689896584,
-0.018302878364920616,
0.019137009978294373,
-0.05814662203192711,
-0.010483482852578163,
-0.0018603248754516244,
0.002136882860213518,
-0.006003217305988073,
-0.020632822066545486,
-0.01802395097911358,
-0.048422202467918396,
0.012373986653983593,
0.015491005964577198,
-0.013308102265000343,
-0.04996765777468681,
-0.02813773974776268,
-0.012207183986902237,
0.03888433799147606,
0.026556309312582016,
-0.00036080347490496933,
-0.01736784167587757,
0.017581138759851456,
-0.017400706186890602,
0.051049958914518356,
-0.03131942078471184,
-0.005951091647148132,
-0.018722645938396454,
-0.04473752900958061,
0.05164428427815437,
0.03499128669500351,
-0.04181985929608345,
0.024318622425198555,
-0.017472129315137863,
0.0317811518907547,
0.019894827157258987,
0.05873747169971466,
-0.01440941821783781,
-0.02435794286429882,
0.014330360107123852,
-0.02281341515481472,
-0.020761357620358467,
-0.044184111058712006,
-0.02089460752904415,
-0.03927562013268471,
-0.04154224693775177,
-0.005326213780790567,
-0.00032585900044068694,
-0.024740951135754585,
0.059400931000709534,
0.027706624940037727,
0.00291873374953866,
0.014031307771801949,
-0.014346720650792122,
-0.04310913011431694,
0.014202622696757317,
0.006584052462130785,
-0.016607170924544334,
0.06337626278400421,
0.00651329942047596,
-0.013577243313193321,
0.028266772627830505,
-0.056741442531347275,
-0.007074904162436724,
0.02599041350185871,
-0.014666174538433552,
-0.03779667988419533,
-0.013308428227901459,
0.002812435384839773,
0.03621557727456093,
-0.060225676745176315,
-0.0026447377167642117,
0.038257528096437454,
-0.03796697035431862,
0.013714682310819626,
0.0843440592288971,
0.03595903888344765,
0.02712949924170971,
0.03215090185403824,
0.025300193578004837,
0.01532996166497469,
-0.0026683092582970858,
0.02839074842631817,
0.021293841302394867,
0.023841289803385735,
0.01752910204231739,
0.02094370871782303,
0.03396964073181152,
-0.022149059921503067,
0.035935673862695694,
0.010780388489365578,
-0.017078867182135582,
-0.04287460073828697,
0.003580566495656967,
0.020392801612615585,
-0.036242879927158356,
0.008077233098447323,
0.02023029513657093,
-0.003264232538640499,
0.05157660320401192,
-0.03770683333277702,
-0.03426681086421013,
0.00582492770627141,
-0.008330980315804482,
-0.010288817808032036,
0.009940861724317074,
0.03221328556537628,
0.01491421926766634,
0.003965557552874088,
-0.0160522498190403,
-0.017096294090151787,
-0.03570055961608887,
-0.011076870374381542,
-0.052057359367609024,
-0.008666186593472958,
-0.0005656387656927109,
-0.03074353188276291,
0.02360723167657852,
-0.015822216868400574,
-0.014025767333805561,
-0.0012385720619931817,
-0.008321854285895824,
0.048564404249191284,
-0.005876843351870775,
0.00675211101770401,
0.02091197483241558,
-0.006447363179177046,
0.06813784688711166,
-0.05578755959868431,
0.04251086711883545,
-0.020996268838644028,
0.025902647525072098,
0.05069391429424286,
-0.0041484651155769825
] |
<p>Me and my friend, both many years from learning string theory, had a recent debate about it anyway. He said he already partially discounts it because after learning waves, he believes any function, and thus any kind of physical process can be created through a superposition of an infinite sum of waves. Since string theory to our understanding is made up of primarily oscillating strings, he argues that it is a mathematical necessity for string theory to create equations for the physical world, regardless of whether the theory actually is "true" or not. </p>
<p>My understanding is that Fourier analysis can only create arbitrary periodic functions, can it in principal create any real world field or particle, etc.? Besides this, I argued that this might be a pointless question anyway, as if we can create a perfect model of the universe with string theory, then the question of whether the universe is really made of oscillating strings is more of a philosophical question that may not mean anything at all.</p>
<p>Through reading Brian Green's books I know that M-theory at least incorporates more than just strings, but I have no clue as to how things such as branes work, can his argument even apply to these other fundamental objects in string theory?</p>
<p>So my question is, is Fourier Analysis essentially what String Theory is? And if so, does that make it any less of a true physical theory of the universe?</p>
| 10,752 |
[
0.021591126918792725,
0.007355735637247562,
-0.0016259910771623254,
-0.0988871157169342,
0.05123886838555336,
0.03280175104737282,
-0.027504444122314453,
-0.04428141564130783,
0.019643045961856842,
-0.01632559858262539,
-0.018458381295204163,
-0.005903293844312429,
0.02812654711306095,
0.008437936194241047,
0.00012512021930888295,
0.017785659059882164,
-0.033013686537742615,
-0.00485045462846756,
-0.0587422251701355,
-0.007919267751276493,
-0.00856960192322731,
0.056951433420181274,
0.03991520032286644,
-0.010983920656144619,
-0.046587083488702774,
0.02880423329770565,
0.005983262788504362,
0.03609008342027664,
0.033159349113702774,
0.024402230978012085,
0.00135725736618042,
-0.01292604673653841,
0.011065052822232246,
0.05428681895136833,
0.02732294611632824,
0.015044168569147587,
-0.047310009598731995,
0.0060364254750311375,
0.0017697233706712723,
-0.022220579907298088,
-0.026853855699300766,
0.0013507700059562922,
-0.0016118097119033337,
0.023845253512263298,
-0.032442037016153336,
0.009522584266960621,
0.011151607148349285,
-0.016019759699702263,
0.04296758025884628,
-0.02372315153479576,
0.06281411647796631,
-0.007539724465459585,
-0.01205065194517374,
0.022143743932247162,
0.004792908672243357,
-0.008078545331954956,
0.10784976184368134,
0.048769570887088776,
-0.002032160758972168,
-0.04938782751560211,
-0.0442686527967453,
0.014114455319941044,
-0.005321916192770004,
-0.024800168350338936,
-0.0193596500903368,
0.037051815539598465,
0.018331369385123253,
0.004691003821790218,
0.014795633964240551,
-0.013293415307998657,
0.010889334604144096,
0.04712649807333946,
0.019243508577346802,
-0.00375415594317019,
-0.01784472167491913,
0.006939062383025885,
0.014723381027579308,
-0.02638123370707035,
0.009462009184062481,
0.02175516076385975,
-0.017966732382774353,
0.002016219310462475,
0.01537459809333086,
0.04394540563225746,
0.04689925163984299,
-0.0034015581477433443,
0.06873617321252823,
-0.001521271769888699,
0.0009162690839730203,
0.033822912722826004,
0.008518002927303314,
-0.013407516293227673,
0.053762130439281464,
-0.012749271467328072,
-0.04787294566631317,
0.039092160761356354,
-0.00270706694573164,
0.04319978505373001,
0.0040149507112801075,
-0.029773421585559845,
0.010478408075869083,
-0.013306030072271824,
0.03302156925201416,
0.06752723455429077,
0.016300244256854057,
-0.039212945848703384,
-0.016609814018011093,
0.02162100188434124,
-0.03621697053313255,
-0.023999828845262527,
-0.0359463170170784,
0.010944428853690624,
0.0025453432463109493,
0.017223723232746124,
0.002463191980496049,
-0.0010077519109472632,
0.03440104424953461,
-0.0015209588455036283,
0.08075761049985886,
0.1303018182516098,
0.042234353721141815,
-0.02535990998148918,
0.013581318780779839,
0.0007182302651926875,
-0.07992620021104813,
-0.0026454192120581865,
-0.0075708371587097645,
-0.005861402023583651,
-0.035416919738054276,
0.03749239444732666,
-0.0006553484126925468,
-0.0012178858742117882,
0.025860369205474854,
-0.012455672957003117,
0.0431220605969429,
-0.04094148427248001,
-0.10780003666877747,
-0.055832669138908386,
0.04318518936634064,
0.002147475490346551,
-0.03423355892300606,
-0.02951757237315178,
-0.030189277604222298,
0.027273250743746758,
0.0780882015824318,
-0.0067983814515173435,
-0.009004025720059872,
0.015884200111031532,
0.05391780659556389,
0.0026657618582248688,
-0.04256819561123848,
-0.04027105122804642,
-0.021821293979883194,
-0.04088869318366051,
-0.01140265166759491,
-0.027101591229438782,
0.017973527312278748,
0.04284672439098358,
-0.017006926238536835,
-0.027321940287947655,
0.09435316175222397,
-0.003199785714969039,
-0.004258477129042149,
0.007068917620927095,
-0.03274623304605484,
-0.03261211887001991,
0.024857381358742714,
0.02116970717906952,
0.006925736088305712,
0.022924678400158882,
0.0008508067694492638,
-0.010622640140354633,
0.024146046489477158,
0.023443883284926414,
-0.008226490579545498,
-0.0436721034348011,
-0.02431049570441246,
0.005173872224986553,
0.022999338805675507,
-0.02257465198636055,
-0.010555325075984001,
0.004408783745020628,
0.0066832308657467365,
0.0033841836266219616,
-0.001019461895339191,
0.038358286023139954,
-0.0006575520383194089,
-0.021704228594899178,
-0.008873212151229382,
-0.04154442995786667,
-0.006676387041807175,
-0.058386921882629395,
0.009189912118017673,
-0.015982137992978096,
0.008253766223788261,
0.0022991609293967485,
0.022492650896310806,
0.020379887893795967,
-0.03833971172571182,
-0.05430064722895622,
0.02043573558330536,
0.0391206368803978,
0.017898553982377052,
-0.0003316258080303669,
0.01306153368204832,
0.06079607084393501,
0.036310095340013504,
-0.0021178300958126783,
0.0049151224084198475,
-0.014280853793025017,
-0.05281716212630272,
0.018785513937473297,
-0.0273347869515419,
0.029588326811790466,
-0.005652477499097586,
0.018860187381505966,
0.04456791281700134,
-0.009756932966411114,
-0.012061832472682,
0.04718244820833206,
-0.04941884055733681,
0.049220744520425797,
0.011735578067600727,
0.009282334707677364,
0.028041819110512733,
0.05544145032763481,
0.015728438273072243,
0.020728465169668198,
0.007662661373615265,
-0.028523197397589684,
-0.0515577457845211,
0.023678693920373917,
0.060931235551834106,
0.05807770788669586,
0.0015935692936182022,
0.022224361076951027,
0.05810842663049698,
0.03640779107809067,
0.0429832860827446,
0.042831335216760635,
-0.024725021794438362,
0.015323599800467491,
-0.01589159108698368,
-0.01395723968744278,
0.006597405299544334,
0.012491275556385517,
0.021442394703626633,
-0.0010567719582468271,
-0.009655702859163284,
0.009929274208843708,
-0.019870122894644737,
0.030647464096546173,
-0.00453147990629077,
0.022652089595794678,
0.02322736568748951,
-0.0025775879621505737,
0.00788915529847145,
-0.03168916329741478,
0.014191006310284138,
0.029488496482372284,
0.007513878867030144,
-0.014761942438781261,
-0.04743202403187752,
-0.015826690942049026,
0.007228596601635218,
-0.01345059834420681,
-0.014858311042189598,
-0.02455582469701767,
0.021454332396388054,
-0.04566594585776329,
-0.038333166390657425,
-0.0026003795210272074,
-0.01239094603806734,
-0.013904878869652748,
0.008349536918103695,
0.042040541768074036,
0.003912187647074461,
0.07562288641929626,
-0.0476972833275795,
-0.03849579766392708,
0.028001466765999794,
-0.03165706247091293,
0.013767831027507782,
-0.024854691699147224,
-0.06588704138994217,
0.015995478257536888,
-0.03616856411099434,
-0.012571929022669792,
0.03389718011021614,
-0.017637021839618683,
0.03576955571770668,
-0.011988268233835697,
-0.009280757047235966,
-0.023914793506264687,
-0.000544049427844584,
-0.028840206563472748,
0.012103233486413956,
-0.018007388338446617,
0.004330373834818602,
0.04161304980516434,
0.010148020461201668,
-0.051617708057165146,
0.03780756890773773,
-0.036329235881567,
-0.04544059932231903,
0.00849972851574421,
-0.0323827788233757,
0.03390480950474739,
-0.04847202077507973,
0.04875379055738449,
-0.026641836389899254,
-0.0733417347073555,
0.010653547011315823,
-0.04312159866094589,
-0.06580560654401779,
0.01090246718376875,
-0.021520184352993965,
0.07050391286611557,
0.010254827328026295,
-0.044118642807006836,
0.045523177832365036,
0.0366399921476841,
-0.05947622284293175,
0.01668163575232029,
0.010866611264646053,
-0.01968090981245041,
-0.03744577243924141,
0.0354447178542614,
0.022899042814970016,
-0.023489192128181458,
0.03313445299863815,
0.020218342542648315,
-0.008206270635128021,
0.019805796444416046,
0.00856580026447773,
-0.035174112766981125,
0.011936437338590622,
-0.0008956390665844083,
0.053844258189201355,
0.038771018385887146,
0.013598713092505932,
-0.01210262905806303,
0.045084595680236816,
-0.012238155119121075,
0.008833158761262894,
0.047985248267650604,
-0.02953322045505047,
0.021528547629714012,
0.015417669899761677,
0.011296634562313557,
-0.04624634236097336,
0.023121068254113197,
-0.020047534257173538,
0.005632482003420591,
-0.016955582424998283,
0.020505579188466072,
0.011062192730605602,
-0.004644232336431742,
0.008914822712540627,
-0.0040830038487911224,
0.021341022104024887,
-0.017399955540895462,
-0.016406448557972908,
0.00030683650402352214,
0.013075844384729862,
0.011126005090773106,
-0.04600941762328148,
-0.03465694189071655,
0.05086517333984375,
0.034721218049526215,
0.04355474188923836,
-0.023018186911940575,
-0.048129841685295105,
-0.009007612243294716,
-0.03764268383383751,
-0.0076537830755114555,
-0.043146975338459015,
0.02562282420694828,
0.007556520402431488,
0.06278850883245468,
-0.004903457127511501,
0.012349262833595276,
0.0054544080048799515,
-0.007226625457406044,
-0.09684199094772339,
-0.001150338095612824,
-0.009278600104153156,
-0.0057426756247878075,
-0.031846411526203156,
-0.018355529755353928,
-0.009636304341256618,
0.01306465920060873,
-0.020019106566905975,
-0.025083214044570923,
-0.037347596138715744,
-0.07933758944272995,
0.02076154388487339,
-0.03672318533062935,
-0.04394174739718437,
0.00854786578565836,
0.0005547375767491758,
0.07223723083734512,
0.0014480985701084137,
-0.00758409034460783,
0.02318529225885868,
-0.05495364964008331,
0.010898817330598831,
-0.008453954011201859,
0.02260785736143589,
0.037288833409547806,
0.012133650481700897,
0.038025230169296265,
0.030634157359600067,
-0.006432749796658754,
0.010592726059257984,
0.04271230101585388,
0.04028318449854851,
0.003769319737330079,
-0.018758241087198257,
-0.013393694534897804,
-0.03211227059364319,
-0.031187519431114197,
0.024307090789079666,
0.0550503246486187,
-0.0023316405713558197,
-0.03151129186153412,
0.035506367683410645,
-0.003645852208137512,
-0.005497280973941088,
0.07515497505664825,
0.02869349531829357,
-0.030184322968125343,
-0.053691472858190536,
-0.04318227991461754,
-0.03376193344593048,
-0.025214286521077156,
-0.03190208971500397,
0.017542624846100807,
-0.00482009956613183,
-0.028692374005913734,
0.0009488715440966189,
0.003030181396752596,
0.02604285255074501,
-0.028555046766996384,
-0.00872756540775299,
-0.018065067008137703,
-0.015588195063173771,
-0.027942001819610596,
0.022506045177578926,
0.022528164088726044,
0.0670807808637619,
0.04109901189804077,
0.016071880236268044,
-0.02579764649271965,
-0.06936495751142502,
0.010731346905231476,
0.013704665005207062,
0.018792904913425446,
0.04170393571257591,
-0.006205074489116669,
-0.049393609166145325,
-0.04165693372488022,
0.020244251936674118,
-0.03703134506940842,
0.02852637879550457,
0.011276718229055405,
0.02373800240457058,
-0.004678056575357914,
-0.027909206226468086,
0.007651215419173241,
-0.024326927959918976,
-0.020604904741048813,
0.03411043807864189,
0.016207275912165642,
-0.04104301705956459,
-0.005284882616251707,
0.030519448220729828,
0.013233916833996773,
0.01070418581366539,
-0.012616203166544437,
-0.01858983002603054,
0.005516947712749243,
0.014187829568982124,
-0.026914529502391815,
-0.0648062601685524,
0.02149263210594654,
0.028312554582953453,
-0.036302562803030014,
0.0336577370762825,
-0.006478582043200731,
-0.025609679520130157,
0.018922889605164528,
-0.017681317403912544,
-0.0014929223107174039,
0.008307620882987976,
-0.04150025174021721,
0.04458180069923401,
0.003708834294229746,
0.03822861239314079,
0.039269208908081055,
0.043974313884973526,
-0.04326239228248596,
-0.006773167755454779,
-0.0045828428119421005,
0.031992483884096146,
-0.027912696823477745,
0.027223657816648483,
-0.03967294469475746,
-0.027227718383073807,
-0.0527770072221756,
0.002726534381508827,
0.020171964541077614,
-0.05183437466621399,
0.021596714854240417,
0.020205624401569366,
-0.011936424300074577,
-0.004828714765608311,
-0.03268909826874733,
0.023996474221348763,
-0.02513113059103489,
0.009604441933333874,
0.018451858311891556,
-0.004032740369439125,
0.030916526913642883,
0.011223360896110535,
0.00839681550860405,
0.03923468664288521,
0.028735173866152763,
0.024423405528068542,
0.0037967434618622065,
-0.01667734421789646,
0.025348246097564697,
-0.01619296707212925,
0.047747593373060226,
-0.006955913733690977,
-0.012867828831076622,
0.03004065342247486,
-0.06140858307480812,
-0.024789873510599136,
-0.024219729006290436,
0.0002799376961775124,
0.020152337849140167,
0.003994181286543608,
0.004780734423547983,
0.020272688940167427,
0.01117157656699419,
-0.07488745450973511,
-0.04129375144839287,
0.003823132487013936,
0.023841984570026398,
-0.020096734166145325,
-0.014436358585953712,
0.04131198301911354,
-0.03435095399618149,
0.006046996917575598,
0.010792877525091171,
0.006405985448509455,
-0.04348708316683769,
-0.011775663122534752,
0.0014114745426923037,
0.01017583254724741,
0.03637198731303215,
0.025265945121645927,
-0.0456976555287838,
0.03908069059252739,
0.004308784380555153,
0.01621236652135849,
-0.02510824427008629,
0.04512189328670502,
-0.016693271696567535,
-0.027682891115546227,
-0.01299754623323679,
0.0024489820934832096,
-0.001409329823218286,
-0.013036731630563736,
0.0066444785334169865,
0.045767851173877716,
0.046673353761434555,
0.04167524352669716,
-0.01644500531256199,
0.01770974136888981,
-0.025757016614079475,
0.01727323979139328,
-0.01755385659635067,
0.02706175670027733,
-0.004922111518681049,
-0.02435900643467903,
-0.0013291852083057165,
-0.0031976355239748955,
0.003741091350093484,
0.050888050347566605,
0.03444535285234451,
0.0069047571159899235,
0.0018661682261154056,
0.01854817382991314,
-0.018803315237164497,
0.003994916100054979,
-0.010686483234167099,
0.026016322895884514,
-0.01617036573588848,
0.008550751954317093,
-0.01132004801183939,
-0.072838693857193,
0.0036855784710496664,
0.009327730163931847,
0.047803983092308044,
-0.0036109299398958683,
0.05740845575928688,
0.0422043576836586,
-0.005314637906849384,
-0.007936338894069195,
-0.015679098665714264,
0.002658521058037877,
0.011051549576222897,
-0.024723222479224205,
0.011152906343340874,
-0.03988514840602875,
-0.034269265830516815,
0.0364181324839592,
0.00008469870226690546,
-0.030304936692118645,
0.020111778751015663,
0.04491971805691719,
0.03376644104719162,
0.03558403253555298,
-0.002000558888539672,
-0.08107457309961319,
0.012471684254705906,
-0.02893911488354206,
0.028816919773817062,
0.03435657173395157,
0.026214199140667915,
0.018064532428979874,
0.026741404086351395,
0.019713837653398514,
-0.0011070832842960954,
-0.0012487766798585653,
-0.058199092745780945,
-0.013057610020041466,
0.00837086234241724,
0.0457356832921505,
0.04323539882898331,
-0.03965705633163452,
-0.0002258467284264043,
0.02221660315990448,
0.0243978388607502,
0.007180513348430395,
-0.055731285363435745,
-0.02866983786225319,
-0.04495185986161232,
-0.03606986999511719,
0.08692096918821335,
-0.010226653888821602,
-0.009003794752061367,
-0.0017105141887441278,
-0.02539580874145031,
0.03366776183247566,
0.010747353546321392,
0.030894767493009567,
-0.06093143671751022,
0.049380600452423096,
-0.04886329919099808,
0.014310515485703945,
-0.025829706341028214,
0.007211744319647551,
0.12226204574108124,
0.04388676583766937,
0.021161990240216255,
-0.064697265625,
-0.010849286802113056,
-0.07172954082489014,
-0.018366726115345955,
-0.014743298292160034,
0.037017952650785446,
0.00391521817073226,
-0.023780211806297302,
-0.01729755848646164,
0.06247853860259056,
-0.020761763677001,
-0.04012167081236839,
0.05105956643819809,
-0.059484656900167465,
-0.04120507091283798,
-0.015872225165367126,
-0.0004890236305072904,
0.008532191626727581,
0.0467178039252758,
-0.033922500908374786,
-0.013446575962007046,
-0.024372737854719162,
-0.01196516677737236,
-0.017827464267611504,
-0.025511572137475014,
0.029421508312225342,
0.018255118280649185,
-0.0289993267506361,
0.0030289071146398783,
0.021573221310973167,
-0.022019777446985245,
-0.0146266408264637,
-0.007691797334700823,
0.027594929561018944,
-0.0007821204490028322,
0.012282487004995346,
0.028224308043718338,
0.019413569942116737,
-0.0032271004747599363,
-0.02427063137292862,
0.011122869327664375,
-0.05401989817619324,
-0.014158857055008411,
-0.04649527743458748,
0.059815626591444016,
-0.0018941230373457074,
-0.010153447277843952,
-0.005706466734409332,
-0.001618479029275477,
0.014632397331297398,
-0.050767891108989716,
-0.010571746155619621,
-0.01065742690116167,
0.0594179593026638,
-0.01593971811234951,
-0.030142812058329582,
0.015958314761519432,
0.04174649715423584,
-0.008734378963708878,
0.009376943111419678,
-0.0037958177272230387,
-0.001971424324437976,
-0.016788985580205917,
0.0367976538836956,
0.05075344443321228,
-0.006247068755328655,
0.0002701793273445219,
-0.05671016126871109,
-0.0060300980694592,
-0.029687857255339622,
0.00876100454479456,
0.02090347744524479,
0.0633058175444603,
0.04297266900539398,
-0.000522010843269527,
0.009701093658804893,
-0.0036888602189719677,
-0.036767859011888504,
0.003099477617070079,
-0.0002514681254979223,
-0.03204041346907616,
0.0018988270312547684,
-0.001425603637471795,
0.020292576402425766,
0.0777900293469429,
-0.027435563504695892,
0.0009478295687586069,
0.013045690953731537,
0.0004696724936366081,
0.023031162098050117,
-0.05433708429336548,
-0.028197046369314194,
-0.005357217974960804,
-0.003557940013706684,
0.004236433655023575,
-0.00963249895721674,
0.02163900062441826,
0.01840694062411785,
0.019978662952780724,
0.006835803855210543,
0.06510760635137558,
-0.002008722862228751,
-0.0021301794331520796,
0.0012162718921899796,
-0.03271688520908356,
0.01257474347949028,
0.03122243471443653,
0.030174491927027702,
-0.027985472232103348,
-0.053492870181798935,
-0.0063304053619503975,
0.017137274146080017,
0.017098864540457726,
0.012424955144524574,
-0.05843169987201691,
0.010670207440853119,
0.0203438438475132,
0.013955434784293175,
-0.0813148096203804,
0.0010980265215039253,
-0.03136937692761421,
0.019547320902347565,
0.0059213233180344105,
-0.003362600225955248,
0.024254485964775085,
-0.013359790667891502,
-0.06732399016618729,
-0.0540807768702507,
0.03668034449219704,
0.009939845651388168,
-0.037465110421180725,
-0.012912648729979992,
0.027022995054721832,
0.00621597608551383,
0.014068586751818657,
0.00005356779001886025,
0.0020010960288345814,
0.056437257677316666,
-0.06112411245703697,
-0.029170533642172813,
0.029381247237324715,
-0.027127660810947418,
0.026231108233332634,
0.03175516426563263,
-0.002607411937788129,
-0.014326565898954868,
0.01568758673965931,
-0.004889336414635181,
-0.006970807444304228,
0.04856708645820618,
-0.025621777400374413,
-0.005949543323367834,
-0.008343379013240337,
0.0031757871620357037,
0.009554150514304638,
0.017717406153678894,
0.010186949744820595,
0.014232148416340351,
-0.00021710607688874006,
-0.004283973015844822,
0.006348785944283009,
-0.04704754427075386,
-0.017231088131666183,
0.0047557055950164795,
0.0010934578021988273,
-0.020025983452796936,
0.014218637719750404,
-0.010047486051917076,
0.01264374889433384,
0.01423082035034895,
-0.010764301754534245,
-0.07149018347263336,
-0.005107618402689695,
0.03054448775947094,
-0.0025554054882377386,
0.03560132905840874,
-0.01811259612441063,
-0.011653142981231213,
-0.004902707412838936,
-0.04902198165655136,
0.04484105482697487,
-0.03320536017417908,
-0.0021046078763902187,
-0.03475889191031456,
-0.021511895582079887,
-0.05111079290509224,
0.013271910138428211,
0.02586597390472889,
0.06553200632333755,
-0.014226458966732025,
0.030126340687274933,
0.01695188507437706,
0.012005934491753578,
-0.0067782411351799965,
0.0019046078668907285,
-0.03689409792423248,
0.01701797917485237,
0.08793246001005173,
-0.03428706154227257,
-0.03533126786351204,
0.02058066613972187,
0.016161365434527397,
-0.006425011437386274,
-0.03875032812356949,
0.014506392180919647,
0.03551354631781578,
0.0035796822048723698,
0.022268472239375114,
-0.03442876413464546,
0.014446447603404522,
0.020081911236047745,
0.006417939439415932,
0.02534734085202217,
-0.007164140697568655,
-0.028002969920635223,
-0.000912511779461056,
-0.07168470323085785,
-0.006567607633769512,
0.020678160712122917,
0.011517509818077087,
0.010915135964751244,
-0.007454806938767433,
0.008318331092596054,
0.005337230861186981,
0.011631188914179802,
-0.001881078933365643,
-0.04766358062624931,
0.007133539766073227,
0.016487756744027138,
0.01839754544198513,
-0.04539800435304642,
0.005223965737968683,
-0.013172757811844349,
-0.04141199588775635,
0.04009953886270523,
0.003171763848513365,
0.013401800766587257,
-0.030199721455574036,
-0.008668328635394573,
0.03977357596158981,
0.022318163886666298,
0.006015147548168898,
-0.03438524901866913,
-0.024390146136283875,
0.0340692438185215,
0.0022964992094784975,
0.036051373928785324,
-0.012673899531364441,
-0.07180951535701752,
-0.01154610887169838,
-0.06405434012413025,
0.057770855724811554,
0.009851205162703991,
0.052098892629146576,
-0.050723399966955185,
-0.033897094428539276,
0.02637515403330326,
0.007333361543715,
0.01945851370692253,
-0.01579343155026436,
-0.03291573375463486,
0.009734833613038063,
-0.033116623759269714,
0.02880590595304966,
-0.008121318183839321,
-0.007088743150234222,
-0.014320933260023594,
-0.031161483377218246,
-0.024845518171787262,
-0.024065105244517326,
-0.03354449197649956,
0.0029827712569385767,
0.023615118116140366,
0.001519079552963376,
0.022792208939790726,
-0.02800186723470688,
-0.05469099059700966,
0.05116700381040573,
0.010760338976979256,
-0.02955201268196106,
0.04167831316590309,
-0.015637045726180077,
0.016558479517698288,
0.019832897931337357,
-0.0393076092004776,
-0.015078727155923843,
0.01572495512664318,
0.012307452969253063,
0.0028433192055672407,
0.02725026197731495,
0.017743345350027084,
-0.0010167110012844205,
0.019159020856022835,
-0.030803080648183823,
0.060977060347795486,
-0.014740614220499992,
-0.01600966416299343,
0.052361294627189636,
-0.01567617990076542,
0.003913068678230047,
-0.02148514613509178,
-0.009452929720282555,
0.028472822159528732,
-0.02589411474764347,
0.004020593129098415,
0.034395210444927216,
0.04086115211248398,
0.0007562666432932019,
0.011153891682624817,
0.022438334301114082,
-0.031231064349412918,
-0.001444417517632246,
0.0027488358318805695,
0.06473535299301147,
-0.08856353908777237,
-0.0056291609071195126,
-0.01727970875799656,
-0.03643844276666641,
0.04142580181360245,
0.04406806454062462,
-0.021761024370789528,
0.1089431494474411,
0.021423501893877983,
0.009682176634669304,
0.0036870515905320644,
-0.01850230060517788,
-0.01606590487062931,
0.015133189037442207,
0.005765686277300119,
0.04609910771250725,
-0.001278584124520421,
-0.016646916046738625,
-0.05781062692403793,
0.015052013099193573,
0.04972001910209656,
-0.05856620520353317,
-0.030397938564419746,
-0.005779386498034,
-0.010034836828708649,
0.008374172262847424,
0.00868232361972332,
-0.01868639886379242,
-0.022661931812763214,
0.0412413515150547,
0.04124261438846588,
-0.0057759955525398254,
-0.03908166661858559,
0.030716169625520706,
-0.03657643869519234,
0.023853525519371033,
-0.06838566809892654,
0.04500029981136322,
-0.032943516969680786,
0.03595832735300064,
0.0017867974238470197,
-0.011898009106516838
] |
<p>Well I've been asked this question, but I haven't been able to come with an answer yet using books and some web searches. The point is as the title says, to answer the question with the whole phenomenon explanation if possible. </p>
| 10,753 |
[
-0.035440653562545776,
-0.07770849019289017,
0.008690607734024525,
-0.034801874309778214,
0.022930283099412918,
0.021229051053524017,
-0.0037491745315492153,
-0.012712536379694939,
-0.0030601671896874905,
-0.015241479501128197,
0.015292246825993061,
0.05827988311648369,
0.022530872374773026,
0.0016603488475084305,
0.008877323009073734,
0.011471088044345379,
-0.01275456603616476,
-0.004146304912865162,
0.013575156219303608,
-0.013236623257398605,
-0.0037426792550832033,
0.058259058743715286,
-0.007167033385485411,
-0.0035726220812648535,
-0.03326769173145294,
0.017662931233644485,
0.038719795644283295,
0.0015345171559602022,
0.03577010706067085,
0.04157496988773346,
-0.010784445330500603,
0.022575100883841515,
-0.010485035367310047,
0.05028245598077774,
0.028295231983065605,
-0.010087347589433193,
-0.035255737602710724,
-0.021488074213266373,
-0.01705728843808174,
0.013884568586945534,
-0.0182392206043005,
-0.018526630476117134,
-0.00902443379163742,
0.04562785476446152,
-0.05432115122675896,
0.006671025417745113,
0.0087741082534194,
-0.04113760218024254,
0.04899454861879349,
-0.08088614791631699,
0.058207813650369644,
-0.005224431399255991,
0.02073759399354458,
0.001455137156881392,
-0.005769600626081228,
0.01032298058271408,
0.09995261579751968,
0.04099100083112717,
-0.0332932285964489,
-0.030439620837569237,
-0.006681919097900391,
-0.019812673330307007,
-0.027110526338219643,
-0.022225653752684593,
-0.03385582193732262,
0.045500967651605606,
-0.0022634451743215322,
-0.0410633347928524,
0.05461530387401581,
-0.009656257927417755,
-0.012124993838369846,
0.005781401880085468,
0.05583804473280907,
-0.0010266929166391492,
0.04480729624629021,
-0.018391311168670654,
0.06546532362699509,
-0.0019879047758877277,
0.03393789008259773,
0.013621962629258633,
0.008887006901204586,
-0.029874596744775772,
0.026863910257816315,
0.05283269286155701,
0.017519453540444374,
0.001658337190747261,
0.07381410151720047,
-0.030777402222156525,
0.02922595851123333,
0.02788488194346428,
-0.04108100384473801,
-0.009082581847906113,
0.011500011198222637,
0.016432972624897957,
-0.03735550120472908,
0.02811790630221367,
-0.023507697507739067,
0.07650995254516602,
0.02779894694685936,
-0.041503436863422394,
0.01144430972635746,
0.02496594563126564,
0.013571650721132755,
0.04687391594052315,
-0.02424469031393528,
-0.017243491485714912,
-0.04120232164859772,
0.017613785341382027,
0.0007955644396133721,
-0.000018975406419485807,
-0.02101999893784523,
0.0068913791328668594,
0.02377091720700264,
-0.016160136088728905,
0.04166674241423607,
-0.03142692148685455,
0.012706419453024864,
-0.03611483424901962,
0.050120025873184204,
0.09531416743993759,
0.022597502917051315,
-0.03875920921564102,
0.021661218255758286,
-0.03461702913045883,
-0.0522117093205452,
0.014891591854393482,
0.031075848266482353,
-0.012749172747135162,
-0.01901601254940033,
0.0038164237048476934,
0.0028900979086756706,
-0.04095129668712616,
0.04643465206027031,
-0.017411580309271812,
0.03169439360499382,
-0.00425697723403573,
-0.09405229985713959,
-0.07073751091957092,
0.06403296440839767,
-0.03440041095018387,
0.0025608898140490055,
-0.09689511358737946,
0.017867211252450943,
-0.006294291466474533,
0.06848479807376862,
-0.012367011979222298,
-0.005929368548095226,
-0.015483231283724308,
0.016056962311267853,
0.011269885115325451,
-0.03677470237016678,
-0.034478042274713516,
-0.007924049161374569,
-0.07178286463022232,
0.0052529447712004185,
-0.07571931928396225,
0.005765232257544994,
0.02453319914638996,
-0.003609698498621583,
-0.0531829334795475,
0.03053579293191433,
-0.011368591338396072,
0.003914560191333294,
-0.02189965359866619,
-0.00315997120924294,
-0.022818783298134804,
0.10561320185661316,
0.0352957509458065,
-0.01791166141629219,
0.042521219700574875,
0.013545913621783257,
0.04425440728664398,
0.020156385377049446,
0.043144069612026215,
0.0028750437777489424,
-0.02821311540901661,
-0.00827462412416935,
-0.020297124981880188,
0.011893078684806824,
-0.01224270649254322,
-0.028333790600299835,
-0.03123791702091694,
0.017593812197446823,
0.014284198172390461,
0.0027404078282415867,
0.0465104766190052,
0.0019830851815640926,
-0.043735940009355545,
-0.01032091211527586,
-0.07356374710798264,
0.001476480858400464,
-0.05703320726752281,
0.0011961313430219889,
-0.02493520826101303,
-0.015086919069290161,
0.026511024683713913,
0.00753891933709383,
0.02397715114057064,
-0.03551365062594414,
-0.030061393976211548,
-0.02798808366060257,
0.005785463377833366,
0.028068099170923233,
-0.036757852882146835,
0.008132916875183582,
0.05111889913678169,
0.029003838077187538,
0.001816426170989871,
0.03009749762713909,
-0.029212014749646187,
-0.018839817494153976,
-0.020855801180005074,
-0.007429562509059906,
0.03126365318894386,
-0.030916109681129456,
-0.007696582470089197,
0.022063151001930237,
0.020846322178840637,
0.005416369531303644,
0.03163447603583336,
-0.01963324472308159,
0.07432910799980164,
0.01210707239806652,
0.023987844586372375,
-0.02487422525882721,
0.014157893136143684,
-0.006695886608213186,
-0.02676851488649845,
0.012998594902455807,
-0.04845239967107773,
-0.04245481267571449,
0.005025940015912056,
0.031025443226099014,
0.008984195999801159,
-0.022371366620063782,
0.022618575021624565,
0.004713262896984816,
0.08053477108478546,
-0.006819701753556728,
0.016267389059066772,
0.001606391160748899,
-0.011446758173406124,
-0.009112045168876648,
0.03165248781442642,
0.009198770858347416,
0.005084684118628502,
0.04791264981031418,
0.015812847763299942,
-0.002762905554845929,
-0.019646739587187767,
-0.020529765635728836,
0.026947425678372383,
-0.0016039328183978796,
0.019111402332782745,
-0.022522542625665665,
-0.004877363797277212,
0.03367554396390915,
-0.05913238227367401,
-0.005466515198349953,
0.013625191524624825,
0.015982413664460182,
0.012146663852036,
-0.033295903354883194,
-0.03053218685090542,
0.03289807587862015,
0.04869886860251427,
-0.011087947525084019,
0.004471300169825554,
0.03810799494385719,
-0.016423650085926056,
0.026511918753385544,
0.016226524487137794,
-0.03908345103263855,
-0.0205331202596426,
0.0005130929639562964,
0.04076700285077095,
0.030450494959950447,
0.0523856095969677,
-0.03505615144968033,
-0.06541808694601059,
-0.04768948256969452,
-0.048340290784835815,
0.014264085330069065,
0.005706313997507095,
-0.03577914834022522,
0.017059478908777237,
-0.007072224747389555,
-0.018876081332564354,
0.0293596088886261,
0.0006280397064983845,
0.0043927025981247425,
0.000020680334273492917,
-0.039140261709690094,
-0.030621811747550964,
-0.019683636724948883,
-0.038195397704839706,
-0.00993198249489069,
-0.05704504996538162,
0.03942546248435974,
0.06419749557971954,
-0.022746864706277847,
-0.02942480705678463,
0.01905578002333641,
-0.06699199229478836,
-0.043862901628017426,
-0.013588767498731613,
-0.00671570748090744,
-0.00722920149564743,
-0.056749846786260605,
0.011662745848298073,
-0.0007248641340993345,
-0.05160177871584892,
0.01112112496048212,
-0.016055600717663765,
-0.0481451191008091,
0.034766752272844315,
-0.007051854394376278,
0.01047834288328886,
-0.024414246901869774,
-0.03438251465559006,
0.03488726541399956,
0.0011422453681007028,
-0.05026049539446831,
-0.01592259854078293,
-0.008037489838898182,
0.00644241226837039,
-0.001621675561182201,
0.02441016212105751,
0.059848617762327194,
-0.0284948218613863,
0.032001934945583344,
0.030307753011584282,
0.04607662931084633,
0.008511119522154331,
0.023587683215737343,
-0.022061055526137352,
0.016426675021648407,
0.008309091441333294,
-0.00645031500607729,
-0.010466953739523888,
0.018764901906251907,
-0.0572638176381588,
0.009997976012527943,
-0.013437961228191853,
0.0057725682854652405,
0.007469009142369032,
-0.038434237241744995,
0.04096284136176109,
0.0233055017888546,
0.026638150215148926,
0.002762421267107129,
0.044300880283117294,
-0.03520071879029274,
0.003491992363706231,
-0.023545585572719574,
0.019549937918782234,
0.05304541438817978,
-0.039154306054115295,
-0.03204083442687988,
0.035300180315971375,
0.05783049762248993,
-0.03730318322777748,
-0.036188866943120956,
-0.015226233750581741,
-0.017165301367640495,
0.035300321877002716,
-0.008340468630194664,
-0.016844134777784348,
0.06102630868554115,
0.051751308143138885,
0.017604142427444458,
-0.00816317554563284,
-0.037280917167663574,
0.0058919163420796394,
-0.0817960798740387,
0.01579834520816803,
0.015027736313641071,
0.034386683255434036,
-0.03401876240968704,
0.04358723759651184,
0.041531313210725784,
0.05291445180773735,
0.012436079792678356,
0.004746359307318926,
-0.09345363825559616,
-0.008996873162686825,
-0.026841770857572556,
0.015292303636670113,
-0.03054409846663475,
0.006172765977680683,
0.015680262818932533,
-0.00692933751270175,
-0.030788682401180267,
-0.016609372571110725,
-0.011601442471146584,
-0.06479353457689285,
0.013117356225848198,
0.003666970646008849,
-0.03319157287478447,
-0.029028138145804405,
0.05738624557852745,
0.021355709061026573,
-0.008374745957553387,
-0.0033835095819085836,
0.05185691639780998,
-0.013975796289741993,
-0.008116338402032852,
-0.0466034971177578,
0.010216426104307175,
0.01047006156295538,
0.027129273861646652,
0.019125105813145638,
-0.00328729092143476,
-0.04561227187514305,
0.02984044700860977,
0.005221295170485973,
0.03036772646009922,
0.009738503955304623,
0.008631440810859203,
-0.053744371980428696,
-0.011450566351413727,
-0.0029501121025532484,
-0.011121474206447601,
0.04318942502140999,
-0.02246958389878273,
0.02497207559645176,
0.020431794226169586,
0.029457125812768936,
-0.03007945977151394,
0.02466324344277382,
0.037837717682123184,
-0.001735377125442028,
-0.03283991292119026,
-0.037061888724565506,
0.02107289433479309,
-0.03357180207967758,
0.020760316401720047,
0.015352047979831696,
0.0018861474236473441,
-0.015449034050107002,
0.011052019894123077,
0.006010628771036863,
-0.01142488420009613,
-0.010544301941990852,
-0.02225736901164055,
-0.01396169327199459,
-0.009304743260145187,
-0.025025025010108948,
0.0013408211525529623,
0.00846315361559391,
0.024540239945054054,
0.059631627053022385,
0.0006290884921327233,
-0.016745511442422867,
-0.08252571523189545,
-0.025663847103714943,
0.030290819704532623,
0.010185602121055126,
-0.025291014462709427,
0.01379786990582943,
-0.04540807008743286,
-0.019812580198049545,
0.02548103779554367,
-0.0029648300260305405,
0.026123210787773132,
-0.016421811655163765,
-0.01562730222940445,
-0.0124838100746274,
0.007263959385454655,
-0.0013192978221923113,
0.006098498590290546,
-0.0062970733270049095,
0.01719096302986145,
-0.012504792772233486,
0.0003258511715102941,
-0.009280458092689514,
0.0012940369779244065,
0.01659754104912281,
0.043262846767902374,
0.01012432761490345,
-0.00003016434311575722,
-0.030883656814694405,
0.03441169485449791,
-0.05800029635429382,
-0.06098272651433945,
0.009796755388379097,
0.024011453613638878,
-0.004388872534036636,
0.034982968121767044,
-0.03515208140015602,
-0.05503802001476288,
0.009104848839342594,
-0.01601911522448063,
-0.005241686478257179,
-0.0123681565746665,
0.012860534712672234,
0.001955061685293913,
0.031034229323267937,
0.013154798187315464,
0.059462763369083405,
0.023165971040725708,
-0.005189035087823868,
-0.01889963634312153,
0.024698646739125252,
0.041665300726890564,
-0.024527231231331825,
-0.014876242727041245,
-0.019380053505301476,
0.014498526230454445,
-0.04320686683058739,
0.10313449054956436,
-0.032950498163700104,
0.011242895387113094,
-0.016132067888975143,
-0.04202437400817871,
-0.008601473644375801,
0.026924626901745796,
0.0024712402373552322,
-0.0010328113567084074,
-0.0096956891939044,
0.0024206778034567833,
0.0013435728615149856,
-0.04378926753997803,
0.03236527368426323,
-0.03536614030599594,
-0.0024414469953626394,
0.0401526540517807,
-0.015541967004537582,
0.032254643738269806,
-0.03511345759034157,
0.032105159014463425,
0.023265749216079712,
-0.020625164732336998,
0.038470685482025146,
-0.014951005578041077,
0.004560321103781462,
0.014808977954089642,
-0.07684364169836044,
-0.006163980811834335,
0.0016146176494657993,
-0.032022859901189804,
0.06413735449314117,
-0.010733472183346748,
0.01809493452310562,
0.021700004115700722,
-0.015353262424468994,
-0.0923626497387886,
-0.09675956517457962,
0.059474822133779526,
0.05527111515402794,
-0.019900327548384666,
-0.014377092942595482,
0.0018662092043086886,
-0.03603549674153328,
-0.04891747236251831,
-0.03015626221895218,
0.03572400286793709,
-0.01730150543153286,
-0.012925595045089722,
0.009096061810851097,
-0.018575962632894516,
0.03434963896870613,
0.03131590038537979,
-0.0407523438334465,
0.00690634548664093,
-0.03051134943962097,
-0.013486984185874462,
0.01545220147818327,
0.0486101470887661,
-0.03298657387495041,
-0.020906459540128708,
-0.01441204734146595,
-0.00003902723256032914,
0.03550627455115318,
-0.03735719248652458,
0.026588784530758858,
0.030524341389536858,
0.021770525723695755,
0.019245414063334465,
-0.05027336999773979,
0.014756377786397934,
0.008021751418709755,
0.00645122304558754,
0.024791715666651726,
-0.03234008327126503,
-0.00972448755055666,
-0.030004510655999184,
0.030128976330161095,
0.03590935468673706,
-0.004991345107555389,
-0.011540022678673267,
0.04775722324848175,
-0.019537195563316345,
-0.03427883982658386,
0.026178084313869476,
-0.010927697643637657,
0.033175110816955566,
0.028798241168260574,
-0.007872922345995903,
0.007699955720454454,
0.04787424951791763,
0.006776143796741962,
-0.025206247344613075,
-0.01084875501692295,
0.026276111602783203,
0.0730237141251564,
-0.04334919899702072,
0.047242071479558945,
0.01943754404783249,
0.00994348619133234,
0.004019144456833601,
-0.011516048572957516,
-0.014756870456039906,
0.014908403158187866,
-0.01819612644612789,
0.0221895482391119,
-0.02185269631445408,
0.02627922035753727,
0.025380976498126984,
0.04273764044046402,
-0.026918428018689156,
0.030236294493079185,
0.054469190537929535,
0.02237875759601593,
0.06274398416280746,
-0.013426678255200386,
-0.04314108192920685,
0.020246198400855064,
-0.04562871903181076,
0.02271164022386074,
0.0007324042380787432,
-0.01359518151730299,
0.03317466005682945,
0.011175190098583698,
0.03162962570786476,
-0.0249345563352108,
-0.05487564578652382,
-0.018628310412168503,
-0.011758942157030106,
0.0018367335433140397,
0.03780357539653778,
0.016151465475559235,
0.008576197549700737,
0.01857484132051468,
0.0033573650289326906,
0.007943734526634216,
-0.030656399205327034,
-0.10058693587779999,
-0.053463127464056015,
0.013207940384745598,
-0.03677583113312721,
0.0417913980782032,
0.002883977023884654,
-0.014109859243035316,
0.006757327821105719,
-0.028775617480278015,
0.003443501191213727,
0.006438055541366339,
0.06365550309419632,
0.017133589833974838,
0.06984418630599976,
0.01256560254842043,
0.01555644441395998,
-0.0008651200914755464,
0.02169531024992466,
0.12177981436252594,
0.043826669454574585,
0.023066753521561623,
-0.07757400721311569,
0.010636033490300179,
-0.016141163185238838,
0.004134752321988344,
-0.00015981259639374912,
0.062167778611183167,
0.018004542216658592,
-0.016705982387065887,
0.036239173263311386,
0.06327503174543381,
0.018948137760162354,
0.010788153856992722,
0.04067925736308098,
-0.04925305023789406,
-0.05402792617678642,
-0.006773679051548243,
-0.0061438982374966145,
0.00497167045250535,
0.010001199319958687,
-0.021551668643951416,
0.0057881856337189674,
-0.017649030312895775,
0.00533466087654233,
0.0041885701939463615,
-0.032848287373781204,
-0.012404161505401134,
0.023257913067936897,
-0.044686947017908096,
0.00953568797558546,
0.016948437318205833,
-0.010803903453052044,
-0.0534873828291893,
0.01671355590224266,
0.04830222949385643,
-0.019293425604701042,
0.011080681346356869,
0.014240791089832783,
0.02642926573753357,
0.002696326235309243,
0.0020319060422480106,
-0.013238494284451008,
-0.031226472929120064,
-0.006051972974091768,
-0.01702594757080078,
0.036319341510534286,
0.01075137872248888,
0.00484999967738986,
0.009845842607319355,
0.0011977271642535925,
0.0246427059173584,
-0.055487796664237976,
-0.045182567089796066,
0.015271543525159359,
-0.01133981067687273,
-0.028877004981040955,
-0.03199027478694916,
-0.017048604786396027,
0.028039420023560524,
-0.0000343712636095006,
0.019371358677744865,
-0.014318731613457203,
0.006438963580876589,
0.02052648738026619,
0.003534778254106641,
0.02210814505815506,
-0.02227102965116501,
-0.009634559974074364,
-0.04477857053279877,
-0.014402110129594803,
-0.01562640070915222,
-0.012660800479352474,
0.019720718264579773,
0.04902755841612816,
0.019921518862247467,
-0.012865917757153511,
-0.03238135948777199,
-0.0010118463542312384,
-0.008465449325740337,
0.028139326721429825,
0.009689821861684322,
-0.011163432151079178,
-0.02219334989786148,
-0.0006750787142664194,
0.009088150225579739,
0.01724729686975479,
-0.012235856615006924,
0.031138915568590164,
-0.04109565168619156,
0.07338634133338928,
-0.0022638796363025904,
-0.01282513327896595,
-0.05580783262848854,
0.01656101457774639,
-0.030596381053328514,
-0.0003581464115995914,
0.000696917821187526,
0.010049915872514248,
-0.0031095650047063828,
0.004537235479801893,
0.016787385568022728,
0.024825967848300934,
-0.01884053274989128,
0.014049191027879715,
0.04126317799091339,
-0.036543525755405426,
-0.03583492711186409,
0.007981311529874802,
-0.031643446534872055,
0.013832641765475273,
-0.03451574221253395,
-0.008732404559850693,
0.027718104422092438,
0.007945419289171696,
0.05322444438934326,
-0.013691635802388191,
0.04017652943730354,
-0.03146379441022873,
-0.0063939024694263935,
-0.021006785333156586,
-0.02553263120353222,
-0.06806859374046326,
0.002209336729720235,
0.01750008761882782,
0.015350647270679474,
0.003989940509200096,
0.04139970988035202,
-0.019428424537181854,
-0.02161095291376114,
0.016506386920809746,
0.010540022514760494,
-0.01561889611184597,
0.004498402588069439,
-0.013457500375807285,
-0.0012281277449801564,
0.04468318447470665,
-0.00877373293042183,
-0.030399013310670853,
0.06059332937002182,
-0.0838225856423378,
-0.029718542471528053,
0.026373539119958878,
-0.019590096548199654,
0.03715389594435692,
0.03992535546422005,
-0.0036910176277160645,
-0.006739475764334202,
0.07301651686429977,
-0.007665127515792847,
-0.0011130021885037422,
-0.0017020109808072448,
0.010341780260205269,
0.009563185274600983,
0.00812514964491129,
0.005747316405177116,
-0.02688639424741268,
-0.006692034192383289,
0.015183407813310623,
0.015727350488305092,
-0.020922230556607246,
-0.02506328374147415,
0.015464084222912788,
0.01683877781033516,
0.011588078923523426,
0.030350500717759132,
0.0028873393312096596,
0.009877310134470463,
0.04792539402842522,
-0.023961057886481285,
0.024536283686757088,
-0.005478797480463982,
0.004535543266683817,
-0.10221409052610397,
-0.01526639237999916,
-0.009676179848611355,
-0.01017333660274744,
-0.005747547838836908,
-0.051822479814291,
-0.006781425792723894,
0.027248697355389595,
-0.06184186786413193,
0.011171224527060986,
-0.03195932134985924,
-0.017294984310865402,
-0.041035931557416916,
0.01436943095177412,
0.004413946066051722,
0.014221454970538616,
0.028939783573150635,
0.025560393929481506,
0.02629133313894272,
0.023826541379094124,
-0.04365888610482216,
-0.0006014707032591105,
0.007009477354586124,
0.018570074811577797,
-0.0010477013420313597,
-0.007430524565279484,
0.05133390799164772,
-0.02755904570221901,
-0.03119342215359211,
0.04295308142900467,
-0.033112891018390656,
0.024852724745869637,
0.005846569314599037,
0.0031187920831143856,
0.0010906998068094254,
0.013664403930306435,
-0.0025430431123822927,
-0.011802762746810913,
0.010188771411776543,
0.07263360172510147,
-0.0008669911767356098,
0.04540826007723808,
-0.005757471080869436,
0.015550374053418636,
0.005600695498287678,
-0.040619201958179474,
-0.0195046104490757,
0.0035412947181612253,
-0.02145565301179886,
-0.002160285832360387,
0.01940162666141987,
0.03393739461898804,
0.04185089096426964,
-0.030909571796655655,
0.026534972712397575,
-0.06616692990064621,
-0.008234729990363121,
-0.018689176067709923,
0.01736012101173401,
-0.007763734553009272,
0.03398236259818077,
-0.04494594410061836,
-0.025240523740649223,
-0.021826444193720818,
0.005967971868813038,
-0.00197009788826108,
-0.01588429883122444,
-0.021930204704403877,
-0.022851059213280678,
0.02968800626695156,
-0.006875729653984308,
-0.02250107191503048,
-0.03874533995985985,
0.0479879193007946,
0.02278178371489048,
0.04421727731823921,
0.010760724544525146,
-0.061092864722013474,
-0.01345103420317173,
-0.03803696855902672,
0.05660561844706535,
-0.03474190831184387,
0.015626829117536545,
-0.02404901199042797,
-0.027736306190490723,
0.009948317892849445,
0.03093443252146244,
0.04859418794512749,
-0.0293408390134573,
-0.019658833742141724,
0.0037803237792104483,
-0.009493522346019745,
-0.00559946009889245,
-0.043080270290374756,
0.013381349854171276,
-0.026427866891026497,
-0.023273890838027,
-0.02384326048195362,
-0.02828199602663517,
-0.014509043656289577,
-0.007272195536643267,
0.011871283873915672,
0.011277706362307072,
0.028281401842832565,
-0.035344768315553665,
-0.0072976164519786835,
0.04978958144783974,
0.02736951783299446,
0.006601450499147177,
0.047363296151161194,
0.018146254122257233,
-0.001724017783999443,
0.04001845791935921,
-0.011547026224434376,
-0.05762510374188423,
0.06265604496002197,
-0.029768817126750946,
0.007142979186028242,
-0.00925908237695694,
0.017452789470553398,
0.021792737767100334,
-0.008247733116149902,
0.0073112910613417625,
0.044289980083703995,
-0.004278100561350584,
-0.01747208647429943,
0.046941328793764114,
0.02965540811419487,
0.0032015987671911716,
-0.026812022551894188,
-0.011530796065926552,
0.012128558941185474,
0.0015317025827243924,
-0.027022866532206535,
0.06813694536685944,
0.0011898124357685447,
0.017565255984663963,
0.051112789660692215,
-0.014013325795531273,
-0.012008078396320343,
0.036754630506038666,
-0.03144289180636406,
0.015267566777765751,
-0.02094610221683979,
0.002403578720986843,
0.007151773665100336,
-0.03262149542570114,
-0.007397180888801813,
0.020886067301034927,
-0.0032796470914036036,
0.09696486592292786,
0.0004168389132246375,
0.045824840664863586,
0.0023013188038021326,
0.036527425050735474,
-0.007076574023813009,
-0.010600398294627666,
0.03314577788114548,
0.010402265004813671,
-0.010456603951752186,
-0.017534008249640465,
-0.0070159658789634705,
-0.011234418489038944,
0.021491123363375664,
-0.010529760271310806,
0.021617751568555832,
-0.03341499716043472,
-0.0060556367971003056,
0.017986325547099113,
0.013593624345958233,
-0.03281252831220627,
-0.024632396176457405,
0.04750475287437439,
0.039801955223083496,
0.005167736671864986,
-0.00625938456505537,
0.0037924558855593204,
-0.04655549302697182,
0.07971400767564774,
-0.060942526906728745,
-0.032953355461359024,
-0.024896562099456787,
0.044169362634420395,
-0.032444313168525696,
-0.0054794480092823505
] |
<p>I read in a book that for $\beta$-decay the electrons have always been found to have an expectation value for their helicity of $h=-v/c$. </p>
<p>Then ist is said in the book, that it follows from this fact that such electrons are in a left-handed chiral state which is characteristic for the weak interaction.</p>
<p>In another article I read that the chiral state of an electron is not conserved in time. The electron will soon evolve a component with a right-handed chiral state and it will be a mixture of right- and lef-handed chiral states.</p>
<p>Suppose after the decay one electron moves like a free particle.<br>
When it evolves a right-handed chiral component in addition to the left-handed component it starts off with, how can its helicity be conserved?</p>
| 10,754 |
[
-0.012030739337205887,
-0.01224835030734539,
0.04056992754340172,
-0.030959799885749817,
0.03242262825369835,
0.03623110055923462,
-0.018267348408699036,
-0.009336440823972225,
0.03834020718932152,
-0.058684926480054855,
0.03208685293793678,
0.008223655633628368,
0.055651381611824036,
0.03133721277117729,
0.01597301848232746,
0.015923285856842995,
0.014983215369284153,
-0.0007977056666277349,
-0.03397544100880623,
0.0001933600433403626,
0.011193941347301006,
0.02591961994767189,
0.016693122684955597,
0.03264906257390976,
-0.01509994175285101,
0.010132839903235435,
0.034686751663684845,
0.02000039629638195,
0.022285504266619682,
0.07600011676549911,
-0.02550607919692993,
-0.05291794240474701,
0.020900988951325417,
0.00341630051843822,
-0.005239338614046574,
-0.03074653632938862,
-0.027454786002635956,
-0.08334989845752716,
-0.01075728889554739,
0.023490868508815765,
-0.02585974708199501,
-0.015372811816632748,
-0.043482810258865356,
0.08149100840091705,
-0.020544273778796196,
-0.0002644977066665888,
-0.020120764151215553,
0.00026473889010958374,
0.08035115152597427,
-0.06873508542776108,
0.03323625028133392,
-0.01590985432267189,
0.06960608065128326,
-0.029555512592196465,
0.028559653088450432,
-0.011593269184231758,
0.03902462124824524,
0.04919612780213356,
0.03290332481265068,
-0.04096680134534836,
0.003173193661496043,
-0.04856236279010773,
0.018041901290416718,
0.004383919760584831,
-0.012262994423508644,
0.017472250387072563,
-0.007981108501553535,
0.0034259690437465906,
0.025331804528832436,
0.002740618074312806,
0.02982630394399166,
0.005822606850415468,
0.015764446929097176,
0.003247745567932725,
0.0033913161605596542,
-0.01799337938427925,
0.02019684389233589,
0.03773593157529831,
0.020759711042046547,
0.004446737002581358,
0.0010093844030052423,
-0.00280903372913599,
0.03481731563806534,
0.027881326153874397,
-0.016627853736281395,
-0.021250993013381958,
0.07123823463916779,
-0.03068479895591736,
-0.01476387307047844,
0.041691944003105164,
0.006919635459780693,
0.023037509992718697,
0.015373386442661285,
-0.00433728052303195,
-0.047904111444950104,
0.03558362275362015,
0.02277521789073944,
0.06302335858345032,
0.014651080593466759,
-0.014633123762905598,
0.03494250401854515,
-0.0035194824449718,
0.017424969002604485,
0.07579798251390457,
0.0037685073912143707,
0.009369922801852226,
-0.021842148154973984,
0.003972155041992664,
-0.008381422609090805,
-0.062238555401563644,
-0.030642693862318993,
-0.013204541988670826,
-0.0168018639087677,
0.012293420732021332,
0.008891483768820763,
-0.03404808044433594,
0.0009305599378421903,
-0.009021315723657608,
0.06389286369085312,
0.05164991319179535,
0.01676754839718342,
-0.03738962858915329,
0.012149928137660027,
-0.023087678477168083,
-0.08163215219974518,
-0.000023736629373161122,
0.026316270232200623,
0.016280077397823334,
-0.03950604051351547,
0.028389208018779755,
0.012479790486395359,
-0.04841145873069763,
0.034323908388614655,
0.004658187739551067,
0.015073657035827637,
-0.0008913305937312543,
-0.10901893675327301,
-0.04540106654167175,
0.023020178079605103,
-0.058500416576862335,
-0.011806443333625793,
-0.0868987888097763,
-0.01058349758386612,
0.027295047417283058,
0.11764344573020935,
-0.013877206481993198,
0.005489616189152002,
0.011163540184497833,
0.02268076501786709,
0.0349949412047863,
0.011205082759261131,
-0.02844482846558094,
-0.007259041536599398,
-0.014848217368125916,
-0.04314656928181648,
-0.04288062825798988,
0.009094002656638622,
0.003384312614798546,
0.016508864238858223,
-0.02670830488204956,
0.05418042838573456,
-0.008036530576646328,
0.033645905554294586,
-0.014844018034636974,
0.0036596159916371107,
-0.03662716597318649,
0.07440575957298279,
0.03002621978521347,
-0.01992499642074108,
0.027141960337758064,
-0.006497237831354141,
0.008042702451348305,
-0.0073385294526815414,
0.040258921682834625,
0.03270037844777107,
-0.02161758579313755,
-0.03975854068994522,
-0.014568393118679523,
-0.007925167679786682,
-0.04047862067818642,
-0.023289820179343224,
-0.017524460330605507,
-0.03290591016411781,
0.04277518391609192,
-0.011810515075922012,
0.030480699613690376,
-0.022804362699389458,
-0.01581028290092945,
0.009389808401465416,
-0.059602703899145126,
-0.04215044528245926,
-0.08601493388414383,
-0.01922510750591755,
0.02019057422876358,
-0.023834120482206345,
0.03954625874757767,
-0.0064611188136041164,
0.022877627983689308,
-0.010615261271595955,
-0.0028452016413211823,
-0.03945202752947807,
0.039567653089761734,
-0.007046418730169535,
0.0035066267009824514,
0.007607967127114534,
0.03674636781215668,
0.0340023897588253,
0.008845259435474873,
0.03481755033135414,
0.017565108835697174,
-0.0602664016187191,
0.022002384066581726,
-0.011211334727704525,
0.015087819658219814,
0.03863947466015816,
0.004386811051517725,
-0.020202336832880974,
-0.007096293848007917,
0.012824822217226028,
0.034520283341407776,
0.012660978361964226,
0.033229731023311615,
0.04173528030514717,
-0.014077900908887386,
0.005856908857822418,
0.022296370938420296,
0.022449418902397156,
0.002544519491493702,
-0.034028492867946625,
-0.051673900336027145,
-0.04610052704811096,
0.01748969964683056,
0.035635482519865036,
0.011055081151425838,
-0.049810197204351425,
0.02817174233496189,
-0.02090698480606079,
0.047082122415304184,
0.02885935828089714,
0.002900524763390422,
-0.009486017748713493,
-0.0425645150244236,
0.009722969494760036,
-0.029032448306679726,
0.002020999789237976,
-0.012065318413078785,
0.021367114037275314,
-0.012352845631539822,
0.026546994224190712,
0.0003431675140745938,
-0.033298932015895844,
0.033698685467243195,
0.0008486395236104727,
-0.02242155931890011,
-0.005315002053976059,
-0.05522240325808525,
0.03359225019812584,
-0.0024570662062615156,
0.033420395106077194,
-0.006405067630112171,
-0.024476828053593636,
0.017214743420481682,
-0.026165328919887543,
-0.008841951377689838,
0.034871313720941544,
0.03179449588060379,
-0.02429674193263054,
-0.042242590337991714,
0.010171232745051384,
-0.0046016750857234,
0.029662059620022774,
-0.005808470770716667,
-0.010949411429464817,
0.015891974791884422,
-0.00855904072523117,
0.046142127364873886,
0.010465950705111027,
0.01629139669239521,
-0.022847119718790054,
-0.03583529591560364,
0.011636259034276009,
-0.026626892387866974,
0.004696556366980076,
0.07083412259817123,
-0.012240778654813766,
0.0024482046719640493,
-0.050873082131147385,
-0.013924682512879372,
0.0026674664113670588,
0.031051164492964745,
0.025312406942248344,
0.008024987764656544,
-0.03979576751589775,
-0.0858619213104248,
-0.02282870002090931,
-0.02176373079419136,
-0.019576437771320343,
-0.00938243418931961,
-0.0012920968001708388,
0.04027961939573288,
0.016288988292217255,
0.007645913865417242,
0.030621280893683434,
-0.027307217940688133,
-0.06487946212291718,
-0.014912644401192665,
-0.019752781838178635,
-0.004661074839532375,
-0.020169954746961594,
0.020051753148436546,
0.027680709958076477,
-0.03725005313754082,
0.01354170311242342,
-0.029231911525130272,
-0.017814062535762787,
0.004726026207208633,
-0.012203166261315346,
-0.007696299348026514,
0.014814486727118492,
-0.04155740141868591,
0.09020339697599411,
0.034984562546014786,
-0.04420572891831398,
-0.003433947218582034,
0.0007799312588758767,
-0.042841389775276184,
-0.04578513652086258,
0.012407618574798107,
0.036577995866537094,
0.015912052243947983,
0.03197578340768814,
0.0015132984844967723,
0.040923506021499634,
0.002247120486572385,
0.033497512340545654,
-0.044289588928222656,
0.022311201319098473,
-0.0011524398578330874,
0.025410421192646027,
0.023206528276205063,
-0.01733926124870777,
-0.009131635539233685,
-0.0061098323203623295,
0.0297810360789299,
0.04887131229043007,
0.028515033423900604,
-0.05297035351395607,
0.06549971550703049,
0.006701903883367777,
0.021219847723841667,
-0.024233343079686165,
0.05874180048704147,
-0.00898045115172863,
0.016073103994131088,
0.014742431230843067,
0.001151654520072043,
0.03929314762353897,
-0.012467188760638237,
-0.003629945684224367,
0.004114515148103237,
0.016672158613801003,
-0.014511658810079098,
-0.04458407312631607,
-0.01746477372944355,
-0.0010412154952064157,
0.03672059625387192,
-0.03610365837812424,
-0.007212669122964144,
0.032618287950754166,
0.028715798631310463,
0.003112149192020297,
0.011816125363111496,
-0.058204036206007004,
-0.024845577776432037,
-0.03773505985736847,
0.03523179516196251,
0.0240061916410923,
0.03247145563364029,
0.01967857964336872,
0.04546476528048515,
0.02516303025186062,
-0.009160317480564117,
0.01043312530964613,
-0.017076855525374413,
-0.09171070903539658,
0.042399801313877106,
-0.025263939052820206,
0.007664669770747423,
-0.05370711535215378,
0.008942481130361557,
0.020653462037444115,
-0.021544434130191803,
-0.027714796364307404,
-0.0468955934047699,
-0.043178800493478775,
-0.02530212514102459,
0.011615604162216187,
-0.05238404870033264,
-0.03941776975989342,
-0.06336800754070282,
0.046518079936504364,
0.043803028762340546,
-0.036042068153619766,
0.003761506639420986,
0.0055232541635632515,
-0.03140571713447571,
0.006950949784368277,
-0.038840387016534805,
0.03359642252326012,
0.006683014798909426,
0.010148296132683754,
0.043357133865356445,
0.007849104702472687,
-0.022054310888051987,
-0.022616123780608177,
0.04866855591535568,
0.06320007145404816,
0.010122302919626236,
0.03473494574427605,
0.00347099918872118,
-0.04132021591067314,
0.015043813735246658,
0.012696127407252789,
0.024459093809127808,
0.05265054106712341,
0.07801473885774612,
0.05967749282717705,
0.01154344528913498,
-0.05833213031291962,
0.044916749000549316,
0.03415975347161293,
0.017462147399783134,
-0.017784928902983665,
-0.04543979838490486,
0.02840907871723175,
0.007307353895157576,
-0.024212677031755447,
-0.009988960810005665,
-0.04007669538259506,
-0.02101268246769905,
0.001014315988868475,
-0.0005325208185240626,
0.0032580553088337183,
-0.006643426604568958,
-0.007714256644248962,
-0.002320645609870553,
0.007359270006418228,
0.0035511504393070936,
-0.03571735695004463,
0.02879360318183899,
0.04474229738116264,
0.02152654342353344,
0.005024759564548731,
0.013795541599392891,
-0.017659412696957588,
-0.01580873318016529,
0.006835049483925104,
0.03796336427330971,
-0.02603447437286377,
-0.024468697607517242,
-0.04484492540359497,
-0.002996365539729595,
0.03085746057331562,
-0.022420698776841164,
0.006985791493207216,
-0.03659399226307869,
-0.01625601202249527,
-0.026056237518787384,
-0.041799090802669525,
-0.03323870524764061,
0.02083352394402027,
0.0045491610653698444,
0.018459154292941093,
-0.057470012456178665,
-0.009267162531614304,
-0.01389077678322792,
0.01419894304126501,
0.027510590851306915,
0.041586264967918396,
0.0057392786256968975,
0.0433034747838974,
0.020094921812415123,
0.01636616140604019,
0.008195803500711918,
-0.12214773148298264,
0.010211329907178879,
0.028868569061160088,
0.016848038882017136,
-0.0020941051188856363,
-0.05394566431641579,
-0.07087516039609909,
-0.007943193428218365,
0.013746991753578186,
0.038100820034742355,
-0.02716975472867489,
-0.07660657167434692,
0.03877527639269829,
0.007921144366264343,
-0.024729976430535316,
0.06895779818296432,
0.024411305785179138,
-0.010203256271779537,
-0.01836368627846241,
-0.010160266421735287,
0.019325630739331245,
-0.025607019662857056,
0.016878245398402214,
-0.04001970216631889,
0.008068200200796127,
-0.0006049409275874496,
0.08853530138731003,
-0.015850530937314034,
0.01951734907925129,
0.008846874348819256,
-0.006978915072977543,
-0.021880853921175003,
0.03502023220062256,
0.0006018130807206035,
-0.01854674145579338,
-0.004613650497049093,
-0.0121275894343853,
-0.004997114185243845,
-0.017988137900829315,
0.008204881101846695,
-0.03794555738568306,
-0.02545357309281826,
0.030329754576086998,
-0.035938411951065063,
0.03214868903160095,
-0.03136393800377846,
-0.00611142860725522,
-0.0014166198670864105,
-0.05423042178153992,
-0.0032954139169305563,
-0.018082095310091972,
-0.002803592709824443,
0.010765875689685345,
-0.054649729281663895,
-0.025992251932621002,
0.04313119128346443,
-0.023960258811712265,
-0.022621920332312584,
-0.04376427084207535,
0.02676178701221943,
0.04659661650657654,
-0.00270980061031878,
-0.08140922337770462,
-0.051612988114356995,
0.011275114491581917,
0.004576715175062418,
-0.026425201445817947,
-0.0012156968005001545,
-0.00988108292222023,
-0.0184293482452631,
-0.033842843025922775,
-0.010182825848460197,
0.013370383530855179,
-0.0015920257428660989,
0.015530455857515335,
0.03241163492202759,
0.00489936163648963,
0.045963142067193985,
-0.0076518491841852665,
-0.008844242431223392,
-0.003922415431588888,
-0.01618911512196064,
-0.002458317903801799,
-0.006146099418401718,
0.03961877152323723,
-0.007959909737110138,
-0.007831990718841553,
0.024345923215150833,
-0.0047510238364338875,
0.03391164541244507,
-0.012192563153803349,
-0.015498689375817776,
0.041849296540021896,
-0.002124740509316325,
0.010979297570884228,
-0.031705453991889954,
0.007871937938034534,
0.018338637426495552,
0.040698036551475525,
0.03591669723391533,
-0.014307835139334202,
-0.01776084676384926,
-0.054755304008722305,
0.03809761628508568,
0.02055678516626358,
0.03234975412487984,
-0.011230970732867718,
0.0023839559871703386,
-0.019204184412956238,
-0.03134674206376076,
0.040336430072784424,
-0.014382809400558472,
0.008496490307152271,
0.004724700935184956,
0.019641952589154243,
0.015977656468749046,
0.03094611130654812,
-0.009567901492118835,
-0.022694768384099007,
-0.02407115139067173,
0.0455988347530365,
0.03191021457314491,
-0.014129112474620342,
0.005967362783849239,
0.00827413983643055,
0.0017076837830245495,
-0.04461902752518654,
-0.03801858425140381,
-0.004252593964338303,
0.014776003547012806,
-0.001667415606789291,
0.00939195416867733,
-0.016225870698690414,
0.0020350029226392508,
0.007826292887330055,
0.048541195690631866,
-0.06321663409471512,
0.016639914363622665,
0.047346506267786026,
0.0014397185295820236,
-0.012747099623084068,
-0.009140904061496258,
-0.03530468791723251,
0.027616674080491066,
-0.017521042376756668,
0.045076459646224976,
0.002352312207221985,
-0.0014883670955896378,
0.02529546059668064,
0.01576411724090576,
0.039763931185007095,
-0.046243052929639816,
-0.018314151093363762,
-0.049291301518678665,
-0.013223686255514622,
0.0014468271983787417,
-0.01866556704044342,
-0.02505265735089779,
0.02870740368962288,
0.03416460007429123,
0.029557283967733383,
0.0018865560414269567,
-0.010634621605277061,
-0.04899945482611656,
0.025737427175045013,
-0.04119616001844406,
0.00395450834184885,
0.051691826432943344,
-0.0364970788359642,
0.016123704612255096,
-0.024703580886125565,
0.009659776464104652,
-0.005256196018308401,
0.02332824282348156,
0.035623859614133835,
-0.011921788565814495,
0.045020852237939835,
-0.0023147885221987963,
0.058128029108047485,
-0.007870367728173733,
0.027393106371164322,
0.11619722843170166,
0.0712028443813324,
0.015910034999251366,
-0.05007755756378174,
0.04198247939348221,
-0.04353002458810806,
0.04505099356174469,
-0.021819522604346275,
0.03474672883749008,
0.022356655448675156,
0.008034626953303814,
-0.041092630475759506,
0.06066225841641426,
0.0022915774025022984,
0.007739392574876547,
0.06420982629060745,
-0.036053773015737534,
-0.035310957580804825,
-0.007832950912415981,
0.015763837844133377,
-0.035721804946660995,
0.01881258748471737,
-0.04959006607532501,
0.018398553133010864,
0.003653369378298521,
-0.015275495126843452,
-0.007868359796702862,
-0.05793150141835213,
-0.010301031172275543,
-0.038681142032146454,
-0.033633843064308167,
-0.007274176925420761,
0.008815504610538483,
-0.002108305227011442,
-0.04234861582517624,
0.007061987183988094,
-0.007464638911187649,
0.00833363737910986,
0.06932656466960907,
-0.0011130075436085463,
0.014355628751218319,
0.0010496112518012524,
0.03759472444653511,
-0.0016904360381886363,
-0.03285181522369385,
-0.014688907191157341,
-0.019152333959937096,
0.058453269302845,
-0.023214191198349,
0.0024869111366569996,
-0.02408386766910553,
0.007147700991481543,
0.005884585436433554,
-0.0594453290104866,
0.003907067701220512,
-0.022593913599848747,
-0.0033453640062361956,
0.00713815912604332,
0.03554448485374451,
-0.032254863530397415,
-0.004760075360536575,
-0.015146428719162941,
0.0030842151027172804,
-0.011995680630207062,
-0.022074826061725616,
0.009039724245667458,
-0.014394596219062805,
0.020952461287379265,
0.009454639628529549,
-0.010458938777446747,
-0.017143625766038895,
-0.010147775523364544,
-0.04016794264316559,
0.023487241938710213,
0.03294909745454788,
0.02216697856783867,
0.02146693505346775,
-0.0016295162495225668,
0.008446840569376945,
-0.021408380940556526,
-0.09450563788414001,
0.04383612051606178,
0.012502968311309814,
-0.03836261108517647,
0.01198756042867899,
0.016566650941967964,
0.020371193066239357,
0.06593823432922363,
-0.05352112650871277,
0.020502762869000435,
-0.031065499410033226,
-0.005078996066004038,
0.00433163158595562,
-0.07043881714344025,
-0.007524952758103609,
0.03390967473387718,
-0.04446108639240265,
-0.0029162189457565546,
-0.08067192882299423,
0.0010048499098047614,
0.011958207935094833,
-0.005963639821857214,
-0.0074769677594304085,
0.01081211306154728,
0.004830585326999426,
-0.0021880134008824825,
0.00997065007686615,
-0.027069631963968277,
0.03917468339204788,
0.0255227442830801,
0.016592063009738922,
-0.029904969036579132,
-0.03726053982973099,
-0.02179686166346073,
-0.002808067249134183,
0.04093446955084801,
0.026530427858233452,
-0.015548059716820717,
-0.006067367270588875,
-0.04640568792819977,
0.02980940043926239,
-0.043140508234500885,
0.0073639643378555775,
-0.06633873283863068,
0.04758983105421066,
-0.028364483267068863,
-0.025083113461732864,
-0.022177033126354218,
0.033522624522447586,
0.025061925873160362,
-0.02535267360508442,
0.02304944209754467,
0.027037175372242928,
-0.007857694290578365,
-0.00991805549710989,
0.016682829707860947,
-0.0038898829370737076,
0.026252303272485733,
-0.012332987040281296,
-0.05340033397078514,
0.04374994710087776,
-0.021306395530700684,
-0.08488762378692627,
0.03175410255789757,
0.002377853961661458,
0.0064161247573792934,
0.02053096890449524,
0.0027844863943755627,
0.008137039840221405,
0.04559876769781113,
-0.03200520575046539,
0.013317754492163658,
0.0320260114967823,
-0.035313986241817474,
-0.007504955865442753,
-0.017702016979455948,
0.002910334151238203,
0.025795988738536835,
0.002012004377320409,
0.047115571796894073,
0.03747183829545975,
0.005004544742405415,
-0.009862933307886124,
-0.0318378321826458,
0.02453906647861004,
0.04987137392163277,
0.06324589252471924,
0.008893271908164024,
0.003403258975595236,
0.05544362589716911,
-0.03759734332561493,
0.02735089510679245,
0.02067265845835209,
-0.029453838244080544,
-0.10081061720848083,
-0.012789220549166203,
-0.009103266522288322,
0.010759872384369373,
0.03402666002511978,
-0.0451679453253746,
0.011389474384486675,
0.000844930880703032,
-0.05898861214518547,
0.026261288672685623,
-0.04050594940781593,
0.004932011011987925,
-0.02623879909515381,
-0.04342740401625633,
-0.04093177989125252,
0.07314473390579224,
0.037211913615465164,
0.08210811764001846,
0.014510192908346653,
0.023342793807387352,
-0.0049706087447702885,
-0.03594689816236496,
-0.01310080848634243,
0.015578321181237698,
0.009109768085181713,
-0.02778092585504055,
0.08369819074869156,
-0.016162758693099022,
-0.047519437968730927,
0.03694877028465271,
0.009905913844704628,
0.01056211069226265,
-0.011430010199546814,
0.017669236287474632,
0.011005055159330368,
0.007793787866830826,
0.0028884224593639374,
-0.00725398026406765,
-0.0027230526320636272,
0.02457132562994957,
0.04157542437314987,
0.0029319399036467075,
0.014803466387093067,
-0.002622127067297697,
-0.04403004050254822,
-0.052150528877973557,
-0.022236019372940063,
0.04267827421426773,
-0.05512866750359535,
-0.030666273087263107,
-0.009899077005684376,
-0.0004908753326162696,
0.0006414243252947927,
0.007807739544659853,
0.012561574578285217,
0.0039308504201471806,
-0.02570340596139431,
0.02666955254971981,
0.015176884829998016,
0.03028925135731697,
0.026512140408158302,
-0.01342259906232357,
-0.035359062254428864,
0.04421951249241829,
0.012098102830350399,
-0.004763189237564802,
-0.02195466309785843,
-0.0073658134788274765,
0.017881879583001137,
0.017253288999199867,
-0.003670113394036889,
-0.03796727582812309,
-0.03711269423365593,
0.0023991086054593325,
0.01481635496020317,
0.0356578603386879,
-0.02174815721809864,
-0.05378983914852142,
-0.0010060345521196723,
-0.02189445123076439,
0.04543516784906387,
0.0060581909492611885,
0.007161596789956093,
0.0023219394497573376,
-0.014559188857674599,
-0.015550332143902779,
0.016795402392745018,
0.05632827803492546,
0.01463368535041809,
-0.007433130871504545,
0.03488333150744438,
0.0009615440503694117,
0.012972268275916576,
-0.023681078106164932,
0.0019803126342594624,
-0.023665575310587883,
-0.005924589931964874,
0.013065522536635399,
-0.02009960450232029,
-0.02262628823518753,
0.06474070996046066,
0.030230412259697914,
-0.012419851496815681,
0.014213772490620613,
0.008127952925860882,
-0.03499103710055351,
0.048956625163555145,
0.016971521079540253,
-0.029151443392038345,
0.05828232690691948,
0.005013772752135992,
0.03422875702381134,
0.012945381924510002,
-0.019132765009999275,
-0.021900679916143417,
0.013847320340573788,
-0.02699737250804901,
-0.010331771336495876,
0.004863131791353226,
0.007226638961583376,
0.05582500621676445,
-0.025195004418492317,
-0.002466930542141199,
0.03796228766441345,
0.005355829373002052,
-0.0014837312046438456,
0.05598339065909386,
-0.0013132455060258508,
0.031145475804805756,
0.027612987905740738,
-0.021654488518834114,
0.01902148872613907,
0.02649519592523575,
0.02227184921503067,
0.02992791123688221,
-0.005284962244331837,
-0.016856223344802856,
0.013916120864450932,
0.015283016487956047,
0.020849619060754776,
0.024011977016925812,
0.007083179894834757,
0.01224515214562416,
0.011148123070597649,
0.02738148346543312,
0.0334322452545166,
-0.011049238033592701,
-0.0012731773313134909,
-0.01833779364824295,
-0.026246091350913048,
0.0548970028758049,
-0.04269023984670639,
0.005227182060480118,
0.01526718121021986,
-0.02514663152396679,
-0.020102083683013916,
0.004677873104810715,
0.0068768286146223545,
0.052571311593055725,
0.016215134412050247,
-0.04002007097005844,
-0.03274505212903023,
0.010726159438490868,
0.01991312764585018,
-0.049126036465168,
-0.011222031898796558,
0.030091628432273865,
-0.024370016530156136,
-0.04195863753557205,
-0.006901039741933346,
-0.03478563576936722,
-0.025649337098002434,
0.009018673561513424,
0.03545426204800606,
0.03429563716053963,
-0.020816760137677193,
-0.036393679678440094,
-0.0403406098484993,
0.04298720881342888,
0.0016539929201826453,
-0.002294473582878709,
-0.02473994717001915,
0.024091504514217377,
-0.03680814430117607,
0.002397720003500581
] |
<p>I am quite interested in the understanding of the relation between p_ip wave superconductor(SC) and the Moore-Read(MR) state.</p>
<p>They share many similar properties, for example, p+ip SC has majorana as vortex excitation, MR has nonabelian quasi hole excitation. More interestingly, their wavefuncions are similar to some extent. All of them can be found in Read and Green's paper: <a href="http://arxiv.org/pdf/cond-mat/9906453v3.pdf" rel="nofollow">http://arxiv.org/pdf/cond-mat/9906453v3.pdf</a>. (where you can find the wavefunction for p+ip SC in eqn.12 and above, MR wavefunction in eqn.5.1 in <a href="http://www.physics.rutgers.edu/~gmoore/MooreReadNonabelions.pdf" rel="nofollow">http://www.physics.rutgers.edu/~gmoore/MooreReadNonabelions.pdf</a>).</p>
<p>These two wave functions are similar only when electrons are separated far from each other, as shown in eqn 16 in Read Green's paper.</p>
<p>Does anyone know how to explain the relation between these two states? Why they share similar property at long distance?</p>
<p>Thanks in advance.</p>
| 10,755 |
[
-0.012131056748330593,
0.00021110946545377374,
0.008388863876461983,
-0.033141445368528366,
-0.005303335376083851,
0.02516724169254303,
-0.012799072079360485,
-0.02469595894217491,
0.05557785555720329,
-0.05431854724884033,
0.029338961467146873,
0.03431277722120285,
0.04470827430486679,
0.02155160717666149,
-0.011622998863458633,
0.015274864621460438,
-0.010001943446695805,
-0.018629804253578186,
0.004177886992692947,
-0.05187066271901131,
0.01709136739373207,
0.03268568217754364,
0.01676623709499836,
0.02287418581545353,
-0.03615155816078186,
0.01728127710521221,
0.03084215335547924,
0.012277244590222836,
0.04443331062793732,
0.045159902423620224,
-0.004775398876518011,
-0.06847289949655533,
-0.009721592999994755,
0.009545376524329185,
-0.010272926650941372,
-0.006267723627388477,
-0.04057859629392624,
-0.036108750849962234,
0.015232675708830357,
0.030357811599969864,
-0.013221808709204197,
0.011595617979764938,
-0.030027959495782852,
0.022612161934375763,
-0.01466675940901041,
0.01616651751101017,
0.012339210137724876,
-0.04829360172152519,
0.04083483666181564,
-0.06724745780229568,
0.04367287456989288,
-0.03428571671247482,
0.01080841664224863,
-0.0006538273300975561,
-0.004596295766532421,
-0.02222272753715515,
0.07656478881835938,
0.11283265799283981,
-0.021942896768450737,
-0.06872953474521637,
0.02839975617825985,
-0.012125898152589798,
-0.010776651091873646,
-0.0341886542737484,
-0.05907811224460602,
0.004234701860696077,
0.014019857160747051,
-0.026079421862959862,
0.019605174660682678,
0.008876010775566101,
0.02633063867688179,
0.022747553884983063,
-0.0006258311914280057,
-0.010611738078296185,
0.03902440145611763,
-0.032012008130550385,
0.017400626093149185,
-0.0004365866188891232,
0.02347181737422943,
0.030041474848985672,
-0.02860378846526146,
0.008177844807505608,
-0.0033754429314285517,
-0.02985985204577446,
-0.01995226927101612,
-0.003465644083917141,
0.053739070892333984,
-0.034907158464193344,
0.006794204004108906,
0.019909285008907318,
0.015592710115015507,
0.0006212983280420303,
0.041588738560676575,
-0.005665121134370565,
-0.046336494386196136,
0.00861961767077446,
0.022328678518533707,
0.03466227650642395,
-0.028428183868527412,
-0.005851186346262693,
-0.0319962315261364,
-0.05213493853807449,
-0.012312786653637886,
0.06301488727331161,
0.024769723415374756,
-0.03837025910615921,
-0.014658290892839432,
0.028930364176630974,
-0.01316282618790865,
-0.005589490756392479,
-0.028607308864593506,
0.014457723125815392,
0.0028233041521161795,
0.003614036599174142,
-0.02431272715330124,
-0.04559134319424629,
0.023849215358495712,
-0.018002832308411598,
0.064762182533741,
0.08297038078308105,
0.026073819026350975,
-0.0391620472073555,
0.034259624779224396,
-0.05326090380549431,
-0.06745216250419617,
0.02760939858853817,
0.020299050956964493,
-0.000209483623621054,
-0.001072577782906592,
0.014135710895061493,
-0.024971622973680496,
0.011166888289153576,
0.056771859526634216,
-0.01703067310154438,
0.023252859711647034,
-0.004589664749801159,
-0.10425220429897308,
-0.025878561660647392,
0.04091466963291168,
-0.018298393115401268,
-0.011024508625268936,
-0.0665048211812973,
0.021724199876189232,
0.025458578020334244,
0.09705449640750885,
-0.005980337038636208,
-0.006736838724464178,
-0.029465852305293083,
0.04365815222263336,
0.02440633624792099,
0.023228177800774574,
-0.02654043585062027,
-0.006729962304234505,
-0.029769688844680786,
-0.02766086719930172,
-0.04841901734471321,
0.0018442001892253757,
0.01777208410203457,
-0.008636517450213432,
-0.00013083322846796364,
0.08239644765853882,
-0.01636185124516487,
0.017341088503599167,
-0.01183883287012577,
0.008809606544673443,
-0.03216753900051117,
0.10888572037220001,
0.003070391248911619,
0.032324571162462234,
0.08373767137527466,
-0.01987731084227562,
0.006850284989923239,
0.00782932061702013,
0.020797530189156532,
-0.0034263681154698133,
-0.021862005814909935,
-0.02754983864724636,
-0.04258822277188301,
-0.00848334189504385,
0.00433596083894372,
-0.03759903088212013,
-0.03030199185013771,
-0.035968270152807236,
0.001729431445710361,
0.0036970151122659445,
0.03314918279647827,
-0.017145324498414993,
-0.031108731403946877,
-0.017817504703998566,
-0.06327304989099503,
-0.00656369561329484,
-0.0004642940766643733,
0.0037230036687105894,
-0.006755162496119738,
-0.019545357674360275,
0.06586906313896179,
-0.023919805884361267,
0.017703868448734283,
0.004865669645369053,
-0.03810061141848564,
-0.004475501831620932,
0.016048725694417953,
-0.025719203054904938,
0.00425349734723568,
0.020070413127541542,
0.020384641364216805,
0.025117848068475723,
-0.009511185809969902,
0.038350023329257965,
-0.06822587549686432,
-0.033161360770463943,
0.007313443347811699,
0.006405213847756386,
0.021891120821237564,
0.03635407239198685,
0.016284724697470665,
-0.005374987609684467,
0.0165745560079813,
-0.028824076056480408,
-0.0007323514437302947,
-0.019465956836938858,
0.06474509835243225,
0.04064767435193062,
0.03812128305435181,
-0.011036636307835579,
0.010974763892591,
0.02858617529273033,
0.03823140636086464,
-0.00811422523111105,
-0.026502693071961403,
-0.07831282168626785,
-0.016871770843863487,
0.0231793113052845,
0.03257385268807411,
-0.029218291863799095,
0.015627391636371613,
0.028776343911886215,
0.04571918025612831,
0.06419917196035385,
0.01874801702797413,
-0.005126609466969967,
-0.01741846278309822,
0.0069926525466144085,
0.040216993540525436,
-0.014774148352444172,
-0.027425017207860947,
0.03217460960149765,
0.022273482754826546,
0.021815212443470955,
-0.014640571549534798,
-0.043291229754686356,
0.04564380645751953,
0.006327459588646889,
0.01758773997426033,
-0.02115548402070999,
-0.03388579562306404,
0.02820650488138199,
-0.038994502276182175,
-0.007891249842941761,
0.02265148051083088,
0.01662132702767849,
0.007160862907767296,
-0.023080047219991684,
-0.019455615431070328,
0.025834325700998306,
-0.025088325142860413,
-0.052787717431783676,
-0.026069102808833122,
0.00682322820648551,
-0.03447311744093895,
-0.004043898545205593,
-0.020797153934836388,
0.015715040266513824,
-0.00614211754873395,
0.06029961630702019,
-0.021903473883867264,
0.035991471260786057,
0.05901592969894409,
-0.033767569810152054,
-0.036096591502428055,
0.009433882310986519,
-0.04671706631779671,
0.016195379197597504,
-0.006677884142845869,
-0.04717453196644783,
0.013397898524999619,
-0.05098526552319527,
-0.007113993167877197,
0.009436060674488544,
-0.012257461436092854,
-0.01329731848090887,
-0.03356918320059776,
-0.022581951692700386,
-0.06483545154333115,
-0.007517090067267418,
-0.020910410210490227,
0.001663446775637567,
-0.037078969180583954,
-0.0057066623121500015,
0.07456232607364655,
0.006046212278306484,
-0.014767571352422237,
0.01771540194749832,
-0.0021539535373449326,
-0.010546707548201084,
0.02928733639419079,
0.003329692641273141,
-0.002542685018852353,
-0.00013682733697351068,
0.016587764024734497,
0.05075479671359062,
-0.017236391082406044,
-0.027070172131061554,
-0.027839163318276405,
-0.05820821598172188,
0.027482010424137115,
-0.0008171082590706646,
0.020542172715067863,
-0.029396042227745056,
-0.03517049923539162,
0.06539760529994965,
-0.023961178958415985,
-0.011800003238022327,
-0.00892048142850399,
-0.003476025303825736,
-0.05086050182580948,
0.014866586774587631,
0.014958055689930916,
0.07070739567279816,
-0.004965647589415312,
0.054554179310798645,
0.02806687168776989,
0.03717808052897453,
0.03475574404001236,
0.016438310965895653,
0.010836907662451267,
0.009856484830379486,
0.023353619500994682,
0.0059995632618665695,
0.09023088961839676,
-0.04116123542189598,
-0.027597742155194283,
0.029652351513504982,
-0.002049311064183712,
0.009689503349363804,
0.022975774481892586,
-0.03798592835664749,
0.05404513329267502,
-0.0157238207757473,
0.008947217836976051,
-0.011309393681585789,
0.041503921151161194,
-0.024215709418058395,
-0.0006079984595999122,
-0.020265702158212662,
0.03649996221065521,
0.046261243522167206,
-0.036465153098106384,
-0.008407262153923512,
0.028952645137906075,
0.006559461355209351,
-0.013709735125303268,
-0.015529393218457699,
-0.00966622307896614,
-0.01214556023478508,
-0.0011865313863381743,
-0.03807831183075905,
-0.03709008917212486,
0.016697676852345467,
0.009394830092787743,
0.03752850741147995,
0.009173143655061722,
-0.0121225630864501,
0.018536563962697983,
-0.057807404547929764,
-0.020591113716363907,
-0.034891583025455475,
0.05207936093211174,
0.02140919491648674,
0.08512002974748611,
0.026722997426986694,
-0.01467145700007677,
-0.014825600199401379,
0.0006165119702927768,
-0.07387975603342056,
-0.012052667327225208,
-0.014981045387685299,
-0.023472147062420845,
0.026051152497529984,
0.004258670844137669,
0.00533052533864975,
0.00160301779396832,
-0.028988691046833992,
-0.002547773765400052,
-0.047521766275167465,
-0.05597815290093422,
-0.009242089465260506,
-0.015102585777640343,
-0.011765099130570889,
-0.0289375688880682,
0.030776910483837128,
-0.015007452107965946,
-0.02692249044775963,
-0.015186234377324581,
0.0340130440890789,
-0.06889063119888306,
0.021553942933678627,
0.015003579668700695,
0.022289518266916275,
0.006962304934859276,
0.001124033471569419,
0.047407303005456924,
-0.00282018119469285,
-0.020472273230552673,
-0.009892323985695839,
-0.0027080231811851263,
0.05347409099340439,
0.023839065805077553,
-0.017013248056173325,
0.006991674657911062,
-0.017898080870509148,
-0.014453569427132607,
-0.009980282746255398,
0.0740322396159172,
0.016370058059692383,
0.004997446667402983,
0.03041631542146206,
0.009375115856528282,
-0.04036705195903778,
0.03604082018136978,
0.03143800422549248,
0.005401399917900562,
-0.01808970421552658,
-0.04789707064628601,
0.004613970406353474,
-0.032866593450307846,
-0.015437803231179714,
0.00947131123393774,
-0.027045805007219315,
-0.011940030381083488,
-0.001933818100951612,
0.029292549937963486,
0.006402670871466398,
-0.02113955467939377,
-0.039212845265865326,
-0.009014942683279514,
0.0159615408629179,
-0.02744520828127861,
0.004965175874531269,
0.008446089923381805,
0.024438505992293358,
0.06593159586191177,
-0.028183920308947563,
0.04145148769021034,
-0.03306343033909798,
-0.012539129704236984,
0.036024827510118484,
0.008052093908190727,
0.015269659459590912,
-0.028256170451641083,
-0.07819627970457077,
-0.018824197351932526,
0.036917947232723236,
-0.003269915236160159,
0.043323814868927,
0.007762730587273836,
-0.010275413282215595,
-0.055036693811416626,
-0.017502954229712486,
-0.02340184897184372,
0.023898422718048096,
0.0060238586738705635,
0.038901716470718384,
-0.023275109007954597,
-0.03444866091012955,
-0.01326845120638609,
-0.015168937854468822,
0.03403046727180481,
0.05102944001555443,
-0.019018439576029778,
-0.000629727088380605,
0.005529097747057676,
0.005175212398171425,
-0.020736318081617355,
-0.10115955024957657,
0.01736527495086193,
-0.0063043213449418545,
0.005754723213613033,
0.008899186737835407,
-0.028901752084493637,
-0.03518366813659668,
0.018019935116171837,
-0.0016672589117661119,
0.026072250679135323,
0.01906684786081314,
-0.01830057054758072,
0.06483664363622665,
0.03465778008103371,
-0.030997231602668762,
0.03345855325460434,
-0.014023801311850548,
0.008307195268571377,
-0.0015470994403585792,
-0.007134473882615566,
0.05093192309141159,
-0.01582336239516735,
0.021242450922727585,
-0.03432278707623482,
0.011302839033305645,
-0.055143143981695175,
0.05910370871424675,
-0.054946642369031906,
0.023122096434235573,
-0.0386202298104763,
-0.0014985406305640936,
-0.014205367304384708,
0.020131945610046387,
-0.02819221094250679,
0.01334221288561821,
0.034268997609615326,
0.009241582825779915,
-0.0006968159577809274,
-0.019052784889936447,
0.03918922320008278,
0.00026560056721791625,
-0.011174685321748257,
0.06443191319704056,
-0.020791132003068924,
0.037002552300691605,
-0.056042272597551346,
-0.021924396976828575,
0.013325391337275505,
-0.07513394951820374,
0.028751315549016,
-0.007794822566211224,
-0.017226645722985268,
0.011638334020972252,
-0.0042838966473937035,
-0.0018136502476409078,
0.06400749832391739,
-0.02063683792948723,
-0.013489981181919575,
-0.01580001786351204,
0.03637124225497246,
0.02274651639163494,
-0.026402831077575684,
-0.08101152628660202,
-0.07412995398044586,
0.041092898696660995,
0.03835850581526756,
-0.018597569316625595,
-0.042369186878204346,
0.004094680771231651,
-0.03147793933749199,
0.013248368166387081,
0.015092958696186543,
0.016148949041962624,
-0.08253167569637299,
-0.03896432742476463,
0.023973863571882248,
0.012394979596138,
0.08724779635667801,
0.015232892706990242,
-0.015979621559381485,
-0.013286609202623367,
-0.017249319702386856,
0.03134685754776001,
0.009480183944106102,
0.04803828150033951,
-0.008352290838956833,
-0.04920823127031326,
-0.046422865241765976,
-0.00433080829679966,
0.06282776594161987,
-0.036607421934604645,
-0.030764063820242882,
0.03449699282646179,
0.009076282382011414,
0.04378240182995796,
0.02368473820388317,
-0.019764859229326248,
0.01935405097901821,
-0.00081981549737975,
-0.0064216116443276405,
-0.026759006083011627,
-0.04244315251708031,
-0.02742844447493553,
0.008201281540095806,
-0.003487737849354744,
-0.0035923232790082693,
-0.0002924450964201242,
0.06731344759464264,
-0.026482170447707176,
0.01701481267809868,
0.04023592919111252,
-0.01426409650593996,
0.02058383636176586,
-0.00628711748868227,
0.012572837993502617,
0.0010760759469121695,
0.02602791227400303,
-0.01288388017565012,
-0.03739485144615173,
-0.0640449970960617,
-0.01490733027458191,
0.052147869020700455,
0.015027749352157116,
-0.004110323265194893,
-0.022747745737433434,
-0.02922535128891468,
-0.02252921089529991,
-0.028267154470086098,
-0.029588399454951286,
0.010682092979550362,
-0.017357435077428818,
0.028222080320119858,
-0.032340358942747116,
-0.008115390315651894,
0.01766418106853962,
0.07870669662952423,
-0.036420002579689026,
0.00530465692281723,
0.03961235284805298,
0.007872479036450386,
0.06685347110033035,
-0.006542429327964783,
-0.012684041634202003,
0.06915360689163208,
-0.02103881537914276,
0.0503876656293869,
-0.012672582641243935,
0.020667411386966705,
0.043304719030857086,
0.023241214454174042,
0.028485901653766632,
-0.02913743630051613,
-0.05486244708299637,
-0.02434985339641571,
0.03231099992990494,
0.04878600686788559,
-0.0011340816272422671,
0.0307155791670084,
0.001877624075859785,
0.016127781942486763,
-0.007859217934310436,
0.031760323792696,
-0.03361058235168457,
-0.04974564164876938,
-0.011530090123414993,
-0.019528858363628387,
-0.04506782069802284,
0.0449925996363163,
-0.009379248134791851,
-0.018445638939738274,
0.036729324609041214,
-0.03117326833307743,
0.04308575019240379,
0.011954526416957378,
-0.021732384338974953,
0.010746092535555363,
0.04564546421170235,
-0.010604750365018845,
0.019384242594242096,
0.0031807490158826113,
-0.02072320505976677,
0.13075211644172668,
0.02581268735229969,
0.032074276357889175,
-0.0819048136472702,
0.027853751555085182,
-0.01952865533530712,
0.028905361890792847,
-0.041686419397592545,
0.001456484547816217,
0.007176951039582491,
-0.0015227777184918523,
0.0157525185495615,
0.045779384672641754,
0.011675504967570305,
0.008166363462805748,
0.028213759884238243,
-0.01663118042051792,
-0.028280090540647507,
0.012124983593821526,
0.022168179973959923,
-0.023652177304029465,
-0.02044547349214554,
-0.0052324808202683926,
-0.010390765964984894,
-0.057195741683244705,
0.007099197246134281,
-0.044156283140182495,
-0.04562767595052719,
0.0468594990670681,
0.0010145650012418628,
0.014581102877855301,
0.009742291644215584,
-0.02952839620411396,
0.015395834110677242,
-0.00009232079901266843,
0.024060020223259926,
0.03577840328216553,
0.006533422507345676,
0.03563692420721054,
0.04356210306286812,
0.024320565164089203,
-0.03696514293551445,
0.026717428117990494,
0.012015719898045063,
-0.0410039983689785,
0.01713641732931137,
-0.02070530876517296,
0.024163048714399338,
-0.01667870208621025,
-0.019675450399518013,
0.014897577464580536,
0.014648627489805222,
0.014367781579494476,
-0.03723138943314552,
-0.03536485508084297,
-0.0050592985935509205,
0.013397551141679287,
-0.019899537786841393,
0.02472974732518196,
-0.009839706122875214,
0.017289333045482635,
0.015154690481722355,
-0.0025569729041308165,
-0.0015170275000855327,
0.011114625260233879,
0.01155075989663601,
-0.01112070307135582,
0.02060161530971527,
-0.004189147148281336,
0.0195440873503685,
-0.017262490466237068,
-0.0016079647466540337,
-0.02356443554162979,
-0.013412857428193092,
0.012309608981013298,
0.014293917454779148,
0.026274727657437325,
0.019466936588287354,
-0.014273921959102154,
-0.006959773600101471,
-0.052994515746831894,
0.008824476040899754,
0.021417783573269844,
-0.0053476872853934765,
0.010042116977274418,
0.009434526786208153,
0.0337265320122242,
0.04065029323101044,
0.0007135781343095005,
0.016699112951755524,
-0.0042193057015538216,
0.02376749739050865,
0.006768857594579458,
-0.051075804978609085,
-0.019281668588519096,
-0.023796124383807182,
-0.05677144229412079,
0.014100211672484875,
-0.0361756905913353,
0.008769968524575233,
0.002228886354714632,
0.0014528862666338682,
-0.0021281414665281773,
0.03633607178926468,
-0.012866332195699215,
-0.02313162200152874,
0.018823858350515366,
-0.05215420946478844,
0.015144088305532932,
0.02090894803404808,
0.03332291916012764,
0.014264854602515697,
0.015825554728507996,
-0.009745367802679539,
0.0006520142778754234,
-0.004941113293170929,
0.005652294028550386,
-0.0706951767206192,
-0.0016908739926293492,
-0.0074939304031431675,
-0.0008097834070213139,
-0.03611437976360321,
-0.030864037573337555,
-0.044119417667388916,
0.013611124828457832,
-0.021327612921595573,
0.017378149554133415,
-0.003899950999766588,
0.033992867916822433,
-0.04079707711935043,
-0.02870367094874382,
0.05296332761645317,
-0.0045557040721178055,
-0.04511824622750282,
0.011584047228097916,
0.0049734776839613914,
0.015490557067096233,
0.02764086425304413,
-0.015224824659526348,
-0.0019025338115170598,
0.020966341719031334,
-0.032535288482904434,
-0.036747220903635025,
0.017576439306139946,
-0.006426141131669283,
0.0546671599149704,
0.023680783808231354,
-0.028270618990063667,
-0.025200337171554565,
0.059385254979133606,
-0.0042880503460764885,
0.00043161233770661056,
-0.014640226028859615,
-0.023105671629309654,
0.022370582446455956,
-0.033721525222063065,
0.002062224317342043,
0.000058564797654980794,
-0.00022612279281020164,
0.039414193481206894,
0.02625199407339096,
-0.00459988322108984,
0.004220912698656321,
-0.038871388882398605,
-0.01566360890865326,
-0.01691046915948391,
0.025704609230160713,
-0.003273519454523921,
0.03325037285685539,
0.0023123063147068024,
-0.009219242259860039,
0.03377727046608925,
-0.008723210543394089,
0.013291310518980026,
-0.07112971693277359,
-0.016504792496562004,
0.009387016296386719,
-0.0036123546306043863,
0.05391140282154083,
-0.03554363548755646,
0.010876096785068512,
-0.0019604831468313932,
-0.07350601255893707,
0.022919759154319763,
-0.02603171393275261,
-0.00241308705881238,
-0.012084218673408031,
0.023878714069724083,
-0.008000236004590988,
0.07762816548347473,
0.004082801286131144,
0.03366061672568321,
0.03869352117180824,
0.017437215894460678,
-0.022788165137171745,
-0.019841423258185387,
-0.05552816763520241,
0.005311263725161552,
0.026259195059537888,
-0.021322079002857208,
0.049167606979608536,
-0.04420249164104462,
-0.007212386466562748,
0.0353410430252552,
-0.006619600113481283,
0.00809831079095602,
0.017663078382611275,
0.008507663384079933,
0.004655200056731701,
0.02211117185652256,
-0.015900293365120888,
-0.000701487879268825,
-0.039846714586019516,
-0.02710283175110817,
0.024266377091407776,
0.02934292145073414,
0.008616391569375992,
-0.021289069205522537,
-0.014772789552807808,
-0.01954299956560135,
-0.01737281307578087,
0.026286166161298752,
-0.0170315932482481,
-0.007453520316630602,
0.011868054047226906,
0.026166116818785667,
0.04036354273557663,
-0.030149828642606735,
0.03269123286008835,
-0.04223804920911789,
-0.015836309641599655,
0.012472555041313171,
-0.011741483584046364,
-0.010542549192905426,
0.02016034536063671,
0.010191898792982101,
-0.06777823716402054,
0.020004572346806526,
-0.0016190820606425405,
0.014939434826374054,
-0.03689683601260185,
-0.011897808872163296,
0.007873228751122952,
0.010486883111298084,
-0.0018865667516365647,
-0.06908402591943741,
-0.015210652723908424,
0.01583988592028618,
-0.03820841386914253,
0.02237640507519245,
-0.026197055354714394,
-0.03544169291853905,
0.0015882147708907723,
-0.02602187544107437,
0.03777667135000229,
-0.007654464803636074,
-0.01104413066059351,
-0.01643439568579197,
-0.04704032465815544,
0.022388827055692673,
0.025194993242621422,
0.07352088391780853,
0.026708396151661873,
-0.008698436431586742,
0.005653834901750088,
-0.0518471859395504,
0.015597733668982983,
-0.012966031208634377,
0.021069668233394623,
0.013571011833846569,
-0.01971065253019333,
0.03379317745566368,
0.006631073541939259,
-0.009508349001407623,
0.044613491743803024,
0.03331805393099785,
0.036881204694509506,
-0.025179803371429443,
-0.009039256721735,
-0.0311273206025362,
0.03152531757950783,
-0.004417027346789837,
-0.013773294165730476,
0.0598287507891655,
-0.006673050113022327,
0.03260813280940056,
0.044106196612119675,
-0.009378776885569096,
-0.046445783227682114,
0.028912778943777084,
-0.05689213424921036,
-0.02598405070602894,
0.018386652693152428,
-0.03220081329345703,
0.05196245387196541,
-0.05237514525651932,
-0.028125658631324768,
0.004481529351323843,
-0.043072331696748734,
-0.00010022343485616148,
0.08557240664958954,
0.03835318982601166,
0.02027406170964241,
-0.007840448059141636,
0.02239842899143696,
-0.00924940686672926,
0.004086845554411411,
0.038103144615888596,
0.05072569474577904,
0.03485335409641266,
0.015674514696002007,
0.025279352441430092,
0.0319526232779026,
0.019107501953840256,
-0.006985231302678585,
0.0010165483690798283,
0.016551649197936058,
0.002801802707836032,
0.004887176211923361,
0.047294601798057556,
-0.017289899289608,
-0.0007425696821883321,
0.02858983539044857,
-0.05037589371204376,
0.09728965908288956,
0.005859644152224064,
0.03439643606543541,
0.004860802553594112,
0.023065540939569473,
-0.022362427785992622,
-0.007648339029401541,
-0.0074462746270000935,
0.03747980669140816,
-0.0003747002047020942,
-0.03772902488708496,
-0.004804854281246662,
0.006477709859609604,
0.01697121560573578,
-0.048362135887145996,
-0.012398965656757355,
-0.019997984170913696,
-0.00045193868572823703,
-0.003154369769617915,
-0.015819396823644638,
-0.05910077318549156,
-0.003308437531813979,
0.03069950081408024,
0.03737511858344078,
-0.001531363115645945,
0.004654427524656057,
-0.02597799338400364,
0.0037367844488471746,
0.06322547048330307,
-0.06256633996963501,
0.010390247218310833,
-0.005702183581888676,
0.03618630766868591,
0.0103070680052042,
0.006467932369560003
] |
<p>I don't understand why there is necessarily a diffraction limitation on optical systems. Where does this limitation in focusing light come from? </p>
| 10,756 |
[
-0.03885958716273308,
-0.02498786523938179,
-0.002043686341494322,
-0.04429773986339569,
0.05011889711022377,
0.017478805035352707,
-0.039292048662900925,
-0.02599639818072319,
-0.028432602062821388,
-0.01149920467287302,
0.030867494642734528,
0.05667928233742714,
0.06258748471736908,
-0.004459063988178968,
0.009855283424258232,
-0.020569991320371628,
0.013136099092662334,
0.007077225483953953,
-0.012106804177165031,
-0.013033553026616573,
-0.036946333944797516,
0.06472314894199371,
0.011392301879823208,
-0.00024209746334236115,
-0.028296418488025665,
-0.0037507680244743824,
0.03352099284529686,
0.006143996026366949,
0.049680788069963455,
0.04560740292072296,
0.019660010933876038,
0.010117408819496632,
-0.014681131578981876,
0.04306905344128609,
0.03806360810995102,
-0.020826373249292374,
-0.0116506889462471,
-0.020900212228298187,
-0.03603163734078407,
-0.018676145002245903,
-0.01796330325305462,
0.0054202270694077015,
-0.02164585329592228,
0.0394802987575531,
-0.014295516535639763,
0.021329542621970177,
-0.0037314516957849264,
-0.034936875104904175,
0.010129748843610287,
-0.06828656047582626,
0.05579632893204689,
-0.016039123758673668,
0.061735861003398895,
0.04409593343734741,
0.0038377749733626842,
0.013042468577623367,
0.09113515168428421,
0.07327873259782791,
-0.02330424264073372,
-0.058813199400901794,
-0.03194227069616318,
0.01844530925154686,
-0.013165714219212532,
-0.015983108431100845,
-0.01841179095208645,
0.010998562909662724,
-0.006220798008143902,
-0.040497928857803345,
0.02268712781369686,
-0.021704019978642464,
-0.00016616440552752465,
0.0334043875336647,
0.03799024224281311,
-0.011317672207951546,
-0.026321230456233025,
-0.05015069991350174,
0.041619040071964264,
-0.03288133442401886,
0.02549154870212078,
0.027707066386938095,
0.00611910643056035,
0.026870181784033775,
0.0019066468812525272,
0.028123192489147186,
0.011491306126117706,
0.0028994064778089523,
0.07970034331083298,
-0.011633260175585747,
0.022450421005487442,
0.007205885369330645,
-0.01455559954047203,
0.03061136230826378,
0.03542013466358185,
0.004298391751945019,
-0.00371486134827137,
-0.012732292525470257,
-0.005736781749874353,
0.050389982759952545,
0.03339694067835808,
-0.03446425125002861,
0.015660827979445457,
-0.004986274056136608,
0.011665376834571362,
0.07337543368339539,
0.024577144533395767,
-0.013995983637869358,
-0.023032190278172493,
0.058825213462114334,
-0.005514792166650295,
0.012954913079738617,
-0.029642222449183464,
0.017478030174970627,
-0.0042103491723537445,
0.026952527463436127,
0.016687743365764618,
-0.014809772372245789,
0.014094630256295204,
-0.022343555465340614,
0.07144168764352798,
0.10824674367904663,
0.016113493591547012,
-0.011036837473511696,
0.0003624474920798093,
-0.01574162393808365,
-0.0708606168627739,
0.04875420033931732,
0.019690312445163727,
-0.021310726180672646,
-0.03415929526090622,
-0.01010388508439064,
0.029381467029452324,
0.010218827985227108,
0.00035132915945723653,
-0.015753449872136116,
0.003832711838185787,
-0.017966225743293762,
-0.10417759418487549,
-0.07008866220712662,
0.03125036135315895,
0.007885445840656757,
-0.02918083593249321,
-0.08309739828109741,
0.02858222834765911,
0.03411686792969704,
0.09857477992773056,
-0.015912819653749466,
0.021027585491538048,
-0.005695174913853407,
0.03967289626598358,
-0.0074926926754415035,
-0.02591175213456154,
-0.007126616779714823,
-0.0019328012131154537,
-0.01782131940126419,
0.01588582433760166,
-0.06830356270074844,
0.016611991450190544,
0.03078019618988037,
0.007552929222583771,
-0.06709699332714081,
0.017160184681415558,
-0.047165222465991974,
0.0050460416823625565,
0.004005468916147947,
-0.007288683671504259,
-0.04194995388388634,
0.07846751809120178,
0.02071068063378334,
0.0386064276099205,
0.06129072234034538,
-0.007635242771357298,
0.02633410133421421,
0.003872354282066226,
0.01723499968647957,
0.016410665586590767,
-0.029140491038560867,
-0.012984003871679306,
-0.0036754426546394825,
0.013091112487018108,
0.029185334220528603,
0.016300270333886147,
-0.023310810327529907,
0.029038205742836,
0.0036009792238473892,
0.013857071287930012,
0.047053396701812744,
-0.004925725981593132,
-0.004022576380521059,
-0.03026147373020649,
-0.05698239430785179,
0.014323038049042225,
-0.03487053140997887,
0.016717666760087013,
0.006926672533154488,
0.005961867514997721,
0.0035222088918089867,
-0.011322696693241596,
-0.005937113426625729,
-0.006936243269592524,
-0.03992301970720291,
-0.027158580720424652,
-0.005031253211200237,
-0.0027799883391708136,
0.017703518271446228,
0.07044938206672668,
0.06937458366155624,
0.058443184942007065,
0.020326314494013786,
0.02839081361889839,
-0.025005513802170753,
-0.015902705490589142,
0.02160239964723587,
-0.03688768297433853,
0.021817883476614952,
-0.012324824929237366,
-0.005606257822364569,
0.01818808540701866,
0.02762947976589203,
0.008799395523965359,
0.030477359890937805,
-0.010118773207068443,
0.08031029254198074,
0.043764617294073105,
-0.0024502582382410765,
0.010573201812803745,
0.030667619779706,
-0.004244075622409582,
-0.0006232316372916102,
-0.005322868935763836,
-0.028817880898714066,
-0.04798237979412079,
0.0029496345669031143,
0.012839295901358128,
0.03740828111767769,
-0.05065291002392769,
0.020429011434316635,
-0.003438979387283325,
0.04343266412615776,
0.04688418656587601,
0.028264356777071953,
-0.03577727824449539,
-0.004616249818354845,
0.008876048028469086,
0.023617364466190338,
0.00164279795717448,
0.023169020190835,
0.02364812232553959,
0.005892629269510508,
0.003066563280299306,
-0.02007180079817772,
-0.028018927201628685,
0.002514437772333622,
-0.017703332006931305,
-0.005671202205121517,
0.008555300533771515,
0.006073015742003918,
0.023600701242685318,
-0.016511136665940285,
0.010452057234942913,
0.007487434893846512,
-0.026002278551459312,
0.02370896376669407,
-0.07193443179130554,
-0.024783099070191383,
0.026927398517727852,
0.0021110069938004017,
-0.015703240409493446,
-0.02523813396692276,
0.03270439803600311,
-0.045164383947849274,
-0.005220114253461361,
-0.03508114442229271,
-0.005370534956455231,
-0.02033637836575508,
0.015231726691126823,
0.04704006016254425,
0.00979709718376398,
0.0565766915678978,
-0.035285383462905884,
-0.047695863991975784,
-0.02166185900568962,
-0.04471088945865631,
0.0015226020477712154,
-0.007045349571853876,
-0.025422638282179832,
0.0025616097263991833,
0.021524658426642418,
-0.03120388090610504,
0.03870004788041115,
-0.03462468460202217,
0.03063025325536728,
-0.02563798427581787,
-0.013730855658650398,
-0.018187347799539566,
-0.012963441200554371,
0.0014471886679530144,
0.003682643873617053,
-0.011984635144472122,
0.01956886425614357,
0.012739053927361965,
-0.025153443217277527,
-0.03576415404677391,
0.005341035313904285,
-0.04429151490330696,
-0.050229672342538834,
-0.0028222850523889065,
-0.004241548478603363,
0.03359545022249222,
-0.08356842398643494,
0.0022394941188395023,
0.017903929576277733,
-0.043688978999853134,
0.02298734337091446,
-0.005428928881883621,
-0.03470497205853462,
0.02768683433532715,
-0.017857281491160393,
0.055131398141384125,
-0.02395128272473812,
-0.026322919875383377,
0.05442740395665169,
0.03399806469678879,
-0.007093031425029039,
-0.048605721443891525,
-0.03352177143096924,
0.0068024275824427605,
-0.010521439835429192,
0.014429131522774696,
0.024863872677087784,
-0.013762158341705799,
0.07925860583782196,
-0.0005807801499031484,
0.0029583859723061323,
0.03235585615038872,
0.026527106761932373,
0.006898115389049053,
0.003158869221806526,
-0.020421044901013374,
-0.00877329334616661,
0.018816201016306877,
0.034561630338430405,
-0.04523668438196182,
0.046231240034103394,
-0.013232325203716755,
0.04233065992593765,
-0.019045190885663033,
-0.02696654573082924,
0.01800469122827053,
-0.038957711309194565,
0.030765855684876442,
-0.01133608166128397,
0.02863207459449768,
-0.019630832597613335,
0.03353303298354149,
0.019902387633919716,
0.012020464986562729,
0.03126927837729454,
-0.022728467360138893,
-0.032326553016901016,
0.007108587305992842,
0.03016936220228672,
-0.018748216331005096,
-0.008656688034534454,
0.015278982929885387,
-0.0033845859579741955,
0.01469692587852478,
0.017702845856547356,
-0.012377290986478329,
0.06551125645637512,
0.017271030694246292,
-0.0015455586835741997,
-0.007460691034793854,
-0.002618567319586873,
-0.008895652368664742,
-0.04662061855196953,
0.014525443315505981,
-0.007627512328326702,
0.0316074937582016,
0.018394842743873596,
0.032597627490758896,
0.042211081832647324,
0.027233527973294258,
0.010918490588665009,
-0.013407092541456223,
-0.0926862359046936,
-0.009713087230920792,
-0.017868543043732643,
-0.03154589235782623,
-0.054748669266700745,
-0.009047115221619606,
-0.02458983100950718,
-0.030362937599420547,
-0.019819386303424835,
-0.05114245414733887,
0.026264218613505363,
-0.04319176822900772,
0.033376943320035934,
-0.0005468604504130781,
-0.020865265280008316,
-0.018561068922281265,
0.021711697801947594,
-0.02127077430486679,
-0.01647387072443962,
0.023086747154593468,
0.029654957354068756,
-0.019976668059825897,
-0.007333350367844105,
0.0038960350211709738,
0.03991362452507019,
-0.002485834527760744,
0.0312962643802166,
0.007956940680742264,
0.04688287526369095,
-0.022987909615039825,
-0.007018569856882095,
0.025614773854613304,
0.04607349634170532,
0.003278263844549656,
0.0071119568310678005,
-0.03576280176639557,
-0.02979462780058384,
-0.026923540979623795,
-0.0099307456985116,
0.03529477119445801,
-0.01759791560471058,
-0.008151545189321041,
0.006635681726038456,
0.002888704417273402,
-0.028189625591039658,
0.0035819162148982286,
0.0007196931983344257,
0.022961320355534554,
-0.004260926507413387,
-0.06945601850748062,
-0.010908589698374271,
-0.05785541981458664,
0.01745712012052536,
0.04234996438026428,
0.008923384360969067,
-0.036487046629190445,
0.013223555870354176,
0.04319952428340912,
-0.02828225865960121,
-0.03067481331527233,
0.03574893996119499,
-0.01646989770233631,
-0.01988842524588108,
0.024415263906121254,
0.04286189004778862,
0.009533497504889965,
0.03599775582551956,
0.055239953100681305,
0.03211185708642006,
-0.010813845321536064,
-0.08048254251480103,
-0.017866164445877075,
0.02119072526693344,
0.004911704454571009,
-0.0065049841068685055,
0.002994196256622672,
-0.02482609637081623,
-0.036222901195287704,
0.021869070827960968,
-0.05165516212582588,
0.030514894053339958,
-0.042384497821331024,
-0.007052885368466377,
-0.02394290082156658,
-0.02918911539018154,
-0.018609076738357544,
-0.006506057921797037,
-0.0018019645940512419,
-0.010210217908024788,
0.014597596600651741,
0.01521147508174181,
-0.02400047704577446,
0.005851083900779486,
0.018854841589927673,
0.04701199010014534,
0.023569688200950623,
-0.0256742425262928,
0.007430599071085453,
0.03691994771361351,
-0.029719742015004158,
-0.06347236037254333,
0.013890307396650314,
0.01448851078748703,
-0.00822562538087368,
0.051037389785051346,
-0.049461428076028824,
-0.0202048160135746,
0.040996648371219635,
0.014167353510856628,
-0.020242560654878616,
0.009612170979380608,
-0.02896638587117195,
-0.01119614951312542,
0.03458114713430405,
0.0023224069736897945,
0.05883091315627098,
0.023595158010721207,
-0.031224824488162994,
0.0020043428521603346,
-0.0351179763674736,
0.07409781217575073,
-0.049886297434568405,
-0.013248877599835396,
0.01892593316733837,
0.019265616312623024,
-0.006402357015758753,
0.07772690057754517,
-0.0017649434739723802,
0.006393515504896641,
0.02392151765525341,
-0.0553956963121891,
-0.0062728384509682655,
0.021887117996811867,
0.027064355090260506,
-0.002050910610705614,
0.022484969347715378,
0.04070691764354706,
0.03277700021862984,
-0.012466884218156338,
0.002218568231910467,
0.002711761509999633,
0.001503374776802957,
0.01801571249961853,
0.017213013023138046,
-0.013856352306902409,
-0.058972109109163284,
-0.00039939963608048856,
0.00010319660214008763,
-0.00754574267193675,
0.07418274879455566,
-0.029144136235117912,
0.01620824635028839,
0.038100555539131165,
-0.06301053613424301,
-0.01013430766761303,
0.012432682327926159,
-0.050694987177848816,
0.06403311342000961,
-0.053443316370248795,
0.014390993863344193,
-0.014577972702682018,
0.005536393728107214,
-0.06461916118860245,
-0.012102806940674782,
0.008531621657311916,
0.0315629318356514,
-0.002473230240866542,
-0.018740518018603325,
0.018938422203063965,
0.006349632516503334,
-0.03829636052250862,
-0.022272663190960884,
0.01813909411430359,
-0.00400625541806221,
-0.039109427481889725,
0.02166554145514965,
0.005692738573998213,
0.02735363319516182,
-0.021945800632238388,
-0.04280376434326172,
0.02308260276913643,
-0.023613253608345985,
-0.0010544453980401158,
0.0028843542095273733,
0.03959307447075844,
-0.0406661294400692,
-0.0670851320028305,
-0.014456043019890785,
-0.034665513783693314,
0.013150419108569622,
-0.02388204261660576,
0.007946884259581566,
0.0215777438133955,
0.018796227872371674,
-0.013077648356556892,
-0.017969414591789246,
0.04341951757669449,
-0.02530321292579174,
0.00712452782317996,
0.011095259338617325,
-0.003908300772309303,
-0.05051175132393837,
-0.045606791973114014,
0.04747575893998146,
0.029390091076493263,
0.016230221837759018,
-0.009557711891829967,
0.055661167949438095,
0.002029114169999957,
-0.0077134608291089535,
0.010296471416950226,
0.011138820089399815,
0.03872300311923027,
0.010489762760698795,
0.017612703144550323,
0.019037431105971336,
0.018157880753278732,
-0.0004952448653057218,
-0.02414935827255249,
-0.015428193844854832,
0.00804708432406187,
0.07540318369865417,
-0.03341054543852806,
0.0604073666036129,
-0.0010849203681573272,
-0.01342057529836893,
-0.02094988524913788,
-0.009308140724897385,
0.0011985241435468197,
0.01420905627310276,
-0.03249943256378174,
0.045451123267412186,
-0.034515395760536194,
-0.009220900945365429,
0.007795865181833506,
0.04267289862036705,
0.01969975419342518,
-0.01733352802693844,
0.01263033039867878,
0.03864607959985733,
0.001627965597435832,
-0.04474451020359993,
-0.04053856059908867,
0.03891921788454056,
-0.05766802281141281,
0.01804802194237709,
0.012183668091893196,
-0.005090645048767328,
0.021204039454460144,
-0.06790103018283844,
0.017523929476737976,
-0.053302403539419174,
-0.011230699717998505,
-0.01734289899468422,
-0.006687259301543236,
0.0002460130781400949,
0.007716359570622444,
0.009304782375693321,
-0.01034022681415081,
0.01486934907734394,
0.008989139460027218,
0.01780572719871998,
0.0029356644954532385,
-0.08569133281707764,
-0.05938529223203659,
-0.07064017653465271,
-0.04453527182340622,
0.03023073635995388,
-0.0012277476489543915,
-0.008411830291152,
-0.019449040293693542,
-0.03803630918264389,
0.007779044099152088,
0.013199854642152786,
0.005523315630853176,
-0.022252487018704414,
0.02129768766462803,
0.03903978317975998,
0.04683857411146164,
0.0228318702429533,
0.00361002329736948,
0.11128468811511993,
0.03272875398397446,
0.018082842230796814,
-0.03933394327759743,
0.01566578820347786,
-0.028347773477435112,
0.006881133187562227,
-0.048222776502370834,
0.05079110339283943,
0.003097226144745946,
0.03482851758599281,
-0.00651848828420043,
0.025818035006523132,
0.033175598829984665,
-0.0038525245618075132,
0.04161664471030235,
-0.06716635823249817,
-0.0445706732571125,
0.04538613185286522,
0.02838382124900818,
0.020608866587281227,
0.03446929529309273,
-0.03451921418309212,
-0.007797237019985914,
-0.040084775537252426,
-0.0017057840013876557,
-0.009363621473312378,
-0.050570759922266006,
0.029078537598252296,
0.006176247261464596,
-0.02381872944533825,
-0.01616038754582405,
0.008194154128432274,
-0.018179621547460556,
-0.046264104545116425,
0.015585513785481453,
0.025247743353247643,
-0.009158007800579071,
-0.003754968987777829,
-0.0008768573752604425,
0.008879918605089188,
-0.011476073414087296,
0.015336870215833187,
-0.010752106085419655,
-0.026581082493066788,
-0.02041548863053322,
-0.02277754805982113,
0.023712601512670517,
-0.026199106127023697,
0.04458673670887947,
0.030918192118406296,
0.011031550355255604,
-0.006700985133647919,
-0.06902599334716797,
-0.005604128818958998,
0.007259681820869446,
-0.0007513439632020891,
-0.020386282354593277,
-0.05157260224223137,
0.00954893697053194,
0.022839907556772232,
0.009805829264223576,
0.028776954859495163,
-0.024471858516335487,
0.027973173186182976,
0.012896973639726639,
0.0016556843183934689,
0.03554550185799599,
-0.004687492735683918,
-0.03880869597196579,
-0.0294042881578207,
0.020040445029735565,
-0.017033325508236885,
-0.021647393703460693,
0.028651108965277672,
0.025345008820295334,
0.025419581681489944,
-0.005900243762880564,
0.007058505434542894,
-0.010871894657611847,
-0.05187077820301056,
0.015653688460588455,
-0.023670198395848274,
-0.04619264975190163,
-0.026069078594446182,
0.03154256194829941,
0.034058015793561935,
0.06465833634138107,
-0.008178941905498505,
0.02555805817246437,
-0.016894863918423653,
0.020852789282798767,
0.021063968539237976,
0.00185663893353194,
-0.06243489682674408,
0.03322431445121765,
0.005170541815459728,
0.01128770224750042,
0.022690998390316963,
0.015244088135659695,
0.024649279192090034,
0.0329689085483551,
0.051427412778139114,
0.02499789372086525,
-0.06166745349764824,
-0.0016021530609577894,
0.03323949873447418,
-0.039456095546483994,
0.02872200682759285,
-0.023160897195339203,
0.004826531745493412,
-0.037435442209243774,
-0.0451948419213295,
-0.03974766284227371,
-0.011599273420870304,
0.05288689583539963,
0.04415401816368103,
0.03699946403503418,
-0.019785355776548386,
-0.017827507108449936,
0.011135537177324295,
-0.02656550519168377,
-0.02364705130457878,
-0.04690641537308693,
0.026875650510191917,
-0.02838563360273838,
-0.006306726019829512,
-0.022484662011265755,
0.024609042331576347,
-0.009784150868654251,
-0.06163018196821213,
-0.008038240484893322,
0.027141863480210304,
0.01647898182272911,
0.016097186133265495,
-0.018479881808161736,
0.013503581285476685,
0.03877691179513931,
-0.019227614626288414,
0.0028307130560278893,
0.033620353788137436,
-0.03609170764684677,
-0.03555715084075928,
0.004996747709810734,
-0.025231147184967995,
0.025388717651367188,
0.03803759813308716,
0.01706598699092865,
-0.02312198281288147,
0.06576917320489883,
-0.0037166797555983067,
-0.03520261496305466,
0.008607120253145695,
0.009209254756569862,
0.01864027790725231,
0.011996756307780743,
0.0012011867947876453,
-0.033903222531080246,
-0.02144753560423851,
0.027896162122488022,
0.015837877988815308,
0.008217966184020042,
0.0011409797007218003,
0.022205622866749763,
-0.0013120122021064162,
0.009535552002489567,
0.012093323282897472,
0.004019979853183031,
0.03788414224982262,
-0.007565307896584272,
-0.0476127564907074,
0.0469086654484272,
0.0581890232861042,
0.028791936114430428,
-0.10252689570188522,
0.04011371359229088,
-0.0074059199541807175,
0.024797040969133377,
0.03339643031358719,
-0.019505299627780914,
0.02169584110379219,
0.00994115974754095,
-0.08198706805706024,
0.017628055065870285,
-0.03221580386161804,
-0.04013622924685478,
-0.06163855269551277,
0.013392132706940174,
-0.004713787231594324,
0.0422930046916008,
0.04061570763587952,
0.04127846658229828,
0.03409240022301674,
0.0016337156994268298,
-0.02797161042690277,
0.02540413662791252,
-0.01129849348217249,
0.00819909106940031,
-0.050481781363487244,
0.0064531355164945126,
0.05210752412676811,
-0.003558456664904952,
-0.026382189244031906,
0.0000237636522797402,
0.013844676315784454,
0.0008484118152409792,
0.030239105224609375,
0.00916457548737526,
-0.0007480355561710894,
0.021400244906544685,
0.019884293898940086,
-0.0069031366147100925,
-0.020363857969641685,
0.02190173789858818,
0.0008943959255702794,
0.010685093700885773,
-0.019358033314347267,
0.013903964310884476,
0.045367900282144547,
-0.07042201608419418,
-0.039218079298734665,
0.026092400774359703,
-0.04161627218127251,
-0.02418789453804493,
0.018027957528829575,
0.012623980641365051,
0.02621489204466343,
-0.04668328911066055,
0.02788637764751911,
-0.043332528322935104,
-0.03388603776693344,
-0.014226416125893593,
0.016502367332577705,
-0.026174752041697502,
0.030794108286499977,
-0.03338922932744026,
-0.04980441927909851,
-0.0059961117804050446,
0.007708235643804073,
-0.005259680561721325,
-0.05031628906726837,
0.04168544337153435,
0.014432160183787346,
-0.026628198102116585,
0.009946633130311966,
-0.020026562735438347,
-0.03225048631429672,
0.05731036141514778,
0.00863887183368206,
0.01893014833331108,
0.037046998739242554,
-0.02987169474363327,
-0.046483565121889114,
-0.08247465640306473,
0.040252331644296646,
-0.030930908396840096,
-0.01905548945069313,
-0.033982496708631516,
-0.008284398354589939,
-0.026596127077937126,
0.05188106745481491,
0.029718751087784767,
-0.01788565143942833,
-0.02295062318444252,
0.015588313341140747,
0.023482030257582664,
0.015763791278004646,
-0.032540589570999146,
0.01550781074911356,
-0.0012742946855723858,
-0.03743533417582512,
-0.03178408741950989,
-0.0281078964471817,
-0.01754375360906124,
0.009677720256149769,
0.00884249247610569,
0.015929069370031357,
0.05288771167397499,
-0.013533358462154865,
-0.03923676162958145,
0.058878153562545776,
0.0013601529644802213,
-0.03177061304450035,
0.052485402673482895,
-0.004205781500786543,
-0.023037517443299294,
0.013708101585507393,
-0.045110203325748444,
-0.06146462634205818,
0.022696437314152718,
-0.03983371704816818,
0.002152877626940608,
-0.015458639711141586,
-0.009918552823364735,
0.03436066955327988,
-0.024347392842173576,
0.022373273968696594,
0.032430484890937805,
-0.034899741411209106,
-0.02207825519144535,
0.047494448721408844,
0.01659253239631653,
0.014847315847873688,
-0.025766488164663315,
0.014280591160058975,
-0.016766000539064407,
-0.010764545761048794,
-0.01789132133126259,
0.05280880257487297,
0.03189011290669441,
0.004515304695814848,
0.04067031294107437,
0.02413126826286316,
0.0025215796194970608,
-0.007661025505512953,
-0.03422839939594269,
0.02708381973206997,
-0.04470627009868622,
-0.04355732351541519,
-0.01946166530251503,
-0.029062753543257713,
0.021862583234906197,
0.03380521014332771,
0.010844912379980087,
0.11283376812934875,
-0.011230889707803726,
0.017012203112244606,
-0.015263530425727367,
-0.002637238707393408,
-0.025049781426787376,
0.008974877186119556,
0.029559805989265442,
0.05942436307668686,
-0.0068838284350931644,
-0.008885875344276428,
-0.004192380700260401,
-0.014391056261956692,
0.012363252229988575,
-0.030092060565948486,
0.04135739803314209,
-0.0016331566730514169,
-0.028555063530802727,
-0.0170149989426136,
0.014379818923771381,
-0.03127533569931984,
-0.0012328241718932986,
0.024298647418618202,
0.04362623393535614,
-0.017720874398946762,
0.034902423620224,
-0.027923550456762314,
-0.015094800852239132,
0.02149975672364235,
-0.06965707242488861,
0.026932109147310257,
-0.016263196244835854,
-0.0012198538752272725,
-0.008891045115888119,
-0.011376406997442245
] |
<p>I have an 134.2 khz RFID antenna for sport events which is basically a 1x1 meter square sheet of rubber with 3 loops of antenna cable embedded. The problem is that the transponder recognition range is drastically reduced when the ground below the antenna contains metal (e.g. reinforced concrete).</p>
<p>Would it be possible to solve this problem by attaching a layer of mu-metal or permalloy to the lower side of the antenna? I read that mu-metal draws magnetic field lines into itself and thus redirects them around what's behind (in this case the metal in the ground). Would this make sure that the magnetic field on the upper side of the antenna is the same as if there was no metal in the ground? (and that the transponder recognition range is as good as without the metal) What thickness of the material would be required, would a foil be sufficient?</p>
| 10,757 |
[
0.004057405982166529,
-0.055344101041555405,
0.049675103276968,
0.00030859833350405097,
0.022427331656217575,
0.03272591531276703,
-0.029974916949868202,
-0.03624714910984039,
0.018347106873989105,
-0.020324507728219032,
0.02357502467930317,
0.029062025249004364,
0.02271328680217266,
0.004551320802420378,
0.03532320633530617,
-0.030082780867815018,
0.0038502682000398636,
-0.01991460844874382,
0.010257668793201447,
-0.08291555196046829,
0.010900643654167652,
-0.013700416311621666,
-0.01140138041228056,
0.01787535659968853,
-0.021861741319298744,
0.00061969825765118,
0.018849708139896393,
-0.011031207628548145,
0.04502055048942566,
0.011191903613507748,
-0.028641188517212868,
-0.0007997648790478706,
-0.011239818297326565,
-0.01226151455193758,
0.0323941633105278,
-0.012540471740067005,
-0.0572492741048336,
-0.04120858013629913,
-0.008162814192473888,
-0.018775394186377525,
-0.013282681815326214,
-0.008293209597468376,
-0.0010885043302550912,
0.048499878495931625,
0.009726169519126415,
-0.003595635062083602,
0.008467285893857479,
-0.017943358048796654,
0.04909858480095863,
-0.03737794607877731,
0.024613261222839355,
0.032115913927555084,
0.024822359904646873,
0.03986235707998276,
0.00617141742259264,
-0.00890144519507885,
0.07582129538059235,
0.03743838891386986,
0.03344462811946869,
-0.05627036467194557,
0.010934640653431416,
-0.058413632214069366,
-0.03614308685064316,
-0.045549631118774414,
-0.008465702645480633,
0.040490228682756424,
-0.038374654948711395,
-0.03580644354224205,
0.03396055847406387,
0.027465898543596268,
0.033228516578674316,
0.002365001244470477,
0.005883210804313421,
0.0010519475908949971,
-0.0011558802798390388,
-0.025253012776374817,
-0.015644047409296036,
0.007455089595168829,
0.036650173366069794,
0.013137427158653736,
-0.02577798254787922,
0.007544355001300573,
0.0261837150901556,
0.07111676037311554,
0.0008850558660924435,
0.0016279512783512473,
0.005910607520490885,
-0.021105976775288582,
0.030147753655910492,
0.0055067711509764194,
-0.029596546664834023,
-0.0009583602659404278,
0.044389769434928894,
0.02027684450149536,
0.007233928889036179,
0.015437955036759377,
-0.016276666894555092,
0.059237826615571976,
0.0012467748019844294,
-0.0013215409126132727,
0.00934225507080555,
-0.005699906963855028,
0.015638213604688644,
0.07266691327095032,
0.0400119349360466,
-0.010670129209756851,
-0.02225116267800331,
-0.006718568503856659,
0.0077566467225551605,
-0.005999400280416012,
-0.023951176553964615,
0.023173199966549873,
-0.012949636206030846,
-0.018383033573627472,
0.021366745233535767,
-0.05181490629911423,
0.009925192221999168,
0.017241397872567177,
0.025948451831936836,
0.09529312700033188,
0.023251989856362343,
-0.02432505041360855,
0.04303738474845886,
-0.048827290534973145,
-0.09870930761098862,
-0.0011694846907630563,
-0.008877207525074482,
0.012254109606146812,
-0.05331694334745407,
0.026961201801896095,
-0.010096549987792969,
-0.014389961957931519,
0.03774213418364525,
-0.008911174722015858,
0.03145920857787132,
-0.056934863328933716,
-0.08466377854347229,
-0.04983695223927498,
0.00013480664347298443,
-0.014268455095589161,
0.01577049307525158,
-0.047120146453380585,
0.02130657620728016,
0.001084552495740354,
0.09055797010660172,
0.028837187215685844,
0.036148421466350555,
-0.02160896360874176,
-0.017491966485977173,
-0.0006983583443798125,
0.015125693753361702,
-0.056819021701812744,
-0.027241123840212822,
-0.04147953540086746,
0.01625523716211319,
-0.0725313127040863,
0.02553451992571354,
0.011479366570711136,
0.015866843983530998,
-0.0198435690253973,
0.05952875316143036,
-0.007108266931027174,
0.03747811168432236,
-0.03902226313948631,
-0.060500528663396835,
-0.008381014689803123,
0.06581063568592072,
-0.004892956931143999,
-0.007488589733839035,
0.02482219599187374,
0.047336872667074203,
0.02817034348845482,
0.023300210013985634,
-0.0017415237380191684,
0.04384586215019226,
-0.05896071344614029,
0.014943797141313553,
-0.006423913408070803,
0.037602730095386505,
-0.019505174830555916,
-0.008211503736674786,
-0.01009510550647974,
0.008326496928930283,
0.026161642745137215,
0.0003031237283721566,
0.018938330933451653,
0.005911300424486399,
-0.012337028980255127,
0.042778391391038895,
-0.024307766929268837,
-0.004934327211230993,
-0.04019775614142418,
0.024671295657753944,
-0.016485558822751045,
-0.0145524637773633,
0.004957402125000954,
-0.02120511792600155,
-0.03042038530111313,
-0.01462272647768259,
-0.03066209703683853,
0.020816108211874962,
0.021621432155370712,
0.027143841609358788,
-0.010846040211617947,
-0.0010909405536949635,
0.028767481446266174,
0.009115345776081085,
0.009036065079271793,
0.021558061242103577,
-0.038532555103302,
-0.045240722596645355,
0.02311594970524311,
-0.03546568751335144,
0.006934926379472017,
0.02492699585855007,
-0.01788710616528988,
0.03325215354561806,
0.001127647003158927,
-0.00288415071554482,
0.024684814736247063,
-0.00962828192859888,
0.049590639770030975,
0.05357970669865608,
0.045271050184965134,
0.02247028984129429,
0.017792345955967903,
0.011299412697553635,
0.00996448565274477,
-0.03178413584828377,
-0.03953356668353081,
-0.10839149355888367,
0.0006387068424373865,
0.06322357803583145,
-0.015041712671518326,
-0.05347537621855736,
-0.0024909074418246746,
0.01536466833204031,
0.03288300335407257,
0.03641761839389801,
0.04434194415807724,
0.021622268483042717,
-0.026346199214458466,
-0.009508281014859676,
0.01745135709643364,
-0.011435875669121742,
-0.04294794425368309,
0.013479817658662796,
0.00818400178104639,
-0.0032805055379867554,
-0.010444426909089088,
-0.006453067995607853,
0.02290557138621807,
-0.0009914010297507048,
0.0176791250705719,
-0.00010154814663110301,
-0.025858938694000244,
0.04166223481297493,
-0.05565294250845909,
0.023209834471344948,
0.005340424366295338,
-0.012096866965293884,
0.005689287092536688,
-0.04443657398223877,
-0.016914736479520798,
0.04479004442691803,
0.03208080679178238,
0.0004902107175439596,
-0.021166875958442688,
0.017931204289197922,
-0.024757325649261475,
-0.02642850950360298,
0.002944463863968849,
-0.0018446752801537514,
-0.0151863694190979,
0.024271564558148384,
0.02163158915936947,
0.00012124412023695186,
0.032248806208372116,
-0.0022259410470724106,
0.007633776869624853,
-0.00047634891234338284,
0.02827073447406292,
-0.006407981272786856,
-0.005273733753710985,
-0.02391165681183338,
-0.05550914257764816,
-0.01948925107717514,
0.0009327143197879195,
0.04518777132034302,
0.01878194697201252,
-0.015874193981289864,
-0.000645980762783438,
-0.006233904045075178,
-0.02840648591518402,
-0.04311401769518852,
-0.018119599670171738,
0.00830207671970129,
-0.03258179500699043,
-0.03953470662236214,
0.04054974019527435,
0.039240553975105286,
-0.0372212678194046,
0.0036216850858181715,
-0.0716097503900528,
-0.010695299133658409,
-0.017739787697792053,
-0.007076488342136145,
0.0015299685765057802,
-0.010930574499070644,
0.03848852589726448,
-0.005137523170560598,
0.0009671402513049543,
0.006737702991813421,
-0.02179890125989914,
-0.02645881287753582,
0.029679762199521065,
-0.014826718717813492,
-0.005124630406498909,
0.005610949359834194,
-0.028384629637002945,
0.0698891133069992,
0.023529572412371635,
-0.015826724469661713,
-0.03434164077043533,
-0.04262501373887062,
0.022654680535197258,
-0.05068972706794739,
-0.008896701969206333,
0.04895545542240143,
0.030031390488147736,
0.0119803911074996,
0.03308238834142685,
0.013347556814551353,
-0.004038969054818153,
0.01836259849369526,
-0.018740039318799973,
0.0008272667182609439,
0.014525159262120724,
-0.035380247980356216,
0.05176530033349991,
0.014860141091048717,
-0.04463617131114006,
0.022912465035915375,
-0.013606712222099304,
0.025263598188757896,
0.036617305129766464,
0.011515936814248562,
0.006227871403098106,
-0.009640436619520187,
0.04779068008065224,
-0.04185840114951134,
0.0203048437833786,
-0.002024063840508461,
-0.025617245584726334,
-0.004975461401045322,
0.04176289215683937,
0.03356656804680824,
-0.00000985755195870297,
0.0017104141879826784,
0.036760516464710236,
0.06191311404109001,
-0.04208856076002121,
-0.009165220893919468,
-0.007090226747095585,
0.002046336652711034,
0.022324293851852417,
-0.023572798818349838,
-0.015979738906025887,
0.013720582239329815,
0.06547597795724869,
0.038941435515880585,
0.037871845066547394,
-0.04078853875398636,
-0.017524084076285362,
-0.07676836848258972,
-0.0336245559155941,
-0.02851131744682789,
0.08036459237337112,
-0.02885400503873825,
-0.012777335941791534,
0.035027313977479935,
0.01007498987019062,
0.029657093808054924,
0.02140006236732006,
-0.08068865537643433,
0.03220866993069649,
-0.014095243066549301,
0.008785104379057884,
0.004284447990357876,
-0.0483039990067482,
-0.04422065243124962,
-0.05335002765059471,
-0.03890511021018028,
0.015465046279132366,
0.009885615669190884,
-0.04620709642767906,
0.04548819363117218,
0.010300867259502411,
-0.02062419429421425,
-0.028623836115002632,
0.034526143223047256,
0.013856081292033195,
0.00969297531992197,
-0.005762774962931871,
-0.020989883691072464,
-0.0215647891163826,
-0.007836984470486641,
-0.022723820060491562,
0.005751828197389841,
-0.030483396723866463,
0.04830249771475792,
0.019563330337405205,
-0.028545018285512924,
-0.026302946731448174,
-0.012322898022830486,
0.03709829971194267,
0.052197109907865524,
-0.02093440666794777,
0.013112890534102917,
-0.03345748037099838,
-0.07770310342311859,
-0.06010299175977707,
0.0021396749652922153,
0.05703696236014366,
-0.02179405279457569,
0.008146303705871105,
0.005913485772907734,
-0.030475830659270287,
-0.04719199240207672,
0.003105764277279377,
0.04569818452000618,
0.03376978635787964,
0.004269182216376066,
-0.028727447614073753,
-0.029570944607257843,
-0.0347665436565876,
-0.020443834364414215,
0.01625339314341545,
0.011777198873460293,
0.03230917453765869,
0.002479099202901125,
0.047874439507722855,
0.005873683840036392,
-0.0029972640331834555,
0.04459494724869728,
0.014783188700675964,
0.004580164328217506,
-0.026840630918741226,
-0.013196752406656742,
-0.015237375162541866,
0.018543405458331108,
0.09401503950357437,
0.010416032746434212,
-0.03022385761141777,
-0.11009179055690765,
-0.03998393937945366,
0.03589146211743355,
0.07240371406078339,
-0.012480208650231361,
-0.04652976244688034,
-0.042686283588409424,
-0.004820002242922783,
0.027495386078953743,
-0.011598403565585613,
0.03416886180639267,
-0.03300473839044571,
0.004551770631223917,
-0.036242663860321045,
-0.03539096564054489,
-0.017446797341108322,
0.01741628721356392,
0.011603218503296375,
0.025046605616807938,
-0.0020698229782283306,
0.012975797057151794,
0.014601469971239567,
0.022369490936398506,
0.04070783779025078,
0.04609464854001999,
0.055410441011190414,
0.04680098593235016,
0.012778457254171371,
-0.007487691938877106,
-0.02277626469731331,
-0.056372132152318954,
-0.01614958606660366,
0.011264453642070293,
-0.005309754516929388,
0.029292825609445572,
-0.014665398746728897,
-0.03702080249786377,
0.04409772530198097,
0.01357772946357727,
-0.0034815347753465176,
0.004825369454920292,
-0.03628287464380264,
0.011331568472087383,
0.028284406289458275,
-0.009534165263175964,
0.034588523209095,
0.0036947941407561302,
0.04912673681974411,
0.008154544979333878,
0.021475298330187798,
0.030286604538559914,
-0.001992250792682171,
0.028195826336741447,
0.011794766411185265,
0.026625631377100945,
-0.06293419003486633,
0.08304522931575775,
-0.02946568839251995,
0.012376455590128899,
-0.027569031342864037,
-0.03660837560892105,
-0.026301531121134758,
0.032765984535217285,
-0.028892964124679565,
-0.023900924250483513,
-0.005491975229233503,
-0.007639785762876272,
0.0014532781206071377,
-0.024463839828968048,
-0.0010219188407063484,
-0.024586524814367294,
-0.0011449313024058938,
0.04402725026011467,
0.00711568770930171,
0.013738274574279785,
-0.03383367881178856,
-0.029125390574336052,
-0.026757143437862396,
-0.05520675703883171,
0.05243036895990372,
0.0000366666354238987,
-0.008253084495663643,
-0.0030224930960685015,
-0.046204306185245514,
-0.003926579374819994,
0.015863358974456787,
-0.02287868596613407,
0.012311236932873726,
-0.048153169453144073,
0.042277123779058456,
0.03218289092183113,
-0.01638946868479252,
-0.010578065179288387,
-0.048701103776693344,
0.004237918648868799,
0.03421373292803764,
0.008468749932944775,
-0.049689408391714096,
-0.0005609370418824255,
-0.028575029224157333,
-0.0629025399684906,
0.0010191507171839476,
0.04138018190860748,
-0.05316974222660065,
-0.00854275282472372,
0.01997743360698223,
-0.024581147357821465,
0.06018363684415817,
-0.039305679500103,
-0.01592627540230751,
0.022754374891519547,
-0.02348726987838745,
-0.016207149252295494,
-0.04517120122909546,
0.013918587006628513,
-0.04144640266895294,
-0.022239359095692635,
0.01567349024116993,
0.0026041443925350904,
0.06127641350030899,
0.010653591714799404,
-0.005442971829324961,
0.034525107592344284,
0.02820534259080887,
-0.01193589810281992,
-0.026576567441225052,
0.03510453179478645,
0.017604731023311615,
-0.007397247478365898,
-0.01898706704378128,
0.034380894154310226,
-0.0750192329287529,
-0.0022203861735761166,
0.0451565720140934,
0.005923514720052481,
0.02065061219036579,
-0.03364288806915283,
0.07488685846328735,
-0.020528731867671013,
-0.0009794856887310743,
0.004895161371678114,
-0.01756535843014717,
0.03215283900499344,
-0.02239837497472763,
0.020919209346175194,
0.03656039759516716,
0.020758694037795067,
-0.025438794866204262,
-0.02753508649766445,
-0.008110997267067432,
-0.02798432484269142,
0.006709909997880459,
-0.03573938459157944,
0.033350974321365356,
0.008793971501290798,
-0.03029172308743,
-0.022985056042671204,
0.04538251459598541,
-0.029445284977555275,
0.014336735010147095,
-0.03779332712292671,
0.04189928248524666,
0.003709179349243641,
0.02319411374628544,
-0.0005220886669121683,
0.0017082479316741228,
0.021604809910058975,
0.024595405906438828,
0.05135297402739525,
0.07361576706171036,
-0.004379706457257271,
-0.04115608334541321,
-0.029804928228259087,
-0.0002696453011594713,
-0.04970206692814827,
0.012877489440143108,
0.02119455859065056,
0.006611295510083437,
0.02879212610423565,
0.05048969015479088,
0.02766403742134571,
0.022215116769075394,
-0.0033670016564428806,
-0.08234187215566635,
0.026741735637187958,
0.016201388090848923,
-0.02562803402543068,
-0.019724644720554352,
0.0032206804025918245,
0.026777274906635284,
0.014947432093322277,
0.014080367982387543,
-0.028098437935113907,
-0.04935913532972336,
-0.0011267017107456923,
-0.04239587113261223,
-0.013460468500852585,
0.05794338881969452,
-0.0016246503219008446,
-0.008819464594125748,
0.05012071505188942,
-0.014316742308437824,
0.031036101281642914,
0.0018168179085478187,
0.0024887786712497473,
-0.03139665722846985,
0.06833373755216599,
-0.01357609499245882,
0.04816998168826103,
0.023633282631635666,
-0.01380897406488657,
0.1305747628211975,
0.04770921543240547,
-0.006505156401544809,
-0.039257973432540894,
0.012681012973189354,
-0.026194797828793526,
0.010381011292338371,
-0.047965750098228455,
0.015033834613859653,
-0.03656430169939995,
-0.025245029479265213,
0.009653912857174873,
0.02965383790433407,
-0.016641732305288315,
-0.013282827101647854,
0.056983090937137604,
-0.00532339233905077,
0.025401577353477478,
0.007297508884221315,
0.039380207657814026,
-0.0066488925367593765,
0.00033153113326989114,
-0.046664848923683167,
0.042319945991039276,
0.023778263479471207,
-0.00805424153804779,
-0.025882044807076454,
-0.002109091728925705,
0.023912932723760605,
-0.003827509703114629,
-0.025889379903674126,
0.0006415550014935434,
0.010555927641689777,
0.014777891337871552,
-0.03382306173443794,
0.01891167089343071,
0.009663636796176434,
-0.00029017485212534666,
-0.010022901929914951,
0.015016144141554832,
0.06513133645057678,
-0.01710577681660652,
0.03768014535307884,
0.029915880411863327,
-0.07155574858188629,
0.030097629874944687,
-0.03836890682578087,
0.023827949538826942,
-0.013877548277378082,
-0.03586528077721596,
0.021918220445513725,
0.028173020109534264,
0.037664130330085754,
-0.03862958028912544,
-0.03152948245406151,
0.0012702515814453363,
0.006616106256842613,
-0.011864624917507172,
-0.010513735003769398,
-0.0084691746160388,
0.0647025853395462,
-0.003862919984385371,
-0.04301925376057625,
0.003400444285944104,
0.005770957097411156,
0.018426071852445602,
-0.0053029838018119335,
0.09680498391389847,
-0.011560237966477871,
-0.053709935396909714,
-0.050283338874578476,
-0.012233152985572815,
-0.020362870767712593,
0.02259845659136772,
-0.025329556316137314,
0.01556879747658968,
-0.004566860850900412,
-0.0015451007056981325,
-0.02053632028400898,
0.034298885613679886,
-0.034672293812036514,
0.06525720655918121,
-0.04725025221705437,
-0.0010133561445400119,
-0.021246444433927536,
-0.04986921325325966,
0.02726120315492153,
0.031788770109415054,
-0.01531492080539465,
0.02637283317744732,
0.020482363179326057,
0.03290975093841553,
0.0009489906951785088,
-0.011966471560299397,
0.014159999787807465,
-0.034188222140073776,
-0.057291388511657715,
0.06424742937088013,
-0.028185328468680382,
-0.012747243046760559,
0.03533123433589935,
-0.0028742183931171894,
0.002954233204945922,
-0.011877967044711113,
-0.03350578993558884,
-0.012718698009848595,
-0.0073319305665791035,
-0.028532058000564575,
0.0009639928466640413,
-0.026223691180348396,
0.02373494580388069,
-0.03282340243458748,
-0.034925930202007294,
-0.027355264872312546,
-0.004647106397897005,
0.01063859649002552,
0.035990722477436066,
-0.016115086153149605,
-0.007262099534273148,
-0.031179822981357574,
-0.062087155878543854,
0.015621709637343884,
0.0019231932237744331,
-0.019179923459887505,
-0.0032902348320931196,
0.023045409470796585,
-0.02461497113108635,
-0.030007997527718544,
0.004032994154840708,
-0.03859462961554527,
0.04065750166773796,
0.00778730446472764,
-0.0038641663268208504,
0.00619021151214838,
0.018563244491815567,
0.009284818544983864,
0.025334229692816734,
0.05393165722489357,
-0.018848830834031105,
0.03510099649429321,
0.04081393778324127,
-0.01982356421649456,
-0.03806597366929054,
0.013267306610941887,
0.0004061046347487718,
0.013614583760499954,
-0.018815333023667336,
-0.024594169110059738,
-0.012094241566956043,
0.04946347698569298,
-0.0004551329475361854,
-0.0019356778357177973,
0.016410375013947487,
0.006731351371854544,
0.05325018987059593,
-0.015246731229126453,
-0.005790588445961475,
-0.0235887598246336,
0.008393427357077599,
0.0435861237347126,
-0.030042417347431183,
0.012467212043702602,
0.006191631779074669,
0.00974363461136818,
-0.023296071216464043,
-0.04049515351653099,
0.016807686537504196,
0.0033222546335309744,
0.021607134491205215,
0.06306403130292892,
-0.0022750520147383213,
0.005672885570675135,
0.007053454406559467,
-0.006824843119829893,
-0.06863687187433243,
-0.018043268471956253,
0.020992619916796684,
0.009777565486729145,
0.005340766627341509,
-0.0577358640730381,
0.035679079592227936,
0.0043611079454422,
-0.06074860319495201,
-0.025501050055027008,
-0.015890855342149734,
-0.029895411804318428,
-0.023508548736572266,
-0.01842346414923668,
-0.01451997458934784,
0.013738485053181648,
0.019292937591671944,
0.056588806211948395,
-0.004965105559676886,
0.030219998210668564,
-0.03667464479804039,
-0.010827483609318733,
-0.024235162883996964,
0.02439926005899906,
0.011050698347389698,
-0.029545549303293228,
0.07684418559074402,
-0.0015191943384706974,
-0.02666393481194973,
0.007635254412889481,
-0.05073224753141403,
0.003965694457292557,
0.006818197201937437,
0.021444184705615044,
-0.0036194820422679186,
0.004688183777034283,
0.010574531741440296,
0.024793479591608047,
-0.01540120504796505,
0.01274734828621149,
0.005898822098970413,
-0.033063244074583054,
-0.012938701547682285,
-0.005925523117184639,
0.015318652614951134,
0.01215314120054245,
0.008119132369756699,
0.044886816293001175,
-0.06538611650466919,
-0.019836556166410446,
0.02043186128139496,
0.028381450101733208,
0.03754373639822006,
-0.017725544050335884,
-0.010469929315149784,
-0.010609322227537632,
-0.002882090164348483,
0.004914382938295603,
0.019528869539499283,
-0.0032576133962720633,
0.000023333119315793738,
-0.05466064065694809,
-0.02451120689511299,
-0.020963354036211967,
0.030983218923211098,
-0.031855810433626175,
-0.04180898517370224,
-0.005832100287079811,
-0.0014110564952716231,
0.031074421480298042,
0.010018016211688519,
0.0030751468148082495,
-0.027985183522105217,
0.01984321139752865,
0.02036127820611,
0.048381853848695755,
0.034395910799503326,
0.008008892647922039,
-0.0014078001258894801,
-0.05476592853665352,
0.03521100804209709,
-0.02167324908077717,
-0.03750390559434891,
0.001792347989976406,
-0.07241082936525345,
-0.04011408984661102,
0.053979355841875076,
0.08047991991043091,
-0.03145737573504448,
0.011338964104652405,
-0.013154342770576477,
-0.019782457500696182,
0.024949267506599426,
-0.04987465962767601,
0.06139739230275154,
0.0414339154958725,
-0.029027823358774185,
0.007406504359096289,
-0.0036456063389778137,
0.044647086411714554,
-0.01104588620364666,
-0.025560880079865456,
0.006316761020570993,
-0.004925050772726536,
-0.05126291885972023,
-0.01084216870367527,
0.012095741927623749,
-0.0017708349041640759,
0.016077736392617226,
0.03964629024267197,
0.0006035873666405678,
0.02859407663345337,
-0.00865057110786438,
-0.011989272199571133,
-0.03207556903362274,
0.06242327019572258,
-0.0571347214281559,
0.04950625076889992,
-0.02091008611023426,
0.050569433718919754,
0.045290201902389526,
-0.059378281235694885,
0.04270405322313309,
-0.008130261674523354,
-0.036701835691928864,
-0.019427966326475143,
0.06416022032499313,
0.004671728704124689,
0.019751403480768204,
-0.006014264188706875,
0.043269090354442596,
0.010724198073148727,
-0.007991059683263302,
-0.01902773790061474,
0.006410030648112297,
-0.0010342069435864687,
-0.009187235496938229,
0.009377055801451206,
0.0746171697974205,
0.0012838902184739709,
0.047478530555963516,
0.012493087910115719,
-0.011309306137263775,
0.018341563642024994,
0.005256516393274069,
0.01278625801205635,
-0.002434541704133153,
-0.0082545792683959,
0.031824156641960144,
-0.024998042732477188,
0.05194231867790222,
-0.028060464188456535,
-0.03724660724401474,
-0.00188824615906924,
-0.010056107304990292,
0.028226645663380623,
0.036276672035455704,
0.01751783676445484,
0.024190345779061317,
0.02332071028649807,
0.019678493961691856,
-0.008373808115720749,
-0.02593657560646534,
0.05196363478899002,
-0.005402428098022938,
0.0035765436477959156,
-0.0062313261441886425,
0.0058393762446939945,
-0.03529553860425949,
-0.027871856465935707,
-0.02442191354930401,
0.01057860441505909,
0.011148165911436081,
0.024292102083563805,
0.0019031984265893698,
-0.00595173379406333,
0.008485228754580021,
-0.002027790993452072,
0.03162446618080139,
-0.06063451990485191,
-0.004557008855044842,
-0.059410855174064636,
-0.012150854803621769,
0.027243556454777718,
0.025585876777768135
] |
<p>I've been asking myself a question for quite some time :</p>
<ul>
<li>say that a bullet gets out of a gun at 900 km/h (I'm european, hence the metric system).</li>
<li>say a train could go in a straight line at 900 km/h</li>
<li>say you're at the back of that train, and you'd shoot a bullet backwards. The bullet exits your gun at 900km/h and flies away from the train at the same speed.
However, what would happen for an earth observer?</li>
</ul>
<p>You'll agree that if you shoot in an open field, the bullet will stay at the same altitude for several seconds before falling to the ground (with a field large enough).
So from that train, same thing applies.
So for the earth observer, the bullet will not have an horizontal speed, and will stay at the same altitude for several seconds before falling to the ground.
So basically it'll float up in the air without falling. That'd be strange for the earth observer, right?</p>
<p>But the horizontal speed will decrease of course.
So for the earth observer, the bullet will, for a few seconds, stay still at the same position, and then after several seconds will start to fall down a little bit, and will start to move towards the train, because its horizontal speed towards the train will decrease. Strange again!</p>
<p>OK last one: what would happen if the earth observer tried to catch the bullet with his bare hands? Nothing right? Just maybe a very hot bullet because of the explosion but it'd be basically as easy to catch as a stone floating up in the air?
And don't tell me that the bullet will slow down due to air friction, because remember the bullet is not moving. Or very slowly.</p>
| 10,758 |
[
-0.020621445029973984,
-0.03943905234336853,
-0.004505552817136049,
0.0003537132288329303,
0.050786279141902924,
0.021517030894756317,
-0.006891835946589708,
-0.042700525373220444,
0.0008953098440542817,
0.013818830251693726,
0.02321428433060646,
0.028450699523091316,
0.050824057310819626,
0.03225919231772423,
0.032062288373708725,
-0.000816923682577908,
0.002195799956098199,
-0.0055906083434820175,
-0.004161004442721605,
-0.04358546808362007,
-0.007395648397505283,
0.027102556079626083,
0.03749590739607811,
0.00677079614251852,
-0.02879290282726288,
-0.00442082341760397,
-0.005502060521394014,
-0.009537813253700733,
0.03870914876461029,
0.03292875364422798,
0.026636308059096336,
-0.004746770020574331,
-0.00059951824368909,
0.013568286783993244,
0.025498388335108757,
0.02358933910727501,
-0.051248949021101,
-0.01870129071176052,
-0.005162088666111231,
-0.0227236058562994,
-0.029684536159038544,
0.00750412791967392,
0.022030098363757133,
0.05184545740485191,
-0.044437821954488754,
0.015531599521636963,
-0.012619012035429478,
-0.013070307672023773,
0.07245176285505295,
-0.057996150106191635,
0.03016776777803898,
0.005593221168965101,
0.0023225077893584967,
0.04025914520025253,
0.016452275216579437,
-0.018753429874777794,
0.06152733787894249,
0.03715244680643082,
0.0067187342792749405,
-0.016886094585061073,
-0.001305081881582737,
-0.019677510485053062,
-0.032358840107917786,
0.003125710180029273,
0.020792564377188683,
0.022991877049207687,
-0.032541364431381226,
-0.02674173004925251,
0.016851676627993584,
0.005496927071362734,
-0.0027553229592740536,
0.006162495352327824,
0.01272533554583788,
-0.0006775186629965901,
0.03646601736545563,
-0.027618370950222015,
0.05269011855125427,
0.00788512546569109,
0.05400357022881508,
0.03878292813897133,
-0.025010069832205772,
-0.015259438194334507,
0.0119789345189929,
0.05457068607211113,
0.03373542055487633,
-0.02514999359846115,
0.08488114178180695,
0.022690903395414352,
0.015633216127753258,
0.049863699823617935,
0.010593181475996971,
0.0021997597068548203,
0.015291035175323486,
0.00041409817640669644,
-0.05052163824439049,
-0.001027072430588305,
0.03402642905712128,
0.06176666542887688,
0.040043145418167114,
0.002736200112849474,
-0.016266081482172012,
-0.013677087612450123,
0.0416354276239872,
0.052050668746232986,
0.014672688208520412,
-0.029842237010598183,
-0.018330782651901245,
-0.008640184067189693,
-0.011552332900464535,
-0.019757859408855438,
-0.03269281983375549,
0.043404802680015564,
0.007319271098822355,
0.0166484322398901,
0.021466104313731194,
-0.00774731207638979,
0.032696161419153214,
-0.02010696940124035,
0.0035625724121928215,
0.035785648971796036,
0.06577608734369278,
-0.005769095849245787,
0.01722222939133644,
-0.007653708104044199,
-0.06165114417672157,
-0.014668173156678677,
0.027788644656538963,
-0.015986472368240356,
0.0043112728744745255,
0.016973741352558136,
0.01115354336798191,
-0.04642995819449425,
-0.007886986248195171,
0.011180044151842594,
0.022929320111870766,
0.015055042691528797,
-0.10304752737283707,
-0.06465495377779007,
0.014323765411973,
0.027802404016256332,
-0.010215298272669315,
-0.11132685095071793,
-0.023861020803451538,
0.010786767117679119,
0.07059262692928314,
-0.011487714014947414,
-0.019595075398683548,
0.020168757066130638,
0.012729093432426453,
0.010763421654701233,
-0.01175318006426096,
0.005446782801300287,
-0.03206748515367508,
-0.06936603039503098,
-0.015093540772795677,
-0.04860571399331093,
0.019841985777020454,
-0.010679157450795174,
-0.015408896841108799,
-0.03490849584341049,
0.018664663657546043,
0.007126059383153915,
-0.00031244775163941085,
-0.0224941186606884,
0.00923972949385643,
0.006750180386006832,
0.0763482078909874,
0.03963572904467583,
-0.03603411465883255,
0.01805873028934002,
0.057605672627687454,
0.04727848991751671,
-0.033952828496694565,
-0.018983175978064537,
0.025282548740506172,
-0.05605407431721687,
-0.006997740361839533,
-0.05129801109433174,
-0.017179127782583237,
0.00865970179438591,
-0.005588450003415346,
-0.03646757826209068,
-0.009899201802909374,
-0.023933609947562218,
0.005821716971695423,
0.0479540191590786,
0.013945486396551132,
0.04126694053411484,
-0.014529872685670853,
-0.03219536691904068,
-0.02135271020233631,
-0.04327153414487839,
0.06740434467792511,
0.0022282623685896397,
0.016880949959158897,
0.014100953936576843,
-0.008829904720187187,
-0.012663450092077255,
-0.02451997995376587,
0.007212676573544741,
-0.005734817590564489,
0.06354161351919174,
-0.0049000815488398075,
-0.019618967548012733,
-0.015032434836030006,
0.0659698098897934,
0.041239943355321884,
0.02631969191133976,
-0.0006735274218954146,
-0.016271529719233513,
-0.011397739872336388,
-0.013160244561731815,
0.010430670343339443,
-0.011305741034448147,
0.03250103071331978,
0.010051017627120018,
-0.014373015612363815,
-0.010786891914904118,
0.000264418515143916,
0.006547033786773682,
-0.04301679879426956,
0.06755620241165161,
0.026865797117352486,
-0.05274704098701477,
-0.013587675988674164,
0.0902876928448677,
0.026195526123046875,
-0.01451803557574749,
0.028442494571208954,
-0.04058659449219704,
-0.04362071305513382,
-0.028563397005200386,
0.00628213956952095,
-0.02900208905339241,
0.008914968930184841,
0.06042082980275154,
0.010288452729582787,
0.029930323362350464,
0.003434498328715563,
-0.011827804148197174,
0.01208236999809742,
-0.03919471055269241,
-0.006512271706014872,
-0.010946567170321941,
0.02769298106431961,
-0.009602539241313934,
-0.003951084800064564,
0.006933301221579313,
0.010053092613816261,
-0.030461706221103668,
-0.023756861686706543,
-0.0126785384491086,
0.004961817990988493,
0.009390536695718765,
-0.005366744939237833,
0.001360891037620604,
0.03222189098596573,
0.0034793599043041468,
0.02783326990902424,
0.036203738301992416,
0.0010697449324652553,
0.018873177468776703,
-0.0652364194393158,
0.027899913489818573,
-0.006295495200902224,
-0.0070197852328419685,
-0.009090567007660866,
-0.020551636815071106,
0.01884811744093895,
-0.06579487025737762,
-0.03454545512795448,
0.01820477657020092,
0.010962252505123615,
-0.024550335481762886,
0.0008643811452202499,
-0.0011845306726172566,
0.04099255055189133,
0.00402607349678874,
-0.02966676838696003,
-0.03798260539770126,
-0.009366963058710098,
-0.016883142292499542,
0.01300822850316763,
0.011861137114465237,
-0.030107878148555756,
0.040120285004377365,
-0.028139082714915276,
-0.034206923097372055,
0.06473036110401154,
0.022443924099206924,
0.00893506407737732,
0.053270839154720306,
-0.042023345828056335,
-0.0589229054749012,
0.005843691993504763,
-0.02972186543047428,
-0.023204337805509567,
-0.014600937254726887,
-0.005735206883400679,
0.08435913175344467,
-0.006572239100933075,
0.0049186768010258675,
0.028462525457143784,
-0.03027407079935074,
-0.050197746604681015,
-0.03411225974559784,
0.0011084297439083457,
-0.0017313968855887651,
-0.0019223116105422378,
0.028846895322203636,
0.012096024118363857,
-0.027245815843343735,
-0.005034351721405983,
-0.04905439168214798,
-0.023836111649870872,
0.0081082284450531,
0.02588840201497078,
0.05449875816702843,
0.0004402518679853529,
0.017603492364287376,
0.06770478188991547,
0.05120270699262619,
-0.022627368569374084,
-0.025911998003721237,
0.0010174905182793736,
-0.004996879491955042,
-0.00013013002171646804,
-0.012011918239295483,
0.02753874845802784,
-0.0012063650647178292,
-0.0008049955358728766,
0.005538973491638899,
0.04973471537232399,
0.025052018463611603,
0.0028717448003590107,
-0.0032026360277086496,
-0.01102336123585701,
0.010934663936495781,
0.021631350740790367,
0.04442254453897476,
0.04248998314142227,
0.0021177625749260187,
0.04366020858287811,
-0.013776646926999092,
0.023180268704891205,
0.02632545307278633,
-0.041432276368141174,
0.08599485456943512,
0.04685370251536369,
-0.05064745992422104,
-0.04141838476061821,
0.0355510376393795,
-0.002699387026950717,
-0.009130666963756084,
-0.027532191947102547,
0.017441850155591965,
0.04643850028514862,
-0.013575485907495022,
0.004797105211764574,
-0.01561746932566166,
0.059331122785806656,
-0.026747100055217743,
-0.03904842957854271,
-0.0061363335698843,
0.03896793723106384,
0.026423955336213112,
-0.016885563731193542,
0.005653041414916515,
0.048122696578502655,
0.0408252514898777,
0.0019744508899748325,
-0.020404459908604622,
-0.02166905254125595,
-0.029977185651659966,
-0.06885726749897003,
-0.008876144886016846,
-0.05376134812831879,
0.03076842613518238,
0.020940599963068962,
0.04109867289662361,
-0.005506020504981279,
0.03414960205554962,
-0.009827258065342903,
0.04839872196316719,
-0.051254939287900925,
0.00867915153503418,
-0.04252765700221062,
-0.03364443778991699,
-0.033380452543497086,
0.03404046595096588,
-0.02580338716506958,
-0.019337886944413185,
-0.0038667297922074795,
-0.041242215782403946,
-0.02092084102332592,
-0.027899891138076782,
-0.014998868107795715,
-0.03255714476108551,
-0.05419112369418144,
-0.03863227739930153,
0.031071292236447334,
0.04964320361614227,
0.015316588804125786,
0.03574056923389435,
-0.0136982137337327,
-0.04275206848978996,
-0.007272860500961542,
-0.008439230732619762,
-0.011842809617519379,
0.03293164446949959,
0.04834241047501564,
-0.009457823820412159,
-0.028177345171570778,
-0.035181231796741486,
0.005696333013474941,
0.04859359934926033,
0.012103361077606678,
-0.003524135798215866,
0.010963055305182934,
-0.02226462960243225,
-0.01672307774424553,
-0.011323423124849796,
-0.0050319163128733635,
0.044986531138420105,
-0.030938858166337013,
-0.014086863026022911,
0.011226877570152283,
-0.00033736322075128555,
0.019827792420983315,
0.03307365998625755,
0.044440265744924545,
-0.02486589550971985,
0.03832437843084335,
-0.018346251919865608,
0.019653450697660446,
-0.03198488801717758,
-0.014506778679788113,
-0.01060708612203598,
0.013367881067097187,
-0.0003785844019148499,
-0.01704414375126362,
0.02402227744460106,
0.012912273406982422,
0.005424536764621735,
0.03624175116419792,
-0.002818536013364792,
0.024522744119167328,
0.012325270101428032,
0.017049461603164673,
0.0023334340658038855,
0.04580214247107506,
0.038260530680418015,
0.006557190790772438,
-0.009119058027863503,
-0.05754035338759422,
-0.008904700167477131,
0.006820681504905224,
0.008868222124874592,
-0.004717616364359856,
0.001509263995103538,
-0.06389786303043365,
-0.01445972453802824,
0.02224152535200119,
-0.005372015293687582,
0.028486918658018112,
-0.027279438450932503,
-0.01698632724583149,
-0.030218029394745827,
-0.039768170565366745,
-0.06347756832838058,
-0.0011654315749183297,
-0.031428150832653046,
0.010841249488294125,
-0.03946782648563385,
-0.0027001318521797657,
0.002415209077298641,
0.015075437724590302,
0.030815722420811653,
0.024817289784550667,
0.01988106220960617,
0.0053953626193106174,
-0.021549886092543602,
-0.037836987525224686,
-0.03433139622211456,
-0.07540971040725708,
-0.0028268243186175823,
-0.00801114272326231,
-0.005183471366763115,
0.029864829033613205,
-0.02619251422584057,
-0.034457091242074966,
0.034535326063632965,
-0.012332448735833168,
-0.05701391398906708,
0.006895815953612328,
-0.06802140921354294,
0.006588981952518225,
0.055388443171978,
0.01846393756568432,
-0.02448122203350067,
-0.00530008552595973,
0.0025350346695631742,
0.027858920395374298,
0.024064218625426292,
0.02127614989876747,
-0.03491969406604767,
0.006887589581310749,
-0.033819545060396194,
0.02149261347949505,
-0.042925406247377396,
0.02485404908657074,
-0.0009130057296715677,
0.0011493099154904485,
0.009823319502174854,
-0.05940089374780655,
-0.010827609337866306,
0.0005964788724668324,
-0.031110679730772972,
0.01950664632022381,
-0.033001165837049484,
-0.003413112135604024,
-0.02597680129110813,
0.013099160976707935,
0.019395725801587105,
0.004570631310343742,
0.029182342812418938,
0.061395928263664246,
-0.023945290595293045,
0.0033724370878189802,
-0.0340360552072525,
0.011745992116630077,
0.00834267120808363,
-0.09245137125253677,
0.07782740890979767,
-0.03377373889088631,
0.008176112547516823,
0.05618986114859581,
-0.017341846600174904,
-0.04896598681807518,
0.004232385195791721,
-0.012475978583097458,
0.06858403980731964,
-0.04390662536025047,
0.010279040783643723,
0.01792902685701847,
-0.00244645937345922,
-0.05676376074552536,
-0.043553683906793594,
0.05965397506952286,
-0.012979983352124691,
-0.04734903573989868,
-0.025946667417883873,
-0.01685612089931965,
-0.026071760803461075,
-0.013378169387578964,
0.0009498611907474697,
0.06059180572628975,
-0.026744304224848747,
0.003482498461380601,
0.01504822913557291,
0.014169572852551937,
0.06663580983877182,
-0.018884463235735893,
-0.009702671319246292,
0.029773762449622154,
-0.0049661980010569096,
-0.019411126151680946,
-0.000637280463706702,
0.1006634384393692,
-0.01668018288910389,
-0.04625220596790314,
-0.006383617874234915,
-0.01981954276561737,
-0.002543763490393758,
-0.014712071046233177,
0.00904832687228918,
0.04074147716164589,
-0.01572754979133606,
-0.0053588468581438065,
0.027856813743710518,
0.02981717884540558,
-0.0009295151685364544,
0.011651984415948391,
-0.03384910523891449,
0.01697530411183834,
-0.009942813776433468,
-0.04512565955519676,
0.026925187557935715,
0.019599616527557373,
0.009748403914272785,
-0.004866375122219324,
0.043933186680078506,
0.010612111538648605,
-0.0065133399330079556,
0.06084267422556877,
0.02844800427556038,
0.04016154631972313,
-0.03191019967198372,
-0.025773344561457634,
0.016293585300445557,
-0.027597839012742043,
-0.02679174579679966,
-0.017818577587604523,
-0.01760121062397957,
0.0348421111702919,
0.04662616550922394,
-0.02788756974041462,
0.054200299084186554,
-0.018441414460539818,
0.009248209185898304,
0.014073321595788002,
-0.028203291818499565,
0.015781830996274948,
-0.004313675686717033,
-0.010720590129494667,
0.02185342088341713,
-0.019352689385414124,
-0.006606850773096085,
0.031114041805267334,
0.08918566256761551,
0.01424467097967863,
-0.031228629872202873,
0.0022556791082024574,
0.03574935346841812,
0.04735124856233597,
-0.014544686302542686,
-0.03344050422310829,
0.006044776178896427,
-0.025222456082701683,
0.007621070370078087,
0.03900391608476639,
0.0026386957615613937,
0.033648476004600525,
0.03164404630661011,
-0.0015319474041461945,
-0.04602925106883049,
-0.02434016764163971,
-0.057364508509635925,
-0.032114505767822266,
0.02102379873394966,
0.013249081559479237,
0.012071128003299236,
-0.020729539915919304,
0.03919277712702751,
-0.01631825603544712,
0.00395997054874897,
-0.007114632986485958,
-0.08702903240919113,
-0.02021368220448494,
-0.046209774911403656,
-0.03719576075673103,
0.06725382059812546,
0.004015043843537569,
-0.015656670555472374,
0.009983228519558907,
-0.030747009441256523,
0.035706691443920135,
0.05547170341014862,
0.03873268887400627,
-0.0229962058365345,
0.07419037073850632,
-0.021991273388266563,
-0.020500926300883293,
-0.04239795729517937,
0.04232800751924515,
0.12093643099069595,
0.007591868285089731,
0.016795188188552856,
-0.010045448318123817,
0.009153468534350395,
-0.01973414421081543,
0.017713461071252823,
0.013729545287787914,
0.009179186075925827,
-0.01847618818283081,
0.03171657398343086,
0.016030535101890564,
0.018680837005376816,
0.007397412788122892,
-0.026497026905417442,
0.03474953770637512,
-0.08460299670696259,
-0.02087782509624958,
0.009894592687487602,
0.005632105283439159,
0.005320088472217321,
0.037578050047159195,
-0.028179435059428215,
0.024283606559038162,
-0.0036776303313672543,
0.03296754136681557,
-0.04035750404000282,
-0.07303712517023087,
0.03301704674959183,
0.014790006913244724,
-0.03458718955516815,
-0.009937148541212082,
0.03412608429789543,
-0.05137838423252106,
-0.0322103351354599,
0.014268654398620129,
0.02854812517762184,
-0.02236310765147209,
0.013492502272129059,
0.032855186611413956,
0.018254149705171585,
0.012876034714281559,
0.025220105424523354,
-0.014959065243601799,
-0.04261971637606621,
0.006695976015180349,
-0.016848886385560036,
0.05411337688565254,
0.000746368314139545,
0.0028511544223874807,
-0.008764212019741535,
0.01384978648275137,
0.02955370955169201,
-0.06062017008662224,
0.007744234520941973,
-0.01829575002193451,
0.011737307533621788,
0.038798172026872635,
-0.041743483394384384,
-0.02105140872299671,
0.05363504961133003,
0.021557819098234177,
-0.005664256401360035,
0.011106896214187145,
0.01389890443533659,
-0.016124067828059196,
-0.009222142398357391,
0.03284315764904022,
-0.013240564614534378,
-0.03618033975362778,
-0.013155024498701096,
-0.014969903975725174,
-0.047747235745191574,
0.004617226310074329,
0.011442365124821663,
0.03507409617304802,
0.03061937540769577,
-0.018801270052790642,
0.016846317797899246,
-0.06206917017698288,
-0.03521684929728508,
0.01900145597755909,
-0.0164172425866127,
0.0163427647203207,
-0.01144109945744276,
-0.012320894747972488,
-0.010052758269011974,
0.02535240724682808,
0.0021713923197239637,
-0.015348085202276707,
0.003922715317457914,
0.07429713010787964,
0.011379659175872803,
-0.015666209161281586,
-0.0171361081302166,
0.03570336103439331,
-0.004327548202127218,
0.024996642023324966,
-0.009373809210956097,
0.03273181989789009,
0.043604571372270584,
-0.0006579731125384569,
0.04335911199450493,
0.01106993667781353,
0.0038765454664826393,
0.01688648946583271,
0.029292862862348557,
-0.022864067927002907,
-0.03212129324674606,
0.03709321841597557,
0.011086656711995602,
0.003268921747803688,
-0.03990153595805168,
-0.020057085901498795,
-0.023489605635404587,
-0.030593419447541237,
0.04452268406748772,
-0.008342009037733078,
0.023580944165587425,
-0.045467134565114975,
0.023451369255781174,
-0.017835060134530067,
-0.0011981799034401774,
-0.04319661855697632,
0.027251334860920906,
-0.009329420514404774,
-0.025801682844758034,
-0.05096231773495674,
0.03285711631178856,
-0.05463976785540581,
-0.052919719368219376,
-0.0056389798410236835,
0.00044572213664650917,
-0.040107082575559616,
0.009627899155020714,
-0.05181574448943138,
0.023612473160028458,
-0.003213339252397418,
-0.017299341037869453,
-0.01006393227726221,
0.02786504477262497,
0.018879041075706482,
-0.053414344787597656,
0.06992577761411667,
0.009512157179415226,
0.06287144124507904,
0.011530585587024689,
-0.011469651944935322,
0.010847393423318863,
0.08790905773639679,
-0.006436046212911606,
0.003518021199852228,
0.0024886897299438715,
-0.04281654581427574,
0.004678185097873211,
0.01149219460785389,
0.0042141457088291645,
-0.024019377306103706,
-0.027308989316225052,
0.04678057134151459,
0.005730706267058849,
-0.018710091710090637,
0.05176917091012001,
0.016178933903574944,
-0.02535558119416237,
-0.0377117395401001,
0.010412287898361683,
0.003879258409142494,
0.012055043131113052,
0.02437938004732132,
-0.04183012247085571,
0.0067081269808113575,
0.008386781439185143,
0.017444536089897156,
-0.09447323530912399,
-0.014733711257576942,
0.029067283496260643,
0.003789781127125025,
0.03776843100786209,
-0.05561738461256027,
-0.022673942148685455,
0.07785908132791519,
-0.0823182761669159,
-0.018432699143886566,
-0.034853629767894745,
-0.0397438183426857,
-0.040489986538887024,
-0.020426465198397636,
-0.005657062865793705,
0.051835961639881134,
0.024495592340826988,
0.03167424350976944,
0.014089422300457954,
0.0083863390609622,
-0.02046363614499569,
-0.03332646191120148,
-0.020883429795503616,
0.04069896414875984,
0.01890300214290619,
0.04785137623548508,
0.050802137702703476,
-0.06646860390901566,
0.019946813583374023,
0.004301541950553656,
-0.02473374642431736,
0.007781637366861105,
-0.0007909896085038781,
-0.008512498810887337,
0.039362672716379166,
0.01006392389535904,
0.0033954803366214037,
0.014673720113933086,
0.01264124270528555,
0.0359744094312191,
0.021960418671369553,
0.030697600916028023,
-0.021494122222065926,
-0.02430485002696514,
0.010857139714062214,
-0.02725212275981903,
-0.02157231792807579,
0.06329537183046341,
-0.020569343119859695,
-0.019474266096949577,
0.012949569150805473,
0.021855469793081284,
0.004365302622318268,
-0.008862505666911602,
0.0009130740654654801,
-0.005292059388011694,
-0.013289745897054672,
-0.01044036727398634,
0.014017520472407341,
-0.030392134562134743,
0.00763378432020545,
-0.02574034407734871,
0.0014520752010867,
-0.025523154065012932,
0.003184378379955888,
-0.026819145306944847,
-0.006522961426526308,
0.0017491943435743451,
0.01655985414981842,
0.004627527669072151,
0.01187537144869566,
-0.043858062475919724,
-0.026967337355017662,
0.014281190000474453,
0.05234016850590706,
0.0024714539758861065,
0.012318318709731102,
-0.05355004966259003,
-0.03019680455327034,
-0.07725823670625687,
0.01865736022591591,
0.007873272523283958,
-0.020617874339222908,
-0.03055214136838913,
-0.02792312577366829,
-0.004434770438820124,
0.04284326359629631,
0.04546599090099335,
-0.022085154429078102,
-0.025176331400871277,
0.04613031446933746,
-0.05372200906276703,
0.02062343619763851,
-0.06893228739500046,
-0.010268350131809711,
0.009794770739972591,
-0.007016870193183422,
-0.020868659019470215,
-0.00013003064668737352,
-0.05523977428674698,
-0.021073924377560616,
0.02414822205901146,
-0.008279147557914257,
0.007617967668920755,
-0.0022651972249150276,
-0.04198296368122101,
0.018610723316669464,
0.024967698380351067,
-0.02834046073257923,
0.048655979335308075,
0.01708812266588211,
-0.02918192930519581,
-0.0015871155774220824,
-0.053299129009246826,
-0.04485201835632324,
0.014989630319178104,
-0.02341974526643753,
0.003334333188831806,
-0.002567433286458254,
-0.015758050605654716,
0.02777703106403351,
-0.015304801985621452,
0.01217457465827465,
0.016633018851280212,
0.018934255465865135,
-0.010249651037156582,
0.0012067037168890238,
0.05783621221780777,
0.017102772369980812,
-0.008616776205599308,
0.03813993185758591,
0.027854928746819496,
0.0016983012901619077,
-0.031069066375494003,
0.004980414640158415,
0.02717307023704052,
-0.008314326405525208,
0.024476848542690277,
0.027620986104011536,
0.009508104994893074,
0.0051218182779848576,
0.009565014392137527,
0.048238031566143036,
0.0018623028881847858,
0.016631051898002625,
0.01881282962858677,
0.016824984923005104,
-0.02721364051103592,
0.014521719887852669,
-0.013792380690574646,
0.07491201162338257,
-0.011766096577048302,
0.010975445620715618,
0.006660873536020517,
-0.007094579748809338,
-0.012736184522509575,
0.019080733880400658,
0.019084108993411064,
-0.016157113015651703,
-0.014058072119951248,
-0.018475908786058426,
-0.027744175866246223,
0.02276638150215149,
0.04086935892701149,
-0.05225732922554016,
0.015077145770192146,
-0.05134178698062897,
-0.022405175492167473,
-0.01240538153797388,
-0.032689280807971954,
-0.00916496105492115,
0.010792690329253674,
0.04340019449591637,
0.016337964683771133,
0.022119522094726562,
-0.019081871956586838,
-0.026207227259874344,
-0.014522657729685307,
0.054405577480793,
-0.07843786478042603,
-0.032808899879455566,
-0.0314890556037426,
0.07489519566297531,
0.028879813849925995,
-0.003063427982851863
] |
<p>As can for example be learned from chapter I.2 of Anthony Zee's <em>Quantum field theory in a nutshell</em>, path integrals can be used to to calculate the amplitude for a system to transition from one state to another by considering all possible paths between the two states.</p>
<p><a href="http://motls.blogspot.com/2012/11/when-truths-dont-commute-inconsistent.html?m=1" rel="nofollow">This</a> article gives a nice technical introduction to <a href="http://en.wikipedia.org/wiki/Consistent_histories" rel="nofollow">consistent histories</a> and explains that this method can be used to calculate the answer to questions about alternative histories in a consistent set. For two histories to be consistent, their probabilities must be mutually exclusive such that their probabilities are "additive".</p>
<p>Looking at these two methods to calculate answers to meaningful questions in quantum mechanics (and how the relevant formulas are derived), they seem very similar to me. </p>
<p>So my question is:</p>
<p>What is the exact relationship between the method of path integral and consistent histories? Could one say that the consistent histories are some kind of the "classical limit" of the path integrals? Or does coarse graining (by an appropriate method?) Feynman's path integrals lead to consistent histories as a limit (IR fixed point)?</p>
<p>(In the article about the consistent histories it is mentioned, that if one considers too fine grained histories, they are due to the uncertainty principle no longer consistent and would resemble Feynman's path integrals. But I'd like to see an extended technical / mathematical explanation of the relationship between the two things to really understand it.)</p>
| 10,759 |
[
-0.00041382503695786,
-0.02088134177029133,
-0.000689739768858999,
-0.010836680419743061,
0.02837185002863407,
0.01923724077641964,
-0.015279851853847504,
-0.02454165555536747,
0.018479494377970695,
-0.014983577653765678,
0.028538445010781288,
0.022468209266662598,
0.04787334427237511,
-0.0028833607211709023,
0.026970062404870987,
-0.00011152138176839799,
0.01867850124835968,
-0.03609006851911545,
-0.01918436773121357,
-0.017557458952069283,
-0.021682189777493477,
0.03592541813850403,
-0.017240427434444427,
-0.010651351884007454,
-0.025557322427630424,
-0.00629510497674346,
-0.017186010256409645,
0.004890125710517168,
0.003849390894174576,
0.09152646362781525,
-0.035235445946455,
-0.021507298573851585,
0.0022241303231567144,
0.003165104426443577,
0.006035163998603821,
0.0073052928782999516,
-0.0005678089219145477,
-0.04507943615317345,
-0.01648521050810814,
0.016826722770929337,
-0.07330172508955002,
-0.004373594652861357,
-0.030632996931672096,
0.03753260150551796,
-0.027272677049040794,
-0.006593008991330862,
-0.0020439059007912874,
-0.02760213240981102,
0.05223812162876129,
-0.03454755246639252,
0.05928618088364601,
-0.01779046095907688,
0.024201910942792892,
0.049418188631534576,
0.0006833922816440463,
-0.039587754756212234,
0.06380799412727356,
0.06220436468720436,
-0.006431635469198227,
-0.05120518058538437,
-0.03376372531056404,
-0.04796717315912247,
0.021217338740825653,
-0.015272898599505424,
-0.01262344978749752,
0.0481586828827858,
0.046006184071302414,
-0.025742944329977036,
0.019522206857800484,
-0.04411226138472557,
-0.009043698199093342,
0.016879679635167122,
0.08099131286144257,
0.006618355866521597,
0.023816686123609543,
-0.015266531147062778,
0.03295478969812393,
0.010075709782540798,
0.015741508454084396,
0.048220425844192505,
-0.014582469128072262,
0.03572792187333107,
0.037151437252759933,
0.010165599174797535,
0.023856060579419136,
-0.009556155651807785,
0.07080189138650894,
-0.009462782181799412,
-0.015578143298625946,
0.03402557596564293,
-0.010565041564404964,
0.01779155619442463,
0.037160925567150116,
-0.007637834642082453,
-0.04706462472677231,
0.0504482127726078,
0.025592254474759102,
0.03170369565486908,
-0.032427165657281876,
-0.003571011358872056,
-0.011969978921115398,
-0.03658461570739746,
-0.0049546388909220695,
0.0508444607257843,
-0.030187059193849564,
-0.015855535864830017,
-0.02074800431728363,
0.0009854439413174987,
-0.041058775037527084,
-0.004355614073574543,
-0.04666409268975258,
0.027315746992826462,
0.00859667919576168,
0.01908503845334053,
-0.004833002109080553,
0.004120295867323875,
-0.031439393758773804,
-0.0063366577960550785,
0.08379453420639038,
0.07782740890979767,
0.05193348973989487,
-0.034128446131944656,
0.0031542449723929167,
-0.01753261312842369,
-0.058145325630903244,
-0.01344078965485096,
0.0529552698135376,
-0.003684819443151355,
-0.020823802798986435,
0.03981884568929672,
0.001469126553274691,
-0.007204345427453518,
0.00955450814217329,
0.026408053934574127,
0.03072122298181057,
-0.03198268264532089,
-0.07945685088634491,
-0.05413277819752693,
0.035113535821437836,
-0.056865572929382324,
-0.019147265702486038,
-0.05893222987651825,
0.03865649923682213,
0.009988341480493546,
0.09760850667953491,
-0.000852512544952333,
0.02568191848695278,
-0.019725484773516655,
0.02171269617974758,
0.020262336358428,
-0.032934918999671936,
-0.03804715350270271,
0.04329640790820122,
-0.03173251822590828,
-0.04070490971207619,
-0.04276524856686592,
0.08638207614421844,
0.022319525480270386,
-0.014637649990618229,
-0.02597663924098015,
0.07076575607061386,
-0.022998694330453873,
-0.0016943158116191626,
-0.0011142075527459383,
0.014167921617627144,
-0.0049987477250397205,
0.09064961969852448,
0.027700550854206085,
0.005568596068769693,
0.036521587520837784,
-0.002385250758379698,
0.01191679760813713,
0.01791209541261196,
0.011813826858997345,
0.014618918299674988,
-0.03801717981696129,
-0.03647183999419212,
-0.013927782885730267,
-0.010267778299748898,
-0.004637797828763723,
-0.02066658064723015,
-0.008649895898997784,
-0.019562700763344765,
-0.020470604300498962,
-0.03306567296385765,
0.016365230083465576,
0.02053295634686947,
-0.0002226840879302472,
-0.04271835461258888,
-0.04325303062796593,
-0.004811068996787071,
-0.0917980968952179,
0.010604835115373135,
0.0006071192910894752,
-0.009599686600267887,
0.08442821353673935,
-0.02577243186533451,
0.012222071178257465,
-0.021914660930633545,
-0.060651227831840515,
-0.04876962676644325,
0.03320596367120743,
-0.015725838020443916,
-0.01701061986386776,
0.00857437402009964,
0.0406915657222271,
0.019158879294991493,
-0.026926876977086067,
0.019720399752259254,
-0.06272737681865692,
-0.06142835319042206,
0.012531920336186886,
-0.023944515734910965,
0.03928546607494354,
0.04514578357338905,
-0.008133684284985065,
0.007133653853088617,
0.0041239503771066666,
-0.02038213610649109,
0.008545354939997196,
-0.046630553901195526,
0.02884673699736595,
0.05325953662395477,
0.023620815947651863,
-0.031102841719985008,
0.05730561539530754,
-0.007316193077713251,
0.015849644318223,
0.007719119545072317,
-0.03917967900633812,
-0.025940604507923126,
-0.02426840551197529,
0.045204345136880875,
0.03839406743645668,
-8.425280384471989e-7,
-0.004700192250311375,
0.04015927389264107,
0.03510860353708267,
-0.008533322252333164,
0.046303242444992065,
-0.02706930972635746,
-0.0065178354270756245,
0.017707962542772293,
-0.005222933366894722,
0.02231505885720253,
0.007981525734066963,
-0.028786493465304375,
-0.0036302467342466116,
0.0015215618768706918,
0.009386024437844753,
-0.055886562913656235,
-0.007476782891899347,
-0.02370934933423996,
0.003804679960012436,
-0.009733976796269417,
-0.050842396914958954,
-0.009052416309714317,
0.007785063702613115,
0.05041658878326416,
-0.0017887447029352188,
-0.024047479033470154,
-0.02226346917450428,
-0.025152424350380898,
-0.032377783209085464,
0.0270904079079628,
-0.0061332182958722115,
-0.031805891543626785,
-0.029098954051733017,
0.010120893828570843,
-0.0018643529620021582,
-0.01788823865354061,
-0.030863847583532333,
-0.00673909205943346,
-0.02053968608379364,
0.0019881518092006445,
0.008979016914963722,
0.005077789071947336,
0.05257613956928253,
-0.044848404824733734,
-0.02284921333193779,
0.01998828910291195,
-0.022166606038808823,
0.003848159220069647,
0.04405437409877777,
-0.040438212454319,
0.009960116818547249,
-0.04031628370285034,
-0.010029965080320835,
0.03144064545631409,
-0.016428623348474503,
0.04066595435142517,
0.005905534606426954,
0.009818377904593945,
-0.05582472309470177,
-0.019077293574810028,
0.00004637082383851521,
-0.017965959385037422,
-0.006761396769434214,
-0.019104812294244766,
0.04722030088305473,
-0.028250394389033318,
-0.030601782724261284,
0.022804435342550278,
-0.01743967831134796,
-0.052001748234033585,
-0.038344528526067734,
0.0010925979586318135,
0.018835468217730522,
-0.03032190538942814,
0.02839346043765545,
0.03535587340593338,
-0.058840375393629074,
-0.021663134917616844,
-0.042973726987838745,
-0.06629981845617294,
0.043988410383462906,
-0.018782759085297585,
0.026864178478717804,
-0.004008044023066759,
-0.014122003689408302,
0.0536910817027092,
0.04085925593972206,
-0.06117703393101692,
0.010737129487097263,
-0.01409066654741764,
0.01451844722032547,
0.03180577605962753,
-0.0010929469717666507,
0.038576461374759674,
-0.014198554679751396,
0.03280676528811455,
0.016878049820661545,
0.022795431315898895,
0.024772316217422485,
0.013149827718734741,
0.04685218259692192,
0.011046835221350193,
0.005073774605989456,
0.0025330448988825083,
0.005136696621775627,
0.008044014684855938,
-0.031981274485588074,
-0.01676608808338642,
-0.01670941151678562,
0.018811235204339027,
0.018114548176527023,
-0.07652969658374786,
0.08140592277050018,
0.029148632660508156,
0.022229650989174843,
-0.04422672837972641,
0.06427197903394699,
0.0006848605116829276,
-0.012977023608982563,
0.009749216958880424,
0.02750810608267784,
0.04333203285932541,
0.0032960514072328806,
0.023220282047986984,
0.03425389528274536,
0.04366016015410423,
-0.030435482040047646,
0.002186320023611188,
0.001303064520470798,
-0.006255787797272205,
0.023104434832930565,
-0.06173606589436531,
-0.04058096930384636,
0.07560662180185318,
0.02107856050133705,
0.012899565510451794,
-0.03441184386610985,
-0.034131865948438644,
-0.0021648479159921408,
-0.04882653430104256,
0.014584305696189404,
-0.021238647401332855,
0.04573919624090195,
0.02223138138651848,
0.07070966064929962,
-0.005554759409278631,
0.005780178587883711,
0.015116944909095764,
-0.007354422006756067,
-0.09607088565826416,
0.04242413118481636,
0.015187413431704044,
-0.03578179329633713,
-0.016312342137098312,
-0.01877797208726406,
0.02311486378312111,
-0.007133773062378168,
-0.025752494111657143,
-0.021929826587438583,
-0.020609533414244652,
-0.04126248136162758,
0.02853461541235447,
-0.05365956574678421,
-0.06170227751135826,
-0.013628637418150902,
0.028308480978012085,
0.03780970349907875,
-0.017427688464522362,
0.03928817808628082,
0.016007861122488976,
-0.02864057756960392,
0.017015421763062477,
-0.019220620393753052,
0.028217395767569542,
0.025817643851041794,
0.007909471169114113,
0.030339643359184265,
0.029302019625902176,
-0.0036306108813732862,
0.03449533134698868,
0.027586527168750763,
0.06743349879980087,
0.04332214221358299,
-0.029931386932730675,
-0.028476765379309654,
-0.03846113756299019,
0.012118604965507984,
0.013532977551221848,
0.043503280729055405,
0.02560870721936226,
-0.02294832468032837,
0.04129347950220108,
0.019895043224096298,
-0.03632093593478203,
0.032871462404727936,
0.02138160914182663,
-0.00558254262432456,
-0.0062784296460449696,
-0.04201590642333031,
-0.004465199075639248,
0.014529438689351082,
0.016591152176260948,
0.014774974435567856,
-0.01214106846600771,
0.017299773171544075,
0.004589996766299009,
0.032450780272483826,
0.021714242175221443,
-0.0352591872215271,
-0.02854057028889656,
-0.00009123383642872795,
0.021712496876716614,
0.01078538317233324,
-0.04581718519330025,
0.01583218015730381,
0.0486752949655056,
0.0093008978292346,
0.015083438716828823,
-0.0031873479019850492,
-0.04082292690873146,
0.00016950244025792927,
0.03222839906811714,
0.011952292174100876,
0.0005457946681417525,
0.005304412450641394,
-0.036691922694444656,
-0.05687901750206947,
0.06570154428482056,
-0.00976634956896305,
0.022106695920228958,
-0.007334169466048479,
0.008875524625182152,
-0.05354785546660423,
-0.025846296921372414,
0.006443682126700878,
0.0255497545003891,
0.013414976187050343,
0.010000865906476974,
-0.039110735058784485,
0.008229202590882778,
-0.03241020441055298,
-0.0009207947296090424,
0.008280790410935879,
0.06756395101547241,
0.003908652812242508,
0.0326620414853096,
0.00046526413643732667,
0.030064236372709274,
-0.02170349471271038,
-0.09612683206796646,
-0.012059403583407402,
-0.002617472317069769,
-0.022105606272816658,
0.032421957701444626,
-0.02609318122267723,
-0.05956016853451729,
0.013426868245005608,
-0.02984146773815155,
-0.014007382094860077,
0.03591173514723778,
-0.04623699560761452,
0.057740237563848495,
0.010664661414921284,
-0.01520377118140459,
0.042752619832754135,
0.036200810223817825,
-0.03090093471109867,
-0.018288686871528625,
-0.0001821748592192307,
0.041695401072502136,
-0.024160580709576607,
0.04179682955145836,
-0.046526603400707245,
-0.0012526876525953412,
-0.01761796325445175,
0.0423547588288784,
-0.026305731385946274,
-0.000767892284784466,
-0.010605932213366032,
-0.02441999688744545,
-0.0030626035295426846,
-0.005028840154409409,
-0.01837303303182125,
-0.014798324555158615,
0.016367105767130852,
0.02485428936779499,
0.03397918865084648,
-0.006121382582932711,
0.01662421226501465,
0.0004611987969838083,
-0.016383280977606773,
0.019064676016569138,
-0.007596644107252359,
0.038124438375234604,
-0.050397131592035294,
-0.016416728496551514,
0.010094057768583298,
-0.03446876257658005,
0.023284295573830605,
0.022233938798308372,
0.000997907598502934,
0.004375598393380642,
-0.03344988822937012,
-0.02486097440123558,
-0.020584359765052795,
-0.02257515862584114,
0.011185074225068092,
-0.04635205864906311,
0.010760495439171791,
0.026896152645349503,
-0.004852801561355591,
-0.0691140666604042,
-0.03795048967003822,
0.004731487017124891,
0.01730623096227646,
-0.038160860538482666,
-0.02660256251692772,
0.029767347499728203,
-0.02820485457777977,
-0.015367868356406689,
0.001473623444326222,
0.03321021422743797,
0.012857750058174133,
-0.030880969017744064,
0.017248909920454025,
0.059928394854068756,
0.03241141885519028,
-0.008572177961468697,
-0.011692725121974945,
0.022382205352187157,
-0.04843994230031967,
-0.016041027382016182,
0.0037749032489955425,
0.032776132225990295,
-0.023328015580773354,
-0.0021708558779209852,
0.011997375637292862,
0.005314149893820286,
0.0402466244995594,
-0.0026941311080008745,
-0.02064012922346592,
0.013771450147032738,
-0.025211792439222336,
-0.00819564051926136,
-0.027524881064891815,
-0.006015837658196688,
0.0010732082882896066,
0.015712987631559372,
0.022845324128866196,
-0.004102665465325117,
-0.006961686536669731,
-0.04391273483633995,
0.02826075628399849,
-0.015247206203639507,
-0.03961675241589546,
0.018755998462438583,
0.03503969684243202,
0.0021333028562366962,
-0.0110228406265378,
0.04649849236011505,
-0.032852448523044586,
-0.00253337062895298,
-0.03591807559132576,
0.005344224162399769,
0.009879267774522305,
0.014299461618065834,
-0.030751315876841545,
-0.02584514208137989,
-0.03323542699217796,
-0.011163531802594662,
0.05697774887084961,
-0.031038323417305946,
0.02746981382369995,
0.01993776671588421,
-0.028905050829052925,
-0.025603361427783966,
-0.029237428680062294,
-0.0012560858158394694,
0.006594954989850521,
0.00040899121086113155,
0.04136275872588158,
-0.06432659178972244,
-0.012685445137321949,
0.03382230922579765,
0.030699865892529488,
-0.0008990528294816613,
0.005326422397047281,
-0.016317816451191902,
0.00830604787915945,
0.01956004463136196,
-0.0012268124846741557,
-0.005901488941162825,
0.06233667954802513,
-0.028546441346406937,
-0.006839210167527199,
0.010962402448058128,
-0.0010949007701128721,
0.0265984907746315,
0.02208211086690426,
-0.007187352981418371,
-0.006342805456370115,
-0.010699446313083172,
-0.029258979484438896,
0.018239004537463188,
-0.022994372993707657,
0.036253783851861954,
0.04487933591008186,
-0.0037291438784450293,
0.013578249141573906,
0.01726703532040119,
-0.013976612128317356,
0.0030124294571578503,
-0.05713031068444252,
0.00029593531507998705,
-0.04972173646092415,
-0.04723465442657471,
0.0399213545024395,
0.018589334562420845,
-0.012886825017631054,
0.02655103988945484,
-0.03482479229569435,
0.031101444736123085,
0.02020740881562233,
0.023833349347114563,
-0.035240430384874344,
0.06790634244680405,
0.0028718390967696905,
0.05475271865725517,
-0.03956681489944458,
0.005385667085647583,
0.13435688614845276,
0.062450140714645386,
0.03284028545022011,
-0.06485750526189804,
-0.02757946029305458,
-0.0015796087682247162,
0.016708068549633026,
-0.01786501705646515,
0.04370430111885071,
0.016781799495220184,
-0.02256331592798233,
-0.013672913424670696,
0.05740690976381302,
-0.013674401678144932,
-0.026274006813764572,
0.04288479685783386,
-0.03297095000743866,
-0.0512784905731678,
-0.018465422093868256,
0.024970768019557,
-0.009325787425041199,
-0.021523617208003998,
-0.02528006210923195,
-0.022819198668003082,
-0.034996397793293,
0.01255025900900364,
0.01310561504215002,
-0.039776530116796494,
0.044675201177597046,
0.029688449576497078,
-0.02194184809923172,
-0.0023062704131007195,
-0.001097256550565362,
0.01380801573395729,
-0.027284104377031326,
0.005115612875670195,
0.01845994032919407,
0.023370688781142235,
0.041555117815732956,
0.06389493495225906,
0.016755755990743637,
-0.014061870984733105,
0.0024575015995651484,
0.033104222267866135,
-0.002793650608509779,
-0.04552413523197174,
-0.05648673698306084,
0.054549142718315125,
-0.024787819012999535,
0.0035365435760468245,
-0.021385369822382927,
-0.04863889887928963,
0.04420681670308113,
-0.03190428763628006,
0.025734441354870796,
0.03957832232117653,
0.04558674246072769,
0.006646123249083757,
0.019701195880770683,
-0.007032232824712992,
0.018440846353769302,
0.014331474900245667,
0.010219947434961796,
-0.004525512456893921,
-0.05958085507154465,
0.000648276531137526,
-0.0022752562072128057,
0.02231569215655327,
-0.006304145324975252,
-0.00691619236022234,
-0.03298194333910942,
-0.016147546470165253,
-0.0778852328658104,
-0.015168252401053905,
0.0207492858171463,
0.012363938614726067,
0.06448468565940857,
-0.004742858465760946,
0.00683753052726388,
-0.01769145019352436,
-0.04532155767083168,
0.016657881438732147,
-0.012126851826906204,
-0.010910511016845703,
0.011006000451743603,
-0.008918446488678455,
0.008053271099925041,
0.035727959126234055,
-0.006689499132335186,
0.027377229183912277,
-0.008717617020010948,
0.014105638489127159,
0.03528006374835968,
-0.02441556379199028,
-0.017735378816723824,
-0.00450553372502327,
-0.021633852273225784,
0.014097698964178562,
-0.03659228980541229,
0.025624869391322136,
-0.025358594954013824,
-0.008200112730264664,
-0.0033049716148525476,
0.03523527458310127,
0.03847706317901611,
0.011412485502660275,
0.008331953547894955,
0.005562296602874994,
-0.011653860099613667,
0.032960813492536545,
0.059952035546302795,
-0.03365934267640114,
-0.04195338487625122,
-0.012365554459393024,
0.015547128394246101,
-0.007334290072321892,
0.003844078164547682,
-0.047542326152324677,
0.004205137025564909,
-0.030377576127648354,
0.009992116130888462,
0.0008595375693403184,
-0.010684091597795486,
-0.04439665004611015,
0.034973759204149246,
-0.029695667326450348,
-0.00730659905821085,
0.003203869564458728,
0.06136586144566536,
-0.014905250631272793,
-0.051861006766557693,
0.04288744553923607,
0.035135384649038315,
-0.035943809896707535,
-0.02178301103413105,
0.027085380628705025,
0.029515881091356277,
0.02525758370757103,
-0.015905238687992096,
-0.05500240996479988,
0.01146851945668459,
-0.012144272215664387,
-0.07238730788230896,
0.04080432280898094,
0.026014938950538635,
-0.004279620945453644,
0.04387177899479866,
-0.012342260219156742,
0.010150843299925327,
0.0382365919649601,
-0.024865834042429924,
-0.0110932607203722,
0.01229365449398756,
-0.0338444784283638,
-0.0011559813283383846,
-0.002048920374363661,
0.029285402968525887,
0.04066753387451172,
-0.025663988664746284,
0.018265489488840103,
0.023180333897471428,
0.004851826466619968,
0.011479699984192848,
0.005991985555738211,
-0.022911710664629936,
0.012554878368973732,
-0.007819280959665775,
-0.02493623085319996,
0.029686816036701202,
0.07935873419046402,
-0.009749441407620907,
0.02097710780799389,
0.049975380301475525,
-0.025320209562778473,
-0.07825525104999542,
0.010814638808369637,
-0.019234979525208473,
0.049316927790641785,
0.025053761899471283,
-0.036262236535549164,
0.007624566089361906,
-0.0000708649167791009,
-0.06789273023605347,
0.02759120985865593,
-0.021220123395323753,
0.0009065237827599049,
-0.026896296069025993,
0.010037901811301708,
-0.03123253770172596,
0.05782333388924599,
0.030799157917499542,
0.05806323513388634,
0.0267771165817976,
-0.018363548442721367,
-0.008047490380704403,
0.005852994509041309,
-0.01981649547815323,
-0.003460796782746911,
-0.021073395386338234,
-0.017682651057839394,
0.07258598506450653,
-0.026453448459506035,
-0.061489708721637726,
0.02803492732346058,
-0.007562628481537104,
0.022258272394537926,
-0.03346863389015198,
-0.0131016094237566,
0.000664175022393465,
0.0014440733939409256,
0.0030758343636989594,
-0.028340918943285942,
0.012286470271646976,
0.01079799234867096,
0.020641406998038292,
0.001870006788522005,
0.0008425635169260204,
0.02956560254096985,
0.013045614585280418,
-0.04482201486825943,
-0.05288951098918915,
0.05657263472676277,
0.028095941990613937,
0.01655140146613121,
0.0004667356261052191,
-0.020002709701657295,
0.024865567684173584,
0.030455730855464935,
0.021014336496591568,
-0.030916834250092506,
0.012860511429607868,
0.016874544322490692,
0.03605339676141739,
-0.004567519295960665,
0.04297642782330513,
0.003463763277977705,
-0.035495758056640625,
0.03760257363319397,
0.011899368837475777,
-0.011197931133210659,
-0.049492109566926956,
-0.0004392719129100442,
-0.01822114922106266,
-0.02166072092950344,
-0.0003216840559616685,
-0.01812174543738365,
-0.034794360399246216,
0.017441026866436005,
-0.02026452124118805,
0.016707301139831543,
0.0020223374012857676,
-0.031108135357499123,
-0.024681739509105682,
-0.039338503032922745,
0.03179405257105827,
0.002236583037301898,
0.008826718665659428,
-0.052080895751714706,
-0.00026461182278580964,
0.029752710834145546,
-0.004770688246935606,
0.03917912021279335,
-0.004190961364656687,
0.011386116966605186,
-0.008092328906059265,
-0.016443835571408272,
0.03891592472791672,
-0.05025636404752731,
0.004190473351627588,
-0.02150542475283146,
0.038862038403749466,
0.002508574863895774,
0.010893324390053749,
-0.019136877730488777,
0.026880567893385887,
0.04310724511742592,
-0.013331321068108082,
0.016357000917196274,
0.030904419720172882,
-0.048537589609622955,
0.05603654310107231,
0.018236685544252396,
0.018215253949165344,
0.055070001631975174,
-0.034936822950839996,
0.03483543172478676,
0.059850554913282394,
-0.02744589000940323,
-0.031196698546409607,
0.03303423151373863,
-0.02894505485892296,
-0.04792424663901329,
-0.006873518694192171,
-0.015449619852006435,
0.006116862874478102,
-0.06036932021379471,
-0.028112296015024185,
0.03695498779416084,
-0.008236963301897049,
0.010653273202478886,
0.05489760637283325,
-0.02076703868806362,
0.037245139479637146,
0.019521597772836685,
0.010291081853210926,
0.02483191341161728,
0.004824611358344555,
-0.023142479360103607,
0.01836147904396057,
0.05975119024515152,
-0.004550849553197622,
0.03882816433906555,
0.03259686753153801,
-0.030999930575489998,
-0.00991737563163042,
0.013357199728488922,
0.03138836473226547,
-0.05477190390229225,
0.012826868332922459,
0.008913443423807621,
-0.020953785628080368,
-0.0023913593031466007,
0.042784981429576874,
-0.03251273185014725,
0.05373730883002281,
-0.026128822937607765,
0.0013167090946808457,
-0.011253626085817814,
0.007282945327460766,
-0.032145436853170395,
-0.0026714219711720943,
0.02338479273021221,
0.05220412090420723,
0.006610104348510504,
-0.012081636115908623,
-0.005975519772619009,
0.01787574775516987,
-0.005744634196162224,
-0.06912895292043686,
-0.011318513192236423,
-0.008802198804914951,
-0.01616387628018856,
0.007416303735226393,
-0.03989960998296738,
-0.025909200310707092,
-0.014546503312885761,
-0.008209934458136559,
0.039551980793476105,
0.010038306936621666,
-0.02623658813536167,
0.0008959045517258346,
-0.06577868014574051,
0.060298532247543335,
-0.06262804567813873,
0.02655704878270626,
-0.014078056439757347,
0.035103749483823776,
-0.012202529236674309,
-0.007058462128043175
] |
<p>Are there any non magnetic materials that attract to each other as if they were magnetic?</p>
<p>This is an argument I am having with a friend. </p>
<p>Thanks,</p>
| 10,760 |
[
-0.022859865799546242,
0.0025804152246564627,
-0.010491771623492241,
-0.035845205187797546,
0.034114159643650055,
0.01960083842277527,
-0.014497636817395687,
0.01842021383345127,
0.010827320627868176,
-0.03171356022357941,
0.04245397821068764,
0.02414696291089058,
0.047640006989240646,
0.02403128892183304,
0.015182217583060265,
0.005135850049555302,
-0.01150814350694418,
0.02257731556892395,
0.008582851849496365,
-0.04333410784602165,
0.0034793918021023273,
-0.010005127638578415,
-0.002130565932020545,
0.019689509645104408,
-0.015539496205747128,
0.013303739950060844,
0.03207287937402725,
-0.019551608711481094,
0.039877112954854965,
0.015162387862801552,
-0.020563116297125816,
-0.03406725823879242,
-0.005939682945609093,
0.024960698559880257,
0.04701441526412964,
0.006700735539197922,
-0.03342817723751068,
-0.0010483020450919867,
-0.02557162195444107,
0.025112971663475037,
-0.016861259937286377,
-0.019335811957716942,
0.017986416816711426,
0.04307558014988899,
-0.01307735312730074,
0.007632592227309942,
0.014287919737398624,
-0.04654330387711525,
0.04696154594421387,
-0.07489830255508423,
0.05641240254044533,
-0.028406837955117226,
0.024311764165759087,
0.04057946801185608,
0.012419017031788826,
-0.030770285055041313,
0.04770663008093834,
0.056162383407354355,
-0.0024649074766784906,
-0.05306011810898781,
-0.008355775848031044,
-0.024980301037430763,
-0.02444666437804699,
-0.06500647962093353,
-0.04726136475801468,
0.062493711709976196,
-0.013386891223490238,
-0.007397418841719627,
0.03584573045372963,
0.02198544703423977,
0.00023634606623090804,
0.033945195376873016,
0.034802522510290146,
-0.008083689957857132,
-0.04052230343222618,
-0.014798860996961594,
0.010908502154052258,
0.02173713408410549,
0.0570853166282177,
0.040178317576646805,
-0.026484383270144463,
-0.0009580575278960168,
0.02475753054022789,
0.028684761375188828,
0.029516614973545074,
-0.012959985062479973,
0.04849104583263397,
-0.025271352380514145,
0.012182299979031086,
0.04902192950248718,
0.012037317268550396,
-0.01581857167184353,
0.025192325934767723,
0.0016618133522570133,
-0.04252450913190842,
0.005727060604840517,
0.0008721431368030608,
0.05848017334938049,
0.03911759704351425,
-0.027175726369023323,
-0.004300413653254509,
0.00466484110802412,
0.028594782575964928,
0.08811521530151367,
0.06550338864326477,
-0.04722269997000694,
-0.03503631055355072,
0.022537756711244583,
0.013918598182499409,
0.010985050350427628,
0.011810156516730785,
0.013932895846664906,
0.01929789036512375,
-0.02081434242427349,
0.009829350747168064,
0.010017607361078262,
-0.008701186627149582,
-0.026443002745509148,
0.029069971293210983,
0.09330492466688156,
0.024762826040387154,
-0.04019967466592789,
0.018868213519454002,
-0.022091683000326157,
-0.043500009924173355,
-0.003642452647909522,
0.014253019355237484,
0.007909432984888554,
-0.021450864151120186,
0.021711725741624832,
-0.007495816797018051,
-0.014589137397706509,
-0.0031864948105067015,
-0.027646450325846672,
0.05195264518260956,
-0.018171526491642,
-0.0882098451256752,
-0.06364929676055908,
0.020894760265946388,
-0.010243654251098633,
-0.011491884477436543,
-0.06594143062829971,
0.0065528713166713715,
0.02126077190041542,
0.0675547644495964,
0.01257884968072176,
-0.0020450688898563385,
-0.006361520383507013,
0.046070776879787445,
-0.009699701331555843,
-0.011516004800796509,
-0.0581490620970726,
0.00448159035295248,
-0.06700734794139862,
0.01230029296129942,
-0.03391394764184952,
-0.0034656196366995573,
0.010251151397824287,
0.017879996448755264,
0.0007662144489586353,
-0.008538858033716679,
-0.03981994092464447,
0.0004193374188616872,
0.022938629612326622,
-0.005809101276099682,
-0.05201615020632744,
0.07475496083498001,
0.010256776586174965,
0.01801546849310398,
0.02709888108074665,
0.00723916245624423,
0.037081122398376465,
0.042776819318532944,
0.049881864339113235,
0.029841212555766106,
-0.05880146101117134,
-0.02591853402554989,
-0.01093262992799282,
0.00698850816115737,
0.016272636130452156,
-0.04822980612516403,
0.0025633664336055517,
0.008955076336860657,
0.04826383292675018,
-0.007993573322892189,
0.04664149135351181,
0.010106408037245274,
-0.06374803930521011,
0.020062681287527084,
-0.07490332424640656,
0.0013429089449346066,
-0.028176985681056976,
0.006249106954783201,
-0.02845998853445053,
-0.027461867779493332,
0.020781947299838066,
0.03549851104617119,
0.008983085863292217,
-0.05535685271024704,
-0.03230437636375427,
0.017186090350151062,
0.014830704778432846,
0.0013899628538638353,
-0.014437324367463589,
-0.016380073502659798,
0.06592795252799988,
0.01363220252096653,
-0.004135367926210165,
0.025770273059606552,
-0.043738123029470444,
-0.04395029693841934,
-0.004912625532597303,
-0.0176552701741457,
0.008039639331400394,
0.0044172294437885284,
0.005843698978424072,
0.03613942861557007,
0.016086990013718605,
-0.010970868170261383,
0.05330050364136696,
-0.033736951649188995,
0.05789387971162796,
0.021085815504193306,
-0.0008986593456938863,
0.005909831263124943,
0.013991580344736576,
0.03100273758172989,
0.006470239255577326,
-0.016721466556191444,
-0.01940283179283142,
-0.09144081920385361,
0.03535730391740799,
0.0250018909573555,
0.03532734140753746,
-0.03863726183772087,
0.033137328922748566,
0.0015504879411309958,
0.08402514457702637,
-0.005869525484740734,
0.006910615600645542,
-0.015524312853813171,
-0.020678550004959106,
0.0012988228118047118,
0.00011134958185721189,
0.038964856415987015,
0.02911192551255226,
0.03430534154176712,
-0.004048820119351149,
0.01689029112458229,
0.007356969173997641,
-0.04443787783384323,
0.008161375299096107,
0.0076346625573933125,
0.004492505919188261,
0.008274851366877556,
-0.049696408212184906,
0.029675522819161415,
-0.016864113509655,
0.028327733278274536,
-0.011304008774459362,
0.005363846197724342,
-0.03450049087405205,
0.0021482850424945354,
-0.03572908043861389,
-0.031554579734802246,
-0.0068775624968111515,
-0.032435446977615356,
-0.013781878165900707,
0.0492006279528141,
-0.03757048025727272,
-0.0039847781881690025,
0.007590282708406448,
0.03313238173723221,
-0.01946943998336792,
0.012137812562286854,
0.009513339959084988,
0.022942161187529564,
0.058151353150606155,
-0.015474790707230568,
-0.01767686940729618,
-0.0037529657129198313,
-0.04431888461112976,
-0.03409367799758911,
-0.003452081000432372,
-0.0459216833114624,
0.035316888242959976,
-0.004901829641312361,
-0.02762061171233654,
0.025374364107847214,
0.011575743556022644,
-0.019725048914551735,
0.031037673354148865,
-0.01677212305366993,
-0.06008514016866684,
-0.005349983461201191,
-0.011466268450021744,
0.0016471657436341047,
-0.044619351625442505,
0.011459781788289547,
0.02583041973412037,
-0.007960909977555275,
-0.04084620624780655,
-0.0037207745481282473,
-0.030252140015363693,
-0.05660281330347061,
-0.003955918829888105,
-0.04331200569868088,
0.022606121376156807,
-0.029318902641534805,
0.008099241182208061,
-0.0042192270047962666,
-0.033458199352025986,
0.007633395027369261,
-0.0528462715446949,
-0.029855770990252495,
0.024440260604023933,
-0.027149541303515434,
0.00511534046381712,
0.0334368459880352,
-0.051388006657361984,
0.02959090657532215,
0.02429463155567646,
-0.05649277940392494,
-0.019260060042142868,
-0.02195373922586441,
-0.03441885486245155,
-0.06396738439798355,
0.04218420758843422,
0.0686967596411705,
0.026977965608239174,
-0.0033553994726389647,
0.026270784437656403,
0.012980125844478607,
-0.023878851905465126,
-0.002423358615487814,
-0.02691241353750229,
0.03351164236664772,
0.053219858556985855,
0.004079468082636595,
0.07533393055200577,
0.01845225691795349,
-0.06573346257209778,
0.028348593041300774,
0.018903078511357307,
0.029827281832695007,
0.01586010307073593,
-0.041027456521987915,
0.04363899677991867,
-0.0012608389370143414,
0.04892054572701454,
-0.042865898460149765,
0.04024174064397812,
-0.0011413419852033257,
-0.001925235497765243,
0.015703119337558746,
0.012793807312846184,
0.012930398806929588,
-0.005348265636712313,
0.042491935193538666,
0.05611444637179375,
0.018966753035783768,
-0.034250933676958084,
-0.010904318653047085,
0.007496751844882965,
0.0151924267411232,
0.014010997489094734,
-0.031158486381173134,
-0.0014728860696777701,
0.03529587388038635,
0.0025465674698352814,
0.020492644980549812,
0.015811998397111893,
-0.037164945155382156,
0.0059269145131111145,
-0.06468875706195831,
0.0026853657327592373,
-0.0073226201348006725,
0.017048057168722153,
-0.0027293963357806206,
0.04281427338719368,
0.003975584637373686,
-0.002164016477763653,
0.016321608796715736,
-0.038152359426021576,
-0.0922892615199089,
0.0363919734954834,
-0.021355323493480682,
0.004435838665813208,
-0.007843025960028172,
-0.03964142128825188,
-0.03695634379982948,
-0.03200682997703552,
0.0006100707687437534,
-0.023149868473410606,
-0.04147307202219963,
-0.03676889091730118,
0.006165339145809412,
-0.02080017328262329,
-0.045064520090818405,
-0.0003928949881810695,
0.020354174077510834,
-0.007783126551657915,
-0.01858372613787651,
0.035118941217660904,
0.004787045065313578,
-0.03487272560596466,
0.012849080376327038,
-0.01536521315574646,
0.010469240136444569,
-0.0026452038437128067,
0.009485667571425438,
0.017200112342834473,
0.0008770942804403603,
-0.018422285094857216,
-0.014881141483783722,
0.013391072861850262,
0.026522209867835045,
-0.027638128027319908,
-0.00408830726519227,
-0.0604989267885685,
-0.06763039529323578,
-0.0342593751847744,
-0.01593530736863613,
0.08120230585336685,
0.007492864038795233,
0.012050713412463665,
0.00852514710277319,
-0.0002904900466091931,
-0.005502235610038042,
0.015081961639225483,
0.01982225850224495,
0.05752347409725189,
-0.042541880160570145,
-0.021897880360484123,
-0.004433559253811836,
-0.013202106580138206,
0.02387133426964283,
0.05159902945160866,
0.01128855999559164,
-0.0047135064378380775,
-0.0029713676776736975,
-0.005458407569676638,
0.02564181759953499,
0.01625405065715313,
0.016253037378191948,
-0.016653092578053474,
-0.00019466935191303492,
-0.014722095802426338,
-0.019470512866973877,
0.007943800650537014,
0.05220688506960869,
0.05671091005206108,
-0.0025004278868436813,
-0.027125099673867226,
-0.10505351424217224,
0.03868025541305542,
0.06633835285902023,
0.03312516212463379,
-0.03205240145325661,
-0.026957858353853226,
-0.02904408611357212,
-0.0008925437578000128,
0.0126777533441782,
-0.03765106201171875,
-0.008518378250300884,
-0.031333066523075104,
0.010269183665513992,
-0.009445003233850002,
-0.025933945551514626,
-0.007451798766851425,
0.0034529699478298426,
0.00510614737868309,
-0.0004266503674443811,
-0.015048644505441189,
-0.03231041878461838,
0.00796089693903923,
0.027813691645860672,
0.05301794037222862,
0.022880857810378075,
0.02217843383550644,
0.021514395251870155,
0.011843117885291576,
-0.0010387466754764318,
-0.00872140284627676,
-0.0907757505774498,
0.03159724920988083,
0.01882747933268547,
-0.0375245176255703,
0.04544904828071594,
-0.02153397724032402,
-0.03532331809401512,
0.0030850074253976345,
-0.02334742248058319,
0.023608548566699028,
0.015084123238921165,
-0.03082529455423355,
0.028247512876987457,
0.04926367104053497,
0.026974981650710106,
0.04629518464207649,
0.0550626665353775,
-0.03221040591597557,
-0.02537539228796959,
-0.03629833087325096,
0.04562836140394211,
-0.057394202798604965,
0.02368326671421528,
-0.004950082395225763,
-0.0020111931953579187,
-0.026527859270572662,
0.023602047935128212,
0.010410608723759651,
-0.004160830285400152,
0.03128063306212425,
-0.02644382417201996,
-0.028607646003365517,
0.004697440192103386,
0.0061850170604884624,
0.004052109085023403,
-0.017012448981404305,
-0.006597731728106737,
-0.002721484052017331,
-0.0030107195489108562,
0.04120161384344101,
-0.003885790938511491,
-0.038749441504478455,
0.04831970855593681,
-0.011162797920405865,
-0.007610278204083443,
-0.06805043667554855,
0.0006743979174643755,
-0.047181740403175354,
-0.051398225128650665,
0.05666258558630943,
-0.017299024388194084,
0.009811334311962128,
0.02438453957438469,
-0.017987223342061043,
0.0025625715497881174,
0.020301315933465958,
0.0035592131316661835,
0.019946707412600517,
-0.034680161625146866,
0.025746537372469902,
-0.011845238506793976,
-0.021052174270153046,
-0.05564389377832413,
-0.08594519644975662,
0.004814993590116501,
0.030906949192285538,
-0.016924094408750534,
-0.03962225839495659,
0.00169677275698632,
-0.022600190714001656,
-0.03783654421567917,
0.02720080316066742,
0.041572511196136475,
-0.03427325561642647,
-0.01568637788295746,
0.03586006537079811,
-0.014560583978891373,
0.05233343690633774,
-0.005795737728476524,
-0.06545098125934601,
0.010194839909672737,
-0.012625954113900661,
0.03042553924024105,
-0.024007271975278854,
0.04298591986298561,
-0.02262183278799057,
-0.005790551658719778,
0.010579871945083141,
-0.00790089275687933,
0.056977007538080215,
-0.003970536403357983,
0.01124998927116394,
0.0407467819750309,
0.013946924358606339,
-0.04448337107896805,
-0.03898010030388832,
0.023958873003721237,
0.0221980269998312,
0.0021676828619092703,
-0.028880489990115166,
0.04287097230553627,
-0.02590259350836277,
-0.06525767594575882,
0.03947081416845322,
0.010673888027668,
0.004659426864236593,
0.008457949385046959,
0.09124287217855453,
0.01546446606516838,
-0.024616029113531113,
0.01926608569920063,
-0.0018162298947572708,
0.038467198610305786,
-0.03854257985949516,
0.014386815950274467,
-0.004955220967531204,
0.026373732835054398,
-0.0328846238553524,
-0.029672550037503242,
0.03378823399543762,
0.011350773274898529,
0.04501108080148697,
-0.05176803469657898,
0.047889914363622665,
0.040694478899240494,
0.016090059652924538,
-0.004127303138375282,
-0.002276810584589839,
-0.0036166964564472437,
0.008166258223354816,
-0.024797795340418816,
0.03134820982813835,
-0.004008305259048939,
0.03777968883514404,
0.027474265545606613,
0.03363216295838356,
-0.024550914764404297,
0.02826341800391674,
0.010899216867983341,
0.034349508583545685,
0.056554339826107025,
0.03670938313007355,
-0.040173958986997604,
0.013425562530755997,
-0.045765772461891174,
0.058628540486097336,
0.019781261682510376,
-0.05379822850227356,
0.03291014954447746,
0.0007981766830198467,
0.03353474661707878,
-0.04298722371459007,
-0.030497701838612556,
-0.006163307931274176,
0.017692068591713905,
0.0321337953209877,
0.047999538481235504,
0.015324549749493599,
0.010070443153381348,
0.04431000351905823,
0.003599585732445121,
-0.044486530125141144,
0.009558456018567085,
-0.0735786035656929,
0.003365774406120181,
-0.011146105825901031,
-0.004763580393046141,
0.012329056859016418,
-0.001398479100316763,
-0.037051063030958176,
0.029639411717653275,
-0.03729088231921196,
-0.02320464514195919,
0.0017103089485317469,
0.026219382882118225,
-0.0038784253410995007,
0.0367240384221077,
-0.02034885622560978,
0.04758808761835098,
-0.024330394342541695,
0.017424697056412697,
0.1109648123383522,
-0.015414347872138023,
0.037581585347652435,
-0.03911818936467171,
0.009680679999291897,
-0.04513265937566757,
-0.013358354568481445,
-0.04665972664952278,
0.023105941712856293,
-0.04020414128899574,
0.024188384413719177,
0.027206292375922203,
0.06513099372386932,
-0.005056804046034813,
0.0004835840663872659,
0.0526401586830616,
-0.012701664119958878,
0.007995633408427238,
-0.0269310362637043,
-0.01664273627102375,
-0.013604317791759968,
0.0013810243690386415,
-0.06789608299732208,
0.015559667721390724,
-0.06381871551275253,
-0.02029893361032009,
-0.01674635335803032,
-0.022194785997271538,
0.0340336374938488,
0.05801767110824585,
-0.01731894724071026,
-0.0004126979038119316,
0.0005372388986870646,
-0.017831264063715935,
-0.03921060636639595,
0.02966197207570076,
0.057782672345638275,
-0.01833847351372242,
0.01884414628148079,
-0.007504385896027088,
0.039275798946619034,
-0.004070568364113569,
0.01602294109761715,
0.013942185789346695,
-0.04603757709264755,
0.01127687282860279,
-0.048973772674798965,
0.0452471561729908,
0.0065500508062541485,
0.016386860981583595,
0.029282283037900925,
0.03293294459581375,
0.01709328219294548,
-0.03282160684466362,
-0.04514094814658165,
-0.04025164246559143,
0.00201441184617579,
-0.0023068527225404978,
0.009977124631404877,
0.0038222833536565304,
0.05546494200825691,
0.0063172755762934685,
-0.00817173719406128,
-0.01711747981607914,
-0.01894243434071541,
0.024623962119221687,
0.018221881240606308,
0.06103036180138588,
-0.023849770426750183,
-0.0185859352350235,
-0.01837138459086418,
-0.010690710507333279,
-0.0008199688163585961,
0.013754559680819511,
-0.0350152961909771,
0.028500720858573914,
0.0459778755903244,
-0.004260451998561621,
-0.022983407601714134,
0.01687719114124775,
-0.040151648223400116,
0.05006175860762596,
-0.024807967245578766,
-0.005470111966133118,
-0.001252285554073751,
-0.028674060478806496,
0.04718531295657158,
0.03627711907029152,
-0.05183294415473938,
0.0038575585931539536,
-0.015899477526545525,
0.01960124261677265,
0.0011160990688949823,
-0.011752467602491379,
-0.05390392616391182,
-0.036553770303726196,
-0.024318194016814232,
0.022590316832065582,
0.006046666298061609,
0.014331077225506306,
0.050862133502960205,
-0.02050137147307396,
0.01757293939590454,
-0.0035466249100863934,
-0.021340686827898026,
0.01348648127168417,
0.021013030782341957,
-0.021973010152578354,
-0.011733758263289928,
-0.011322258040308952,
-0.013059878721833229,
-0.005932307336479425,
-0.06670317053794861,
-0.044836536049842834,
0.0073616039007902145,
-0.0007214010111056268,
0.06671454757452011,
-0.0041814749129116535,
-0.0021039354614913464,
-0.004211327061057091,
0.039656393229961395,
-0.044672686606645584,
0.001915621804073453,
-0.06882233917713165,
-0.04518678039312363,
0.04436594992876053,
-0.003824172541499138,
0.024915123358368874,
0.004666817374527454,
-0.045694079250097275,
0.018968205899000168,
0.051100049167871475,
-0.0025300185661762953,
-0.024663807824254036,
-0.0011863532708957791,
0.007291626650840044,
-0.010451369918882847,
0.015354014933109283,
-0.03733658045530319,
-0.04274548962712288,
0.06520085781812668,
-0.04553455859422684,
-0.05109381303191185,
-0.022388942539691925,
-0.025898031890392303,
0.008891720324754715,
0.020435305312275887,
0.0023859329521656036,
0.04057266563177109,
0.03831806778907776,
-0.0011693313717842102,
-0.010197986848652363,
-0.003025929443538189,
-0.003859823802486062,
0.011976435780525208,
-0.0393255241215229,
-0.007987258955836296,
-0.009234311990439892,
-0.011769137345254421,
0.005530094727873802,
0.03276347741484642,
0.04002036154270172,
-0.010327978059649467,
-0.023168163374066353,
0.01510346308350563,
-0.049773965030908585,
0.042443811893463135,
0.022680286318063736,
-0.018693532794713974,
0.015936229377985,
-0.03786551207304001,
0.03335224464535713,
0.029308374971151352,
-0.01034748274832964,
-0.07316005229949951,
0.007312839850783348,
0.010706993751227856,
-0.010985208675265312,
0.020701881498098373,
-0.05492212250828743,
0.018290897831320763,
-0.0011540713021531701,
-0.09895854443311691,
0.027762021869421005,
-0.012213381007313728,
-0.07013016194105148,
-0.03705744445323944,
0.002839447930455208,
-0.006080944556742907,
0.026714548468589783,
0.029416482895612717,
0.07345209270715714,
-0.022381016984581947,
0.035062264651060104,
-0.024586226791143417,
0.031837835907936096,
-0.01228101272135973,
-0.021558959037065506,
0.0012502108002081513,
-0.01300386618822813,
0.03914898633956909,
-0.0010226900922134519,
-0.023481594398617744,
0.017357857897877693,
0.003039521398022771,
-0.011923677287995815,
0.013190504163503647,
0.0011870493181049824,
-0.011402604170143604,
-0.007903958670794964,
0.0025091227144002914,
-0.012426271103322506,
-0.019907383248209953,
0.020349368453025818,
0.00019661658734548837,
0.05580021068453789,
-0.012330462224781513,
0.0015264725079759955,
-0.010504541918635368,
-0.049892351031303406,
0.029526956379413605,
0.004125188570469618,
-0.05336901172995567,
-0.03976082429289818,
-0.04309983551502228,
0.008584803901612759,
0.04092084616422653,
0.015534267760813236,
-0.03368116170167923,
-0.03672794997692108,
-0.011203797534108162,
0.027636967599391937,
-0.021275857463479042,
-0.003689484903588891,
0.038837045431137085,
-0.02471998892724514,
0.012740268371999264,
-0.010384180583059788,
0.024861687794327736,
0.03454408049583435,
-0.03544103354215622,
0.004475531168282032,
0.004785175435245037,
0.01055772416293621,
-0.005008556880056858,
-0.01512059010565281,
-0.0319906510412693,
0.052913933992385864,
0.0018542392645031214,
0.009329172782599926,
0.014939747750759125,
-0.027739766985177994,
0.004941292107105255,
-0.04438456892967224,
0.032710179686546326,
-0.018414732068777084,
0.015271698124706745,
-0.04945794865489006,
-0.00416706083342433,
0.009262483566999435,
0.025099731981754303,
0.04482192173600197,
0.004257781431078911,
-0.013882556930184364,
0.03402124345302582,
-0.019255446270108223,
0.012108324095606804,
-0.014155443757772446,
0.03427359461784363,
0.022854207083582878,
-0.0251312218606472,
0.05349224433302879,
0.007891218177974224,
0.007428748067468405,
0.006325215566903353,
0.015524142421782017,
0.006417411379516125,
0.024593913927674294,
-0.0059846085496246815,
-0.03171290084719658,
0.05243808403611183,
-0.00409219553694129,
-0.0155223049223423,
0.05156780034303665,
0.010537534952163696,
0.02321341261267662,
-0.036012325435876846,
-0.02264801785349846,
-0.04867146909236908,
0.04310551658272743,
-0.008092744275927544,
0.021997446194291115,
-0.034705013036727905,
0.008702429011464119,
0.018150566145777702,
-0.014854185283184052,
0.03550378605723381,
0.030593641102313995,
-0.027367625385522842,
-0.005893786437809467,
0.04309598356485367,
0.010599604807794094,
0.01769411936402321,
-0.044545818120241165,
0.034721627831459045,
-0.016546908766031265,
0.0011647259816527367,
0.025494614616036415,
0.027759529650211334,
0.001817479613237083,
0.025975145399570465,
-0.02463986910879612,
0.03754907473921776,
-0.008522583171725273,
-0.005285423714667559,
0.04574890434741974,
0.014590704813599586,
-0.013936897739768028,
-0.004144976381212473,
0.02227017842233181,
-0.008756490424275398,
0.018252670764923096,
0.03437916561961174,
0.0006262969109229743,
0.07725317776203156,
-0.05680202692747116,
0.013587643392384052,
-0.015874113887548447,
0.07706750929355621,
0.04520692676305771,
0.044703543186187744,
0.04386807605624199,
-0.006382608786225319,
-0.004551697988063097,
-0.0289391428232193,
-0.0052944510243833065,
-0.025374986231327057,
0.01493930909782648,
-0.03277666121721268,
0.010206100530922413,
-0.010252213105559349,
0.0021266641560941935,
-0.013349241577088833,
-0.01428703311830759,
-0.02262968011200428,
-0.0279098991304636,
0.036725420504808426,
0.014644382521510124,
-0.002052485942840576,
-0.01617306098341942,
-0.007301277946680784,
-0.0185670368373394,
0.04087192192673683,
-0.0609104186296463,
0.01512908935546875,
-0.046078745275735855,
0.03676046058535576,
-0.027608681470155716,
-0.0018958986038342118
] |
<blockquote>
<p>Point A moves uniformly with velocity $v$ so that the vector $\vec{v}$ is continually "aimed" at point B which in turn moves rectilinearly and uniformly with velocity $u < v$. At the initial moment $\vec{v} \perp \vec{u}$ and the points are separated by a distance $l$. How soon will the points converge?</p>
</blockquote>
<p>This seemed a very daunting problem at first, but then I tried to break it down with some calculus:</p>
<p>Consider a coordinate system such that $A$ moves along positive $y$ axis and $B$ along positive $x$.Let the particles meet at time $T$.</p>
<p>At an aribitrary time $t = t_0$, the velocity of the particle is inclined at an angle $\theta$ to the horizontal, so the horizontal component of the velocity is $v\cos\theta$. Displacement in a small time interval $dt$ at $t_0$ along the $x$ axis (along direction of motion of $B$) is:</p>
<p>$$v\cos\theta\ dt$$</p>
<p>Summing from $0$ to $T$. The displacement along $x$ axis of particle $A$ equals $uT$.</p>
<p>$$\int_0^T v\cos\theta\ dt= uT \implies \int_0^T\cos\theta \ dt = \frac{uT}{v} \tag1$$</p>
<p>Similarly, for the displacement along the $y$-axis:</p>
<p>$$\int_0^T\sin\theta\ dt = \frac{l}{v} \tag2$$</p>
<p>I'm not sure how to solve these equations, and I'm not sure if the solution is possible either using my method. How do I go about the problem?</p>
<p>I went over the solutions that have been written on other websites. Most of them first establish the same thing I did in the first step</p>
<p>$$\int_0^T \cos\theta \ dt = \frac{uT}{v}$$</p>
<p>Its the second step I don't understand. At time $t$, </p>
<p><img src="http://i.stack.imgur.com/RsPU5.png" alt="enter image description here"></p>
<p>It is claimed that at time $t$:</p>
<p>$$\frac{dr}{dt} = v - u\cos\theta$$</p>
<p>where $r$ is the distance between the two particles. This is the rate at which $B$ moves away from $A$ at time $t$. They then integrate the above and set it equal to $l$, which I don't understand:</p>
<p>$$\int_0^T(v - u\cos\theta)dt = l \tag3$$</p>
<p>How is this integral equal to $l$? If we consider the time when $A$ is about to meet with $B$, in a small time interval, the displacement of $A$ as given by $(3)$ would be along the line of motion of $B$ rather than perpendicular to it. How is this possible? </p>
<p><strong>EDIT</strong>: This problem is from General Problems in Physics by IE Irodov</p>
| 10,761 |
[
0.019306043162941933,
-0.0015500665176659822,
-0.0007417835295200348,
-0.024817734956741333,
0.048762280493974686,
-0.01993340067565441,
-0.04159534350037575,
-0.016819780692458153,
-0.005380628164857626,
0.004004911053925753,
0.03826060891151428,
0.053046535700559616,
0.06130402535200119,
0.044509634375572205,
0.034980081021785736,
-0.02111739292740822,
-0.017991283908486366,
-0.02666201815009117,
-0.017421284690499306,
-0.01518090907484293,
-0.00023042318935040385,
-0.014698857441544533,
0.02437461167573929,
-0.009518176317214966,
0.004148807376623154,
0.01931041106581688,
0.020435502752661705,
-0.011402776464819908,
-0.05318991094827652,
0.08241571485996246,
-0.03094121627509594,
-0.02001269720494747,
0.00814150646328926,
-0.006293260492384434,
0.027563298121094704,
0.018420100212097168,
-0.017041414976119995,
-0.0078087798319756985,
0.0019496376626193523,
0.014185230247676373,
-0.05764470621943474,
-0.008962235413491726,
-0.018079552799463272,
0.0756269171833992,
0.023498408496379852,
0.00024570594541728497,
0.03044738620519638,
0.010514982976019382,
0.05040006339550018,
-0.03287149965763092,
0.07157629728317261,
-0.010998668149113655,
0.05267776548862457,
-0.03158543258905411,
0.0011363308876752853,
-0.04800773411989212,
0.04634595289826393,
0.05220397934317589,
-0.015129397623240948,
-0.01595710590481758,
0.006113873329013586,
-0.035180047154426575,
-0.033526092767715454,
-0.0034226030111312866,
-0.0025196080096066,
-0.007872607558965683,
-0.037731949239969254,
-0.013771907426416874,
-0.004516140557825565,
-0.04543885588645935,
0.011760705150663853,
-0.0028416926506906748,
0.008671140298247337,
-0.03693008795380592,
-0.006855886895209551,
-0.009427133947610855,
-0.014765030704438686,
0.01904444582760334,
-0.017759287729859352,
0.03799116984009743,
-0.03791622072458267,
0.03595348447561264,
0.05874353274703026,
0.015202322043478489,
-0.002136767143383622,
-0.005835263058543205,
0.04265037178993225,
0.0035910129081457853,
0.023881731554865837,
0.035240162163972855,
0.010926292277872562,
0.05396938696503639,
0.020592452958226204,
0.007637119386345148,
0.007749352604150772,
0.044058602303266525,
-0.0008816952467896044,
0.029068224132061005,
0.03145085275173187,
-0.0628308653831482,
0.04232928156852722,
-0.03571261093020439,
0.009294922463595867,
0.10303855687379837,
-0.006501949392259121,
-0.007747492752969265,
-0.029225945472717285,
0.024255845695734024,
-0.007566848304122686,
-0.029807334765791893,
-0.03999718651175499,
0.032530609518289566,
-0.013941212557256222,
0.01781466230750084,
0.023988915607333183,
-0.00903701689094305,
-0.001020932919345796,
-0.0006511802785098553,
0.04579784348607063,
0.02414584904909134,
0.0694463923573494,
-0.030445581302046776,
0.01594206877052784,
0.0113230524584651,
-0.06347908079624176,
-0.01337161660194397,
0.004632950760424137,
-0.004090420436114073,
-0.03138928860425949,
0.03067389875650406,
0.02477152645587921,
0.00017984230362344533,
0.03252111002802849,
0.019766390323638916,
0.01813894882798195,
0.01813187450170517,
-0.07232972979545593,
-0.04713431000709534,
0.044193610548973083,
0.012036867439746857,
-0.0065096705220639706,
-0.059246595948934555,
-0.038021836429834366,
0.06405355036258698,
0.08431949466466904,
-0.007199711166322231,
0.01909469999372959,
0.016026316210627556,
0.027068428695201874,
-0.009523926302790642,
-0.024476870894432068,
0.017248738557100296,
-0.016532355919480324,
-0.030348392203450203,
0.04640043154358864,
-0.038047727197408676,
0.017374591901898384,
0.028173169121146202,
-0.013372443616390228,
-0.020824473351240158,
0.05643988028168678,
-0.012452665716409683,
-0.0005986320902593434,
0.015478906221687794,
0.0012178141623735428,
0.0016733156517148018,
0.036980509757995605,
0.03098190203309059,
-0.01783464103937149,
0.046323660761117935,
0.006045938469469547,
0.007551301270723343,
-0.014241264201700687,
-0.006822616793215275,
0.04519443213939667,
-0.04770004004240036,
-0.01681959256529808,
0.006985891610383987,
-0.02212502621114254,
0.031507790088653564,
-0.016497943550348282,
-0.07366617769002914,
-0.010712404735386372,
0.017053822055459023,
0.029425041750073433,
0.058066047728061676,
0.005964244250208139,
0.010901392437517643,
-0.02706773765385151,
-0.03546411171555519,
0.006201610434800386,
-0.045986346900463104,
0.02767644263803959,
-0.009105884470045567,
-0.01615961641073227,
0.07180093228816986,
0.020071355625987053,
-0.012467165477573872,
-0.029297783970832825,
-0.00957241840660572,
-0.04816192388534546,
0.03149409219622612,
-0.008587720803916454,
-0.012277803383767605,
0.03558158129453659,
0.07369852811098099,
0.04661470651626587,
0.03212600573897362,
0.016630029305815697,
0.004436375107616186,
0.036240193992853165,
-0.018507691100239754,
-0.00795554369688034,
0.02287841960787773,
0.01414075680077076,
0.011667231097817421,
-0.0034608563873916864,
-0.025553280487656593,
-0.016535799950361252,
0.006556259002536535,
-0.034877922385931015,
0.06923095881938934,
0.044003456830978394,
-0.00874477718025446,
-0.010185172781348228,
0.05146592855453491,
0.019796930253505707,
0.05177316814661026,
0.04156271368265152,
-0.057156216353178024,
-0.03136230632662773,
0.029609359800815582,
0.005445794202387333,
0.076355941593647,
-0.023317206650972366,
-0.01774972677230835,
0.028227226808667183,
0.02322530932724476,
0.019404122605919838,
0.03782545030117035,
-0.009981743060052395,
-0.05794636905193329,
0.03307625278830528,
0.01779337413609028,
-0.01923268847167492,
0.028428632766008377,
0.004473873879760504,
0.004319102503359318,
-0.01005092728883028,
-0.0005450876196846366,
-0.023298529908061028,
-0.024303438141942024,
0.0403204970061779,
0.014207395724952221,
-0.008796194568276405,
-0.018570473417639732,
0.016678402200341225,
0.014170199632644653,
0.037527646869421005,
0.04289836436510086,
0.008491022512316704,
-0.014672175981104374,
-0.025406895205378532,
0.019763926044106483,
0.012088180519640446,
0.004376200493425131,
0.011644302867352962,
-0.04453536495566368,
0.030309412628412247,
-0.05042925104498863,
-0.0007947107660584152,
-0.040304724127054214,
-0.05843832716345787,
-0.003999609965831041,
-0.02713140845298767,
0.02952178381383419,
0.07210300117731094,
-0.03844200447201729,
-0.033467233180999756,
0.013443473726511002,
0.0022763777524232864,
0.011272463016211987,
-0.0042725903913378716,
0.025926316156983376,
-0.06461603194475174,
0.005567008163779974,
-0.009477394632995129,
-0.014821677468717098,
0.043369073420763016,
0.04922746494412422,
-0.006801558192819357,
0.03055807203054428,
-0.015620751306414604,
-0.09459070861339569,
-0.017035862430930138,
-0.011196629144251347,
-0.00534719368442893,
-0.061851803213357925,
0.02317579835653305,
0.02835148386657238,
0.026532523334026337,
-0.04241064190864563,
0.006879935972392559,
-0.048296306282281876,
-0.05036956071853638,
-0.008811704814434052,
-0.004641846753656864,
0.0376703143119812,
0.0038490435108542442,
0.048771511763334274,
-0.012039721012115479,
-0.01862809993326664,
0.004732579458504915,
-0.07128159701824188,
-0.0084868548437953,
0.0019111750880256295,
-0.021417954936623573,
0.06845926493406296,
-0.005088364239782095,
-0.005603307858109474,
0.05539928376674652,
0.013390530832111835,
-0.026471642777323723,
0.0015597966266795993,
0.027775168418884277,
-0.006603335030376911,
0.022939417511224747,
-0.009482902474701405,
0.03385452181100845,
-0.012049294076859951,
-0.006420311518013477,
-0.029433423653244972,
0.005268186330795288,
0.04163364693522453,
0.04655689373612404,
0.04485400766134262,
0.000008202482604247052,
0.03224137797951698,
0.020055552944540977,
-0.02524253912270069,
0.04813117906451225,
-0.0036145078483968973,
0.04844394326210022,
-0.0051913997158408165,
0.03390822187066078,
0.03291533142328262,
-0.04413856565952301,
0.019821764901280403,
-0.009409811347723007,
-0.009523848071694374,
-0.000495344924274832,
0.03115309216082096,
0.0012799460673704743,
-0.007603824604302645,
-0.02112782746553421,
0.011232884600758553,
0.03732983022928238,
0.02026665210723877,
-0.018771689385175705,
0.029368292540311813,
0.016744038090109825,
0.014096608385443687,
-0.032302092760801315,
-0.010299024172127247,
0.0013208240270614624,
0.03382366895675659,
-0.04371519759297371,
0.004872063174843788,
0.0022117055486887693,
0.0265157762914896,
-0.008098863996565342,
-0.016350053250789642,
-0.015216956846415997,
-0.01565094105899334,
-0.04940692335367203,
-0.0023546256124973297,
0.00011444280244177207,
0.02983156591653824,
-0.005649684462696314,
0.03890564292669296,
0.01916060410439968,
-0.003565340070053935,
0.01674642786383629,
0.015579313039779663,
-0.08000292629003525,
0.03806871920824051,
-0.011842397041618824,
-0.006390179041773081,
-0.004235352389514446,
-0.011663231067359447,
0.012309334240853786,
-0.046195510774850845,
-0.000807016680482775,
-0.027556490153074265,
0.007144073955714703,
-0.03119799681007862,
0.05724992975592613,
-0.005757865495979786,
-0.040448471903800964,
-0.015563213266432285,
0.03255254402756691,
0.015888147056102753,
-0.04123365879058838,
0.040087927132844925,
0.052801575511693954,
-0.040720295161008835,
0.017632897943258286,
-0.02937498688697815,
-0.014549662359058857,
0.017442824319005013,
0.029914872720837593,
-0.0011622477322816849,
0.022204777225852013,
0.003202702384442091,
-0.006754548754543066,
-0.03138174116611481,
0.06470362842082977,
-0.004629926756024361,
-0.021198516711592674,
-0.04491688683629036,
-0.05112943425774574,
-0.021619485691189766,
-0.0027836605440825224,
0.05657942220568657,
-0.021695129573345184,
-0.012917651794850826,
0.028860952705144882,
0.011420529335737228,
0.027300922200083733,
0.04999387636780739,
0.02526586875319481,
0.033384595066308975,
0.010008090175688267,
-0.02559535950422287,
-0.026473887264728546,
0.012632799334824085,
0.015502506867051125,
0.043057508766651154,
-0.05063828080892563,
-0.021552473306655884,
-0.0012112503172829747,
0.03458642587065697,
0.04739757627248764,
-0.0189498420804739,
0.007299209013581276,
-0.04615214839577675,
-0.0017880563391372561,
0.020356038585305214,
-0.021893728524446487,
-0.007811036892235279,
0.015495339408516884,
0.014555977657437325,
-0.007263049017637968,
0.038323838263750076,
-0.07583217322826385,
-0.012071755714714527,
0.025950459763407707,
0.03302857279777527,
-0.022218763828277588,
0.022731268778443336,
-0.03668548911809921,
-0.04167744889855385,
0.07912495732307434,
-0.029864376410841942,
0.008368602953851223,
-0.02820625901222229,
-0.002974088303744793,
-0.005410428158938885,
-0.06260602921247482,
-0.07065533846616745,
-0.0171376783400774,
-0.010318996384739876,
-0.006723157595843077,
-0.01349062379449606,
-0.016984181478619576,
0.0025498534087091684,
0.027476686984300613,
0.04035601764917374,
0.05122758448123932,
0.002890933770686388,
-0.03340508043766022,
-0.0046990965493023396,
0.015569306910037994,
-0.020120583474636078,
-0.05311785265803337,
0.01585451327264309,
0.01898995228111744,
-0.03717036172747612,
-0.022404704242944717,
-0.021867090836167336,
-0.038357123732566833,
0.047391682863235474,
-0.027637585997581482,
0.032637353986501694,
-0.012884984724223614,
-0.03218244016170502,
0.045927222818136215,
0.045572225004434586,
0.0076882424764335155,
0.03495723381638527,
0.021355459466576576,
0.0026411942671984434,
-0.004579725209623575,
-0.025884311646223068,
0.01111550722271204,
0.00627503078430891,
-0.012829436920583248,
-0.0197269506752491,
0.024038946256041527,
-0.00966049637645483,
0.07761193811893463,
0.011607992462813854,
-0.018270378932356834,
-0.02652512677013874,
0.0036772931925952435,
-0.007639974821358919,
0.0459882915019989,
-0.0017400014912709594,
0.020252039656043053,
0.021109631285071373,
-0.004621824249625206,
0.025140982121229172,
-0.040873367339372635,
0.01689348742365837,
-0.050059542059898376,
0.008675842545926571,
0.023467950522899628,
-0.006543059833347797,
-0.029677437618374825,
-0.039817389100790024,
-0.015729421749711037,
-0.03112320601940155,
-0.07060494273900986,
0.04780374467372894,
-0.012257194146513939,
0.03404255583882332,
0.03201933205127716,
-0.07351873070001602,
-0.0519120991230011,
0.0206287894397974,
0.03670606017112732,
0.034648969769477844,
-0.03508652746677399,
-0.03609494864940643,
0.013763404451310635,
0.035640403628349304,
-0.037801213562488556,
-0.05659748613834381,
0.01858321577310562,
0.008044011890888214,
-0.028812387958168983,
-0.057019248604774475,
-0.0046361167915165424,
-0.00494021363556385,
-0.012830687686800957,
-0.020523687824606895,
0.03960125520825386,
-0.02394438348710537,
-0.00945124588906765,
0.019198117777705193,
0.04956378787755966,
0.07827549427747726,
-0.021082911640405655,
0.011825235560536385,
0.03660009428858757,
-0.0023416189942508936,
-0.013870172202587128,
0.0021602415945380926,
0.05131753906607628,
-0.042140115052461624,
-0.05228317901492119,
0.02630802057683468,
-0.012639429420232773,
0.022284025326371193,
-0.015536374412477016,
-0.03329167515039444,
0.007965699769556522,
0.022704213857650757,
-0.03792641684412956,
-0.009463883936405182,
0.007010366301983595,
0.03829775005578995,
-0.013878469355404377,
-0.014582613483071327,
-0.00210953364148736,
-0.03291396424174309,
-0.026075370609760284,
0.02180575393140316,
-0.014800160191953182,
-0.01676229201257229,
-0.0033939105924218893,
0.041424404829740524,
-0.04510948807001114,
0.005985446274280548,
0.05007578432559967,
0.05549359694123268,
0.05792592465877533,
-0.027673769742250443,
-0.014858409762382507,
0.02431163191795349,
-0.04510000720620155,
-0.03356144204735756,
-0.0033097409177571535,
-0.04509340599179268,
0.01445042435079813,
0.0703406035900116,
-0.0015698156785219908,
0.07341114431619644,
0.02506101317703724,
0.019414281472563744,
-0.010575054213404655,
-0.0005273539572954178,
-0.005225551314651966,
-0.008284867741167545,
-0.010601362213492393,
0.008376764133572578,
-0.03806695342063904,
-0.04708859696984291,
0.007448490243405104,
0.017762189731001854,
-0.017994437366724014,
-0.022311393171548843,
-0.04568830132484436,
-0.015608194284141064,
0.007983557879924774,
-0.0025950076524168253,
-0.04227845370769501,
-0.003865380072966218,
-0.009743074886500835,
0.05108756199479103,
-0.027276523411273956,
-0.0546819306910038,
0.035614028573036194,
0.030521471053361893,
0.0009663167875260115,
-0.03850932419300079,
-0.006285268813371658,
-0.07072681933641434,
-0.012294442392885685,
0.009443079121410847,
-0.0015372782945632935,
0.0011786050163209438,
0.037527188658714294,
0.01633426919579506,
0.004649163689464331,
-0.011147979646921158,
-0.04552288353443146,
-0.07798343896865845,
-0.013459008187055588,
-0.04328237846493721,
-0.049641042947769165,
0.034675482660532,
-0.008761090226471424,
0.013428859412670135,
0.011823105625808239,
-0.02635098621249199,
0.0019529551500454545,
0.018638843670487404,
0.0030727856792509556,
-0.026232518255710602,
0.08275320380926132,
-0.028655335307121277,
0.03748804330825806,
-0.046595435589551926,
0.02263214997947216,
0.10463134199380875,
0.02554590255022049,
0.013493161648511887,
-0.028166159987449646,
0.01882142201066017,
-0.00044164032442495227,
-0.027706783264875412,
-0.0567404143512249,
0.01691417023539543,
0.02044622227549553,
-0.04360589012503624,
-0.023560063913464546,
0.01823701709508896,
-0.012391469441354275,
0.0056786625646054745,
0.029504425823688507,
-0.03408702462911606,
-0.0761462152004242,
-0.03004569001495838,
0.005791256204247475,
0.004760384559631348,
0.04581032693386078,
-0.013416976667940617,
-0.00034003882319666445,
-0.0584394596517086,
-0.03242477774620056,
-0.04678332805633545,
-0.03338483348488808,
0.02042415179312229,
-0.0003461685264483094,
-0.051511142402887344,
0.03988353908061981,
0.03778922185301781,
-0.04324790835380554,
-0.032217953354120255,
-0.0017094665672630072,
0.007323685102164745,
-0.018096571788191795,
0.0491851307451725,
0.02517157606780529,
0.0015597767196595669,
0.023221027106046677,
0.0236467644572258,
0.030346285551786423,
-0.007200129330158234,
-0.0039832452312111855,
-0.06729720532894135,
0.08971298485994339,
-0.015068979933857918,
0.004563139285892248,
-0.00030598673038184643,
0.04313698410987854,
-0.0025686942972242832,
-0.04573943838477135,
0.013214973732829094,
-0.00003110457328148186,
0.040294285863637924,
-0.0005708641838282347,
0.02657165937125683,
-0.0011355726746842265,
0.020933113992214203,
0.02316359244287014,
-0.005663019139319658,
0.007403498515486717,
-0.005436082370579243,
0.012918105348944664,
0.013237823732197285,
0.05839411914348602,
-0.0007565502310171723,
-0.0070820520631968975,
-0.020710837095975876,
0.0244931410998106,
-0.004857444204390049,
0.012761074118316174,
-0.0026241091545671225,
0.010487673804163933,
-0.0028994688764214516,
0.048442158848047256,
-0.03179546073079109,
-0.030617164447903633,
-0.06699804961681366,
0.01822024956345558,
0.005582955665886402,
-0.021673744544386864,
-0.02272075228393078,
-0.02173864096403122,
0.02177019976079464,
0.07762181013822556,
-0.020483164116740227,
-0.023342523723840714,
-0.011933217756450176,
0.048598241060972214,
0.019128343090415,
-0.0013487865217030048,
-0.03782785311341286,
-0.0004714681417681277,
-0.009473709389567375,
0.01889314316213131,
-0.02999511919915676,
0.041997719556093216,
0.03314286842942238,
0.008250993676483631,
0.0016208298038691282,
0.007965908385813236,
-0.022616326808929443,
-0.008793170563876629,
0.022456858307123184,
-0.025064408779144287,
-0.03906314820051193,
0.052857764065265656,
0.01780925877392292,
-0.011018586345016956,
0.007951894775032997,
-0.006583391223102808,
0.018576841801404953,
-0.02492888644337654,
-0.010973735712468624,
0.015639688819646835,
0.012689643539488316,
-0.03069254755973816,
-0.0022849373053759336,
-0.026562610641121864,
-0.005461310967803001,
0.0009657638147473335,
-0.02333078719675541,
-0.03572913631796837,
0.013325491920113564,
-0.03181031346321106,
0.02150767855346203,
-0.0031037137378007174,
0.0010267517063766718,
-0.010998896323144436,
0.014994158409535885,
0.01062473002821207,
-0.03944912552833557,
0.036071278154850006,
-0.018977293744683266,
0.03431909158825874,
0.015928342938423157,
-0.045544832944869995,
0.002227180637419224,
0.013860935345292091,
-0.043645229190588,
0.003748601535335183,
-0.007116173859685659,
0.02518213540315628,
0.0006067626527510583,
-0.033332303166389465,
0.02096092700958252,
0.051518071442842484,
-0.016319559887051582,
-0.024815190583467484,
-0.021810198202729225,
-0.04896312579512596,
-0.034992486238479614,
-0.04428619518876076,
0.043702322989702225,
0.0008227091166190803,
0.0016369124641641974,
0.041120562702417374,
0.025449765846133232,
-0.03254218399524689,
-0.004047871101647615,
0.032659854739904404,
-0.010060576722025871,
-0.0015542597975581884,
0.03608722612261772,
-0.02337687462568283,
0.02058752067387104,
0.04194484278559685,
-0.020269151777029037,
-0.016927747055888176,
0.0393950380384922,
0.0007392452098429203,
-0.10075028985738754,
0.005581326317042112,
0.053820185363292694,
0.0015589662361890078,
0.059196289628744125,
-0.061714231967926025,
-0.01770368218421936,
0.06045282259583473,
-0.0058463821187615395,
-0.008363708853721619,
-0.0468362495303154,
0.0037029164377599955,
-0.006203006021678448,
-0.04108642414212227,
-0.014849582687020302,
0.02232195995748043,
0.011869427748024464,
0.05536893382668495,
0.007653890643268824,
0.04340142011642456,
-0.032870713621377945,
-0.06296614557504654,
0.037547871470451355,
0.0038797040469944477,
-0.01457410492002964,
-0.011370999738574028,
0.05590062960982323,
-0.02386821247637272,
0.018232759088277817,
0.027180274948477745,
-0.04080541059374809,
0.007981820963323116,
0.005047322250902653,
0.03946952149271965,
0.004447403829544783,
0.02700698748230934,
-0.014023616909980774,
0.03603285923600197,
0.031110307201743126,
0.0024661868810653687,
0.023049181327223778,
0.0008536862442269921,
-0.014032401144504547,
-0.044639647006988525,
0.03147958591580391,
-0.01753825880587101,
-0.029348298907279968,
0.04825824126601219,
0.001563775003887713,
-0.018931172788143158,
0.013274704106152058,
-0.00693722115829587,
0.010223154909908772,
-0.028007125481963158,
-0.030333921313285828,
-0.02312576025724411,
0.0045191505923867226,
0.01757819391787052,
-0.010149982757866383,
-0.018103351816534996,
0.0012290246086195111,
-0.004140991251915693,
-0.0068664844147861,
0.01880655251443386,
-0.01923423632979393,
-0.014316494576632977,
-0.056810688227415085,
-0.012393918819725513,
-0.008406544104218483,
0.00402678269892931,
-0.023713523522019386,
0.014634494669735432,
-0.034933798015117645,
0.0021825111471116543,
-0.013754535466432571,
0.021261950954794884,
0.024526292458176613,
0.016604848206043243,
-0.0508277490735054,
-0.06931035965681076,
0.04267977550625801,
0.008196566253900528,
-0.033812422305345535,
-0.04096224159002304,
-0.04014895483851433,
0.012588013894855976,
0.05255508050322533,
0.07329436391592026,
-0.013917353004217148,
0.028877070173621178,
0.05317988991737366,
-0.03429112583398819,
0.03538987785577774,
-0.04407557472586632,
-0.018857261165976524,
-0.015027896501123905,
-0.013607525266706944,
0.03126147389411926,
-0.001202472485601902,
0.005069080740213394,
0.017636694014072418,
0.014305816031992435,
-0.010445067659020424,
0.010629107244312763,
0.011730335652828217,
-0.024238867685198784,
0.011690076440572739,
0.006376571953296661,
-0.0050332569517195225,
0.03347136825323105,
0.0007384910713881254,
-0.00426832539960742,
0.0062356810085475445,
-0.05233287811279297,
-0.03995874524116516,
-0.01746550388634205,
-0.06326667219400406,
-0.031276050955057144,
-0.005253717768937349,
-0.009271470829844475,
0.00344516197219491,
-0.08805747330188751,
-0.005800043698400259,
0.020738642662763596,
-0.02401624619960785,
-0.01131302211433649,
-0.007015720941126347,
-0.024023419246077538,
0.06437590718269348,
0.023471545428037643,
0.02116154506802559,
0.02371293306350708,
0.01107718050479889,
0.04920113831758499,
0.016092216596007347,
0.009956076741218567,
-0.02858874760568142,
-0.02081969752907753,
0.0010235733352601528,
0.011272827163338661,
0.022056445479393005,
-0.008602418936789036,
0.009095321409404278,
0.010426931083202362,
0.013240225613117218,
0.018403269350528717,
-0.060599058866500854,
-0.03705975040793419,
0.042506344616413116,
-0.024150928482413292,
0.07780604809522629,
-0.031020089983940125,
0.013535748235881329,
0.005854923743754625,
0.0013800454325973988,
0.015148097649216652,
0.01568867824971676,
0.029621785506606102,
0.003778420388698578,
-0.00706866942346096,
-0.012578011490404606,
0.010853482410311699,
0.006033738609403372,
-0.0074349017813801765,
-0.02577112801373005,
0.030144352465867996,
0.037788692861795425,
0.001128469011746347,
-0.011823290959000587,
-0.045823730528354645,
-0.013466346077620983,
-0.033019594848155975,
0.045613933354616165,
0.03984427824616432,
0.011457495391368866,
-0.00588343245908618,
0.006662378553301096,
-0.04184821620583534,
0.06189775839447975,
-0.0784001424908638,
-0.004962649196386337,
-0.006368883885443211,
-0.011686784215271473,
-0.014339899644255638,
0.0065611121244728565
] |
<p>I'm interested in the relation between the probability distribution $p_i$ over states of a system on the one side and the density of states $\rho(\eta)$ of its environment. (Meaning, $\int_{\eta_a}^{\eta_b} \rho(\eta) ~ \mathrm{d} \eta$ is the number of environment states with energies in the interval $[\eta_a, \eta_b]$.)</p>
<p>If the whole (system + environment) is energetically closed ("isolated") with a total energy $E = e + \eta$, but system and environment are in thermal equilibrium (i.e. the whole is described by the microcanonical ensemble), then it holds
$$
p_i = \frac{ \rho(E - e_i) }{ \sum_i \rho(E - e_i) }.
$$</p>
<p>This means, the probability distribution over states of the system is determined by a) something that only characterizes the energetic <em>structure</em> of the system (the $e_i$s), b) something that only characterizes the energetic <em>structure</em> of the environment ($\rho(\eta)$) and c) the total energy $E$.</p>
<p>This relation holds generally, for arbitrary small or large systems and/or environments. Please note that we have not yet taken any limits!</p>
<p>If we now consider the thermodynamic limit, i.e. an environment composed of an infinite number of subsystems, the probability distribution $p_i$ over states of the system becomes the Boltzmann–Gibbs-distribution (aka canonical ensemble)
$$
p_i = \frac{ \exp(- \beta e_i) }{ \sum_i \exp(- \beta e_i) }.
$$
Using the first relation above, this distribution could now be interpreted as corresponding to a <em>limiting density of states of the environment</em> of the form
$$
\rho(\eta) \propto \exp( \beta \eta )
$$
which characterizes the "infinite environment". However, the expression refers to the parameter $\beta$ of the Boltzmann–Gibbs distribution, which represents the temperature and depends on the total energy $E$ (per subsystem). Whereas in the finite case $E$ only serves to connect $\rho(\eta)$ and $p_i$, it here defines $\rho(\eta)$ itself.</p>
<p>To me this suggests that it does not make sense to characterize an infinite environment by a density of states – but maybe there's some way around this? Or is there a mistake in the derivation somewhere else?</p>
| 10,762 |
[
-0.026673950254917145,
-0.0250734593719244,
0.011088431812822819,
-0.009137009270489216,
0.02316996082663536,
0.04429450258612633,
-0.014504057355225086,
0.0038183345459401608,
0.00538259744644165,
-0.0367320217192173,
0.025547998026013374,
0.007030002772808075,
0.011587293818593025,
0.03869130462408066,
-0.005046000238507986,
-0.02063613384962082,
-0.038892779499292374,
-0.004714918322861195,
-0.022267676889896393,
-0.025996515527367592,
0.03806480020284653,
0.05056045576930046,
0.007672396022826433,
0.0025828934740275145,
-0.05183051526546478,
0.07355841994285583,
0.0076524349860847,
-0.04272571578621864,
-0.01011023111641407,
0.0642864853143692,
-0.011235360987484455,
-0.028302162885665894,
-0.008822203613817692,
0.020265629515051842,
0.02684752829372883,
-0.021145131438970566,
-0.008378589525818825,
-0.013556060381233692,
-0.00415580440312624,
0.024968702346086502,
-0.09640882164239883,
-0.00822706613689661,
-0.012930705212056637,
0.008228801190853119,
-0.017960429191589355,
0.009006540291011333,
0.009057583287358284,
-0.012501070275902748,
-0.0043524703942239285,
-0.054671477526426315,
0.056397728621959686,
-0.00007218674727482721,
0.043007705360651016,
0.028569700196385384,
0.030951736494898796,
-0.015321905724704266,
0.03737540543079376,
0.07562464475631714,
0.032879408448934555,
-0.05540825054049492,
-0.01060432568192482,
0.0029247526545077562,
-0.007123133633285761,
-0.015563955530524254,
0.0011213613906875253,
0.04322356730699539,
0.03013654612004757,
-0.05477912351489067,
0.028200408443808556,
0.002676448319107294,
0.0264902263879776,
0.003994409926235676,
0.03466769680380821,
-0.01987021043896675,
0.03869820013642311,
0.026939980685710907,
0.03080296516418457,
0.016985727474093437,
0.01595884934067726,
0.023467283695936203,
0.01630832627415657,
-0.019636277109384537,
0.042396653443574905,
0.019088871777057648,
0.03551945835351944,
-0.003600394818931818,
0.06932836771011353,
-0.028185918927192688,
0.00333139905706048,
0.01519234199076891,
0.0017811181023716927,
0.03578526899218559,
0.03919239342212677,
-0.025931622833013535,
-0.05642140284180641,
0.03986118361353874,
-0.003286963328719139,
0.016974907368421555,
-0.05182971432805061,
-0.020628154277801514,
-0.03570844605565071,
-0.04583246633410454,
0.031927306205034256,
0.06225746124982834,
0.004027636256068945,
-0.023652754724025726,
-0.07467435300350189,
0.019074438139796257,
-0.021121937781572342,
0.000043047031795140356,
-0.01676291413605213,
0.0407634899020195,
0.012089257128536701,
0.008929118514060974,
-0.020617328584194183,
-0.019109167158603668,
0.02338992804288864,
-0.016268596053123474,
0.03454125300049782,
0.05582356080412865,
0.013343789614737034,
-0.0046830251812934875,
-0.003451624419540167,
-0.02103189378976822,
-0.07421159744262695,
0.029555443674325943,
0.06394770741462708,
-0.04505380988121033,
-0.04904206842184067,
0.007412983104586601,
-0.015010147355496883,
0.009534860029816628,
-0.0033241186756640673,
0.04340818524360657,
0.01066935807466507,
-0.02085578441619873,
-0.08434274047613144,
-0.02254941500723362,
0.055006541311740875,
-0.03550815209746361,
-0.021993771195411682,
-0.06564231216907501,
-0.009187881834805012,
0.04961260035634041,
0.045958880335092545,
-0.022316012531518936,
0.005822457373142242,
-0.03825892508029938,
0.015446768142282963,
0.024826664477586746,
-0.041754093021154404,
-0.03361740708351135,
-0.01119960192590952,
-0.016925113275647163,
0.007527428679168224,
-0.0655226781964302,
0.08502193540334702,
0.03234095126390457,
0.008806663565337658,
0.023012761026620865,
0.052022822201251984,
-0.02764943055808544,
-0.04577089101076126,
0.0038901360239833593,
0.007263849023729563,
-0.04251256585121155,
0.07066746056079865,
0.005279471632093191,
0.035855017602443695,
0.01819639839231968,
0.024530766531825066,
-0.019587915390729904,
-0.0053459047339856625,
0.011724566109478474,
0.04347914084792137,
-0.030710851773619652,
-0.03320162743330002,
-0.02690982259809971,
-0.007744892034679651,
0.002361904364079237,
-0.04611857980489731,
0.006024478934705257,
-0.03544875234365463,
-0.0037630153819918633,
0.04484108090400696,
0.013340667821466923,
0.024304142221808434,
-0.03373473882675171,
0.0029841847717761993,
-0.037209466099739075,
-0.022728832438588142,
-0.07878449559211731,
-0.017519084736704826,
0.011208239942789078,
-0.028611749410629272,
0.0597725510597229,
0.005527443718165159,
0.011862829327583313,
-0.013717437162995338,
-0.009251008741557598,
-0.020622054114937782,
-0.005032053217291832,
0.015786685049533844,
-0.05197599530220032,
0.03287683427333832,
0.0400792695581913,
0.07578729838132858,
0.015141510404646397,
0.03808077052235603,
0.01933267153799534,
-0.07202591001987457,
-0.024743568152189255,
-0.06085706502199173,
0.04374811425805092,
0.027137737721204758,
-0.01829538494348526,
-0.0010796531569212675,
0.018881995230913162,
-0.0035416593309491873,
-0.019330808892846107,
-0.029607508331537247,
0.011919941753149033,
0.05882573500275612,
0.030857305973768234,
-0.014347316697239876,
0.05027560889720917,
0.002755306661128998,
0.008623394183814526,
-0.044916775077581406,
-0.012603504583239555,
-0.020769711583852768,
-0.01416951883584261,
0.020890207961201668,
0.04045793041586876,
-0.03166777640581131,
0.03710254281759262,
0.011369370855391026,
0.004782558884471655,
-0.025013424456119537,
-0.0013568236026912928,
-0.026316862553358078,
-0.010599716566503048,
0.03020150400698185,
0.00528830336406827,
0.007891631685197353,
-0.01563546620309353,
-0.0182172991335392,
-0.01652868464589119,
0.010833022184669971,
-0.04138389602303505,
0.008733129128813744,
0.022852275520563126,
0.007134192623198032,
0.0005894579808227718,
-0.025776810944080353,
-0.007881681434810162,
0.03558361902832985,
-0.00314994971267879,
0.021311594173312187,
0.006248096935451031,
-0.02521388605237007,
0.012539799325168133,
-0.039280474185943604,
-0.0506725013256073,
0.015791820362210274,
0.00027688717818818986,
-0.017911052331328392,
-0.034708261489868164,
0.007669216021895409,
-0.03817420452833176,
0.0007977307541295886,
0.013519172556698322,
-0.022336618974804878,
-0.0017778071342036128,
0.0036964057944715023,
0.048932358622550964,
0.004372443072497845,
-0.01387275755405426,
-0.04031820595264435,
-0.018196262419223785,
-0.006092889700084925,
-0.0038208041805773973,
0.0312676802277565,
0.0177024956792593,
-0.03541090711951256,
-0.003374047577381134,
-0.052359502762556076,
-0.025623837485909462,
0.009682964533567429,
-0.04240739345550537,
-0.019920941442251205,
0.015599120408296585,
0.0032188117038458586,
-0.051423393189907074,
-0.023439791053533554,
0.00036294967867434025,
-0.04356316477060318,
-0.05732235312461853,
-0.014309962280094624,
0.04757115989923477,
-0.014536663889884949,
-0.04733644798398018,
0.006882856134325266,
-0.03857199475169182,
-0.06821969151496887,
-0.010113677009940147,
-0.023742472752928734,
0.02963857725262642,
-0.020083298906683922,
0.05255742743611336,
0.07986119389533997,
-0.01092185452580452,
-0.03330492973327637,
-0.0654805526137352,
-0.06606471538543701,
0.011192482896149158,
-0.00040204834658652544,
0.0462646558880806,
0.007691273465752602,
-0.036627110093832016,
0.05593627318739891,
0.005923745688050985,
-0.019607825204730034,
0.01199111994355917,
-0.006117851007729769,
-0.004917924292385578,
-0.0030421768315136433,
-0.02081386186182499,
-0.0003418241685722023,
-0.002738575218245387,
0.026479538530111313,
0.040357571095228195,
0.04252051189541817,
-0.009191084653139114,
-0.013876613229513168,
0.01836789771914482,
0.044676631689071655,
0.0158095546066761,
0.00454143900424242,
0.04432752728462219,
0.011263551190495491,
0.03016318753361702,
0.02938348427414894,
-0.010513314045965672,
0.020412981510162354,
0.03980301320552826,
-0.09302935004234314,
0.04037078469991684,
0.019268948584794998,
0.019412705674767494,
-0.06262433528900146,
0.046510711312294006,
-0.017756862565875053,
-0.012978153303265572,
0.027965564280748367,
0.03167103976011276,
0.027071835473179817,
-0.02420884184539318,
-0.007271410431712866,
0.0327230729162693,
0.05567692965269089,
0.0036133958492428064,
-0.036970850080251694,
0.007921830751001835,
-0.0141414450481534,
0.00910533219575882,
0.004262263420969248,
-0.01052302960306406,
0.03219804912805557,
0.022182071581482887,
0.03081654943525791,
-0.023223457857966423,
-0.04092055931687355,
-0.022731171920895576,
-0.0629032552242279,
-0.004147639032453299,
-0.038149505853652954,
0.0433984138071537,
0.0069444142282009125,
0.048906151205301285,
-0.03999495133757591,
-0.031374089419841766,
0.0005500746774487197,
0.0005869978340342641,
-0.07575954496860504,
0.016939371824264526,
0.012598496861755848,
-0.007284155581146479,
0.0002315912424819544,
0.011793947778642178,
0.06563329696655273,
-0.01434022095054388,
-0.01620345376431942,
0.010798214934766293,
0.01010659709572792,
-0.06416293233633041,
-0.004579625092446804,
-0.03622021526098251,
-0.06902000308036804,
-0.04087432846426964,
0.04444009065628052,
-0.014615198597311974,
-0.006587638985365629,
0.0202178917825222,
0.036235272884368896,
-0.020543621852993965,
0.01850012131035328,
0.0008482618140988052,
0.022134844213724136,
0.030492978170514107,
0.009854277595877647,
0.02139355055987835,
4.527698660439228e-9,
-0.007760185748338699,
0.016057243570685387,
-0.0041290149092674255,
0.014802793972194195,
0.04212608560919762,
-0.030735062435269356,
0.003220443380996585,
-0.03699745610356331,
-0.01589740812778473,
0.011588087305426598,
0.013150573708117008,
0.012733843177556992,
0.019687194377183914,
0.02124967984855175,
0.017091767862439156,
-0.00019101319776382297,
0.04907115176320076,
0.02861783280968666,
-0.01624167710542679,
-0.015028842724859715,
-0.04749998822808266,
0.005540365818887949,
-0.02040988951921463,
0.00848458707332611,
-0.013748672790825367,
-0.0050498805940151215,
-0.022603189572691917,
0.025372754782438278,
-0.022299399599432945,
0.004154637921601534,
-0.015284083783626556,
-0.016780760139226913,
0.008082878775894642,
0.020526032894849777,
0.006808327045291662,
-0.009467278607189655,
0.005758077837526798,
0.00037949028774164617,
0.03442554920911789,
0.022299611940979958,
0.03990352153778076,
-0.017920788377523422,
-0.048332713544368744,
0.05228711664676666,
0.007054706569761038,
0.00615759426727891,
0.017546217888593674,
-0.01556142047047615,
-0.01770862378180027,
0.019294289872050285,
0.00003835692405118607,
0.02413300797343254,
-0.013468585908412933,
0.007730578072369099,
-0.02058243192732334,
-0.08033104985952377,
-0.03058515302836895,
0.009413272142410278,
0.04387873783707619,
0.020864903926849365,
-0.031088292598724365,
0.0013776692794635892,
-0.02672141045331955,
-0.00585605064406991,
-0.019579021260142326,
0.0413915179669857,
-0.024405881762504578,
-0.023245668038725853,
0.01243823766708374,
-0.01493811421096325,
0.009220698848366737,
-0.07968687266111374,
0.03185039386153221,
-0.01639912836253643,
-0.002263119909912348,
0.02845085971057415,
-0.05186797305941582,
-0.04750322550535202,
0.024655917659401894,
-0.010495930910110474,
-0.036459293216466904,
0.0061605279333889484,
0.010652586817741394,
0.09328591078519821,
0.004051614552736282,
-0.017718056216835976,
0.08075671643018723,
0.028287142515182495,
-0.012016784399747849,
-0.00167527562007308,
-0.03461276739835739,
0.028980961069464684,
-0.043791621923446655,
0.02593880705535412,
-0.07295731455087662,
0.027139419689774513,
-0.021601732820272446,
0.02252090908586979,
-0.025108521804213524,
0.02181752771139145,
0.009630974382162094,
-0.06521511822938919,
0.009220880456268787,
0.03366630896925926,
-0.0278801117092371,
-0.013688609935343266,
-0.018997469916939735,
0.03635597601532936,
0.040465500205755234,
-0.0008378980564884841,
0.024107925593852997,
0.007226322311908007,
0.02959262952208519,
0.022921010851860046,
-0.026717420667409897,
0.032931137830019,
-0.030498603358864784,
-0.015001408755779266,
-0.012664053589105606,
-0.0037260940298438072,
0.03267822042107582,
-0.03526485338807106,
0.012099266052246094,
0.022691121324896812,
-0.014511422254145145,
-0.03802601993083954,
0.008520076982676983,
-0.03160781040787697,
0.015726584941148758,
-0.025525176897644997,
0.01992836594581604,
-0.014605425298213959,
-0.00655986275523901,
-0.09024518728256226,
0.02480829320847988,
0.015429331921041012,
0.013715945184230804,
-0.01911867968738079,
-0.0630812868475914,
0.0020478342194110155,
-0.00848567858338356,
-0.029623107984662056,
0.008454051800072193,
0.027024826034903526,
-0.019714465364813805,
0.027005381882190704,
-0.004219890106469393,
0.06292282044887543,
0.017616597935557365,
-0.019004976376891136,
0.013087227009236813,
0.023939896374940872,
-0.001938672037795186,
0.003969892859458923,
0.012738265097141266,
0.008569725789129734,
-0.018987631425261497,
0.026242131367325783,
0.031862773001194,
0.0026349308900535107,
0.01937211863696575,
-0.02534475177526474,
-0.04610101878643036,
-0.0045717922039330006,
0.01157962903380394,
-0.005868302658200264,
-0.0057733734138309956,
-0.003835510229691863,
0.03572380915284157,
0.02496318891644478,
0.0162864588201046,
-0.018281470984220505,
0.012770296074450016,
-0.004156903829425573,
0.0017031223978847265,
-0.0028483013156801462,
-0.0051727513782680035,
0.02604210376739502,
0.06286267191171646,
0.012028343975543976,
0.011592927388846874,
0.012740116566419601,
-0.015582363121211529,
0.03479893505573273,
-0.017625955864787102,
0.025166811421513557,
0.035574741661548615,
-0.008877870626747608,
-0.03195023536682129,
-0.03420634567737579,
-0.10121627897024155,
-0.0017234828555956483,
0.00906774215400219,
-0.001939535839483142,
0.022461673244833946,
-0.004402426537126303,
0.00905162189155817,
-0.019852658733725548,
-0.03412984684109688,
0.022177143022418022,
0.01494810450822115,
0.0006554701831191778,
0.04173586145043373,
-0.04145881161093712,
-0.04947302117943764,
0.0574786514043808,
0.04574698209762573,
-0.06229183077812195,
0.040870871394872665,
-0.00048798538045957685,
0.0019225783180445433,
-0.0043687946163117886,
-0.060726527124643326,
-0.022074401378631592,
0.06614786386489868,
-0.06419343501329422,
0.022852251306176186,
0.024924056604504585,
-0.030074264854192734,
0.020161030814051628,
0.036696773022413254,
-0.01753085106611252,
-0.07400059700012207,
-0.010854954831302166,
-0.0055515216663479805,
0.04531324654817581,
0.009916743263602257,
0.020172057673335075,
0.041486043483018875,
-0.018925387412309647,
0.008706185035407543,
-0.0024137445725500584,
0.00651341350749135,
0.020634444430470467,
-0.033534709364175797,
0.024588076397776604,
-0.016660256311297417,
-0.05968482792377472,
0.020994361490011215,
-0.05290113016963005,
-0.01640833355486393,
0.01905025541782379,
-0.020366353914141655,
0.027929486706852913,
0.022925404831767082,
0.021716218441724777,
0.01668628491461277,
0.04215339571237564,
0.02278466708958149,
0.025279240682721138,
-0.0032658821437507868,
0.0030017311219125986,
0.15213097631931305,
0.053884219378232956,
0.014803629368543625,
-0.02084728144109249,
-0.012324301525950432,
0.004450095351785421,
0.008580049499869347,
-0.009333087131381035,
-0.0032103871926665306,
0.02839873917400837,
-0.005141374189406633,
0.027295289561152458,
0.07074335962533951,
-0.008417091332376003,
-0.04118756949901581,
0.027924690395593643,
-0.03280864655971527,
-0.0291315745562315,
0.009021167643368244,
0.03200232982635498,
-0.06708654016256332,
-0.02456810139119625,
0.0025906318332999945,
-0.03416258469223976,
0.022842979058623314,
0.049609050154685974,
-0.00007033826841507107,
-0.02473791316151619,
0.008897381834685802,
0.00023272722319234163,
-0.034264273941516876,
0.0015006017638370395,
-0.00010855900472961366,
-0.00575984874740243,
0.01448973547667265,
-0.02270381897687912,
0.006617151666432619,
-0.007281119003891945,
0.004247764125466347,
0.02140902541577816,
-0.0005789260612800717,
0.035589441657066345,
0.04660148546099663,
0.025270139798521996,
-0.02545989491045475,
-0.05020179599523544,
-0.024782579392194748,
0.04980705678462982,
-0.032133448868989944,
0.01700711064040661,
-0.006535153370350599,
-0.023668034002184868,
0.019571486860513687,
0.006002665031701326,
0.0037972969003021717,
-0.01736939698457718,
0.031150318682193756,
-0.05381351336836815,
-0.02862047776579857,
-0.00576546136289835,
0.03012985549867153,
0.018866658210754395,
0.025187136605381966,
-0.017340194433927536,
-0.01019381731748581,
0.012846751138567924,
0.009141668677330017,
0.04069942235946655,
0.030772173777222633,
0.03583903610706329,
-0.01812267117202282,
-0.026176562532782555,
-0.07060612738132477,
-0.036601971834897995,
-0.0005492568016052246,
-0.015381605364382267,
0.06785817444324493,
0.0008167431224137545,
0.016520395874977112,
-0.030795425176620483,
-0.04747419431805611,
0.008939306251704693,
-0.025881832465529442,
-0.014616485685110092,
-0.03968346118927002,
0.013221745379269123,
-0.03677792102098465,
0.07853276282548904,
-0.026924291625618935,
0.0009784398134797812,
0.027218811213970184,
0.05250567942857742,
0.015038046054542065,
-0.010165881365537643,
-0.027840295806527138,
0.008615134283900261,
-0.06914979964494705,
0.011851117014884949,
0.01331830769777298,
-0.016110548749566078,
-0.0120238047093153,
0.03351075202226639,
0.021149693056941032,
0.039320725947618484,
-0.013987405225634575,
-0.008100040256977081,
-0.013867092318832874,
0.0024404011201113462,
-0.01228275615721941,
0.0362418033182621,
-0.005033731926232576,
0.005592380650341511,
-0.014019817113876343,
-0.008932786993682384,
-0.023459045216441154,
0.018187662586569786,
0.0005684187053702772,
-0.0036007033195346594,
-0.020513910800218582,
-0.016532793641090393,
0.024537883698940277,
0.002748812548816204,
-0.01921624317765236,
-0.043948590755462646,
0.002614146564155817,
0.034163948148489,
0.025944970548152924,
0.004674599971622229,
0.01607329770922661,
0.009700383991003036,
-0.04303749278187752,
0.023276416584849358,
0.03035648725926876,
-0.006654614116996527,
-0.04630088806152344,
0.018403925001621246,
-0.003741440363228321,
0.04588105157017708,
-0.011306283995509148,
-0.04079192131757736,
0.04643955081701279,
-0.03431088104844093,
-0.04659708961844444,
-0.0019461795454844832,
0.0303408931940794,
0.03985556587576866,
0.052747778594493866,
0.025160666555166245,
-0.03928126394748688,
0.033578574657440186,
0.005725621245801449,
-0.009078980423510075,
-0.028679730370640755,
-0.017971184104681015,
-0.01774800568819046,
0.011365311220288277,
0.055647481232881546,
-0.002467863727360964,
0.005993809085339308,
0.01650295779109001,
0.005275786388665438,
-0.030696310102939606,
-0.037395179271698,
0.029557358473539352,
-0.03436601907014847,
0.0020690332166850567,
0.03379426524043083,
0.009027802385389805,
0.011146214790642262,
0.04691140726208687,
-0.016604913398623466,
0.010142001323401928,
0.021646859124302864,
0.0018026988254860044,
-0.09752193838357925,
-0.012160873040556908,
0.01972385123372078,
-0.008067846298217773,
0.026460302993655205,
-0.021948251873254776,
0.016564249992370605,
0.017090408131480217,
-0.07782427221536636,
-0.008938409388065338,
-0.017840007320046425,
0.024551289156079292,
-0.006087516900151968,
0.018103431910276413,
-0.03564826771616936,
0.03617588058114052,
0.036762677133083344,
0.03837878629565239,
0.01205393299460411,
0.03818992152810097,
-0.031216442584991455,
-0.03325832635164261,
-0.012178302742540836,
0.03788316994905472,
-0.0025979611091315746,
-0.012388634495437145,
0.054955627769231796,
-0.011960244737565517,
-0.019849484786391258,
0.022565040737390518,
0.006824227515608072,
-0.01615106128156185,
-0.010158100165426731,
0.051257289946079254,
0.022190377116203308,
0.03984576091170311,
0.046335943043231964,
-0.038164228200912476,
0.013013814575970173,
0.01764550991356373,
0.0094946613535285,
0.01231635082513094,
-0.03477001190185547,
-0.02093319408595562,
0.022588182240724564,
-0.02007569558918476,
-0.03838466480374336,
0.058653030544519424,
-0.009286240674555302,
-0.019611995667219162,
0.019517051056027412,
-0.009860475547611713,
-0.0018596536247059703,
-0.004039020277559757,
0.019903775304555893,
-0.05946452543139458,
-0.011918650008738041,
0.01234911847859621,
0.01898633874952793,
0.0061131929978728294,
0.005548733752220869,
-0.015356851741671562,
-0.03233162313699722,
0.03041062317788601,
0.02647942490875721,
-0.000985433696769178,
-0.05743437260389328,
-0.02110605686903,
-0.02337067946791649,
0.009278625249862671,
-0.032038696110248566,
-0.0592966191470623,
-0.06153598427772522,
0.021710989996790886,
0.05004400759935379,
0.0533258318901062,
-0.015107573941349983,
-0.06619955599308014,
-0.029726581647992134,
-0.051935818046331406,
0.020504336804151535,
-0.026988038793206215,
0.005780939478427172,
-0.04414486885070801,
0.005386515520513058,
0.011713658459484577,
0.005770761985331774,
0.06091734394431114,
0.043179675936698914,
-0.02212049625813961,
-0.009297067299485207,
0.010958397760987282,
0.03913065791130066,
-0.06304416805505753,
0.008892941288650036,
-0.01984058879315853,
0.006641669198870659,
0.00461992621421814,
-0.01029474288225174,
-0.014980332925915718,
0.019263017922639847,
0.048934388905763626,
-0.03938129171729088,
-0.0038899502251297235,
0.01781848818063736,
-0.015986284241080284,
0.09204331040382385,
-0.007043506950139999,
0.003517791396006942,
0.06566041707992554,
-0.02413984388113022,
0.04401902109384537,
0.02485618367791176,
-0.027298372238874435,
-0.01814820058643818,
0.02515055425465107,
-0.00100889231543988,
-0.02194661647081375,
0.0027142141479998827,
-0.002994907321408391,
0.03449729457497597,
-0.015220792964100838,
0.007796940393745899,
0.010776892304420471,
-0.04710504040122032,
-0.024090951308608055,
0.021944701671600342,
0.011659877374768257,
0.073163703083992,
-0.015955306589603424,
0.04043900594115257,
0.0004811085236724466,
0.0026995185762643814,
-0.009884211234748363,
0.052774827927351,
0.06200128048658371,
-0.021645374596118927,
0.00969060231000185,
-0.005397036671638489,
-0.03966495394706726,
0.028772296383976936,
0.0019304553279653192,
-0.006878146901726723,
-0.01859394833445549,
0.013742828741669655,
0.026442402973771095,
-0.022110968828201294,
-0.01900533400475979,
0.019443724304437637,
-0.002197664463892579,
0.09620293974876404,
-0.0028403685428202152,
0.017044153064489365,
-0.009188317693769932,
-0.004324434790760279,
-0.028304284438490868,
-0.004799152724444866,
-0.016133980825543404,
0.018843121826648712,
0.0022394456900656223,
0.022965550422668457,
-0.019273746758699417,
-0.0037810031790286303,
-0.004027766175568104,
-0.044751133769750595,
0.01326348539441824,
0.06607290357351303,
0.01775718480348587,
-0.020200690254569054,
0.022049814462661743,
-0.006739421747624874,
-0.050105463713407516,
0.03150632604956627,
0.02054700441658497,
0.02098289504647255,
0.0352364145219326,
-0.026986898854374886,
0.01811162754893303,
0.07075946033000946,
-0.002419619355350733,
-0.014433774165809155,
-0.017930788919329643,
0.023257868364453316,
-0.01201564073562622,
-0.003025331534445286
] |
<p>I conducted an experiment which aimed to detail and record the voltage across series resistors in series circuits.</p>
<p>I noticed that:</p>
<ul>
<li>The Final Voltage, V3, stayed the same.</li>
<li>The resistors with the highest resistance had the highest voltage drop.</li>
</ul>
<p>How do I put my observation in words?</p>
| 10,763 |
[
-0.042793914675712585,
-0.04072732850909233,
-0.023127762600779533,
-0.007242661435157061,
-0.01168185193091631,
0.04551677033305168,
0.008000914007425308,
0.018230263143777847,
0.021161813288927078,
-0.010854071006178856,
0.05033260956406593,
0.06211156025528908,
0.02371203899383545,
0.009273665025830269,
0.023635350167751312,
0.00007544434629380703,
0.003211611183360219,
0.014073277823626995,
-0.009870268404483795,
0.005476372316479683,
-0.04952584579586983,
0.03162699192762375,
0.019494477659463882,
0.009009746834635735,
-0.010557763278484344,
0.0452146902680397,
0.04402710124850273,
-0.012624473311007023,
0.005229925736784935,
0.005490292329341173,
0.009870878420770168,
-0.022107591852545738,
-0.011514050886034966,
-0.0012800164986401796,
0.052567388862371445,
0.00837548729032278,
0.005076362285763025,
-0.04355344548821449,
0.017795687541365623,
0.04733571410179138,
0.003161206841468811,
-0.0023957625962793827,
-0.007508125156164169,
0.06581844389438629,
-0.059769611805677414,
-0.009961036965250969,
0.0011537073878571391,
-0.003706402610987425,
0.0025808317586779594,
-0.039897795766592026,
0.04824170470237732,
0.006843617185950279,
0.06657133996486664,
0.042544156312942505,
0.0039026604499667883,
0.011148844845592976,
0.040804773569107056,
0.0453176312148571,
-0.0022356982808560133,
-0.020660102367401123,
0.010493616573512554,
-0.02645721286535263,
-0.0008419685182161629,
-0.01584041118621826,
-0.044065337628126144,
0.030741216614842415,
-0.01550661213696003,
-0.029923802241683006,
0.000028266416848055087,
-0.005063019227236509,
-0.009363027289509773,
0.0028768409974873066,
0.01183540653437376,
-0.005129782482981682,
-0.0030661604832857847,
-0.0306790079921484,
0.016454091295599937,
0.013804513961076736,
0.05428767949342728,
0.048793260008096695,
-0.013366510160267353,
0.02466743439435959,
0.0038459610659629107,
0.05185098946094513,
-0.01776420883834362,
-0.04757426679134369,
0.056260786950588226,
0.001847176579758525,
0.014130735769867897,
0.043396078050136566,
0.01747565157711506,
0.022429972887039185,
0.012654753401875496,
0.01672014780342579,
-0.054837390780448914,
-0.008318689651787281,
-0.011033681221306324,
0.04581863060593605,
0.014704622328281403,
-0.00936974585056305,
0.03817838430404663,
0.0005241752369329333,
0.027253087610006332,
0.07568198442459106,
-0.006548027507960796,
-0.05318863317370415,
-0.0268537737429142,
0.014104215428233147,
0.007202620152384043,
-0.00464656762778759,
-0.047018807381391525,
0.019827133044600487,
0.0172466691583395,
0.07201439887285233,
-0.004778137430548668,
-0.0074376510456204414,
-0.002883089007809758,
-0.010446570813655853,
0.04883124679327011,
0.02700568176805973,
0.010357826016843319,
-0.024171218276023865,
0.009020945988595486,
-0.006428461521863937,
-0.04534122720360756,
0.051904093474149704,
0.01948039047420025,
-0.0013853961136192083,
-0.00451268395408988,
0.03805310279130936,
0.02046867646276951,
0.012521094642579556,
-0.013170694001019001,
-0.016473622992634773,
0.0033410375472158194,
0.031386613845825195,
-0.08612026274204254,
-0.04390902817249298,
0.056445635855197906,
-0.011053151451051235,
-0.015219350345432758,
-0.06329648196697235,
0.014460357837378979,
0.04548289626836777,
0.042564719915390015,
-0.00611348170787096,
-0.005137179046869278,
0.028395192697644234,
-0.015029186382889748,
0.015385167673230171,
0.04019815847277641,
-0.028178192675113678,
0.012318079359829426,
-0.029277019202709198,
-0.008541899733245373,
-0.008097952231764793,
0.014704541303217411,
0.06683705747127533,
0.011414938606321812,
-0.005253784358501434,
0.03608198091387749,
-0.025760579854249954,
0.008836005814373493,
0.001782338134944439,
-0.020355859771370888,
-0.026727868244051933,
0.06459147483110428,
-0.010501667857170105,
0.013792316429316998,
0.02576659619808197,
0.019209180027246475,
0.02574155479669571,
-0.0028439548332244158,
0.014554362744092941,
0.03596212714910507,
-0.021407773718237877,
-0.018620077520608902,
-0.006771882995963097,
0.00773682352155447,
-0.03565596044063568,
-0.03421882539987564,
-0.07080917060375214,
0.007992313243448734,
0.01827363669872284,
0.0095266317948699,
0.054181940853595734,
-0.0028683519922196865,
-0.0011049825698137283,
0.009722457267343998,
-0.030199214816093445,
-0.038243893533945084,
-0.04495223984122276,
0.01814236305654049,
-0.018417054787278175,
-0.03528587147593498,
-0.029208682477474213,
-0.03507225587964058,
0.008467196486890316,
-0.0512748621404171,
0.021952981129288673,
0.0009067765204235911,
-0.010733332484960556,
-0.011171580292284489,
-0.011462131515145302,
0.001256373361684382,
0.03337247297167778,
0.027169978246092796,
-0.014962954446673393,
0.006241201888769865,
-0.039588917046785355,
0.01694035343825817,
0.017094524577260017,
0.004153768066316843,
0.01798943430185318,
-0.0009300245437771082,
0.007034088019281626,
0.0166381374001503,
0.019199497997760773,
0.0034750625491142273,
0.05114463344216347,
-0.011056867428123951,
0.05201662331819534,
0.06270468980073929,
-0.004821818321943283,
0.01907031051814556,
0.012604747898876667,
-0.0032206769101321697,
0.0022854506969451904,
-0.0017372674774378538,
0.029832873493433,
-0.06620990484952927,
0.003678307170048356,
0.04432414472103119,
-0.0014764417428523302,
-0.022713985294103622,
-0.00905581098049879,
0.03553744778037071,
0.023696862161159515,
0.02166592888534069,
0.004462474025785923,
0.028089607134461403,
-0.02835477702319622,
-0.007427284959703684,
0.009234144352376461,
0.03896040841937065,
0.022480150684714317,
0.052808187901973724,
0.049988869577646255,
0.04008205980062485,
-0.038325048983097076,
-0.012469812296330929,
0.027823425829410553,
0.044576987624168396,
0.01066711824387312,
0.0018928226782009006,
-0.04006482660770416,
0.004074998199939728,
-0.06789720803499222,
0.004429043736308813,
0.006945786066353321,
0.018397236242890358,
0.03552371636033058,
-0.02520602196455002,
-0.0021602206397801638,
0.04159018397331238,
0.027528097853064537,
-0.02065923810005188,
-0.013732310384511948,
0.03190356492996216,
-0.03764257952570915,
0.03146650269627571,
-0.06028115376830101,
-0.012682901695370674,
-0.024856818839907646,
0.003936238121241331,
0.016198288649320602,
-0.012828255072236061,
0.007062137592583895,
-0.04722859710454941,
-0.015036782249808311,
-0.014886556193232536,
-0.027861129492521286,
0.04021909832954407,
0.003091494319960475,
-0.013966217637062073,
0.028852788731455803,
-0.005611132830381393,
-0.04576074331998825,
0.016679292544722557,
0.043629951775074005,
-0.003462841035798192,
0.054305266588926315,
-0.019539067521691322,
-0.08092208951711655,
-0.009202330373227596,
0.014307143166661263,
0.018981341272592545,
-0.025095989927649498,
-0.019065503031015396,
0.0796402245759964,
-0.009149143472313881,
-0.029843369498848915,
0.006725915241986513,
-0.02056221477687359,
0.012865794822573662,
0.0014208232751116157,
-0.010237595066428185,
0.01134383212774992,
-0.01252164039760828,
0.04154655337333679,
0.002312932163476944,
0.007516850251704454,
-0.05305531993508339,
-0.04033394530415535,
-0.05340908095240593,
-0.002170923864468932,
0.0063416436314582825,
0.04210784658789635,
-0.03625256195664406,
-0.01889496110379696,
0.07732298225164413,
-0.006442660931497812,
0.0036103923339396715,
-0.024493850767612457,
-0.03890141099691391,
0.0007526724366471171,
-0.04419754445552826,
0.04775596410036087,
0.03792642429471016,
-0.008770155720412731,
0.014154758304357529,
0.015484594739973545,
0.06121128052473068,
0.0025053173303604126,
0.03341292962431908,
0.008308987133204937,
-0.0008400380029343069,
0.01836089789867401,
-0.014188546687364578,
0.06781919300556183,
0.04180927947163582,
-0.050831928849220276,
0.028152761980891228,
0.004023684188723564,
0.025867825374007225,
0.029522718861699104,
-0.055144041776657104,
0.01917823776602745,
-0.013070221059024334,
0.009662006050348282,
-0.007756966631859541,
0.023455316200852394,
0.022394105792045593,
0.006636012811213732,
-0.04278362914919853,
0.028242334723472595,
0.05176771059632301,
-0.047946956008672714,
-0.010144016705453396,
0.017927607521414757,
0.03339074179530144,
-0.042337220162153244,
-0.08155399560928345,
0.01680324226617813,
-0.013361640274524689,
0.028061963617801666,
-0.010218426585197449,
-0.023630576208233833,
0.05134206637740135,
0.01771564409136772,
0.006489489693194628,
0.03328139707446098,
-0.09077072888612747,
-0.012451405636966228,
-0.07172596454620361,
-0.013982200995087624,
-0.0016324189491569996,
0.03379390016198158,
-0.009716103784739971,
0.05730951204895973,
0.03210989013314247,
0.022013608366250992,
0.031205875799059868,
-0.002427597064524889,
-0.09074797481298447,
-0.008544049225747585,
-0.004983797203749418,
-0.023621732369065285,
-0.031069714576005936,
-0.01658591255545616,
0.013210516422986984,
-0.012604538351297379,
-0.0043164510279893875,
-0.006635024677962065,
-0.007403827738016844,
-0.034151677042245865,
0.006264736410230398,
0.0009316445211879909,
-0.0007153850747272372,
-0.016539091244339943,
0.012689493596553802,
0.03495752066373825,
-0.07136020809412003,
0.02183874323964119,
-0.002323937602341175,
-0.015393219888210297,
-0.023844381794333458,
-0.04186173155903816,
-0.0026433460880070925,
0.037574052810668945,
-0.0016763118328526616,
0.010573345236480236,
-0.004670196212828159,
-0.013714213855564594,
0.03078550659120083,
-0.0004852837591897696,
0.028868475928902626,
0.01947924494743347,
-0.03381991386413574,
-0.014940328896045685,
0.014066703617572784,
0.007918673567473888,
0.015529593452811241,
0.03286733105778694,
-0.001977125648409128,
0.0164797380566597,
0.021775122731924057,
0.02782713994383812,
-0.026766803115606308,
0.03754368796944618,
0.023353105410933495,
0.003617374924942851,
-0.012460104189813137,
-0.025166334584355354,
-0.00803292915225029,
-0.011719070374965668,
-0.013299406506121159,
0.039144355803728104,
0.00892455130815506,
-0.024092188104987144,
-0.01845747046172619,
0.048413991928100586,
0.04768992215394974,
-0.038960859179496765,
0.018973402678966522,
-0.010744099505245686,
-0.011526033282279968,
0.007092542480677366,
0.032809313386678696,
0.027194000780582428,
0.002976403571665287,
0.03609428182244301,
0.025633668527007103,
-0.050209999084472656,
-0.07089327275753021,
-0.03960317000746727,
0.03493393585085869,
0.026383331045508385,
-0.02860691212117672,
-0.0003266944258939475,
-0.006849951110780239,
0.0014253860572353005,
0.025048064067959785,
-0.05134688690304756,
0.04678533226251602,
-0.015447878278791904,
-0.014082818292081356,
-0.06271275877952576,
-0.06064731627702713,
-0.027099870145320892,
0.012984962202608585,
-0.012742328457534313,
0.059324659407138824,
0.0026202104054391384,
-0.01645864173769951,
-0.01815057545900345,
-0.01817575842142105,
0.021640103310346603,
0.06970992684364319,
-0.01631552167236805,
0.007879645563662052,
0.003131632227450609,
0.02941804751753807,
-0.057600170373916626,
-0.0750538632273674,
0.049670182168483734,
0.017359422519803047,
0.05470786988735199,
0.04806617274880409,
-0.04843752831220627,
-0.045831385999917984,
0.007903835736215115,
-0.007566807325929403,
-0.00942524615675211,
-0.01817210763692856,
-0.05605156719684601,
0.03156135976314545,
0.04291512444615364,
-0.005194239318370819,
0.061065107583999634,
0.0038698657881468534,
0.023555027320981026,
0.011155917309224606,
0.04909643158316612,
0.013023801147937775,
-0.053925201296806335,
-0.014771372079849243,
0.03169891610741615,
0.019125865772366524,
-0.04308474808931351,
0.04782693833112717,
0.026315756142139435,
0.040331557393074036,
-0.03990822657942772,
-0.033475764095783234,
0.016383901238441467,
-0.019432255998253822,
0.019159583374857903,
-0.01640579104423523,
-0.02895457297563553,
0.005573154427111149,
0.01049488503485918,
-0.01866435632109642,
0.009790497832000256,
-0.04043518006801605,
0.008630448020994663,
0.00955201406031847,
-0.017485225573182106,
-0.007708893157541752,
-0.035890012979507446,
0.0034689733292907476,
0.009197093546390533,
-0.021260827779769897,
0.04163133725523949,
-0.0337710864841938,
-0.0030326335690915585,
0.014359829016029835,
-0.011877008713781834,
-0.05084040388464928,
0.04317695274949074,
-0.006425694562494755,
0.01792655698955059,
-0.06353676319122314,
0.046993669122457504,
0.024612708017230034,
0.03544335439801216,
-0.05882877856492996,
-0.04742448031902313,
0.04495667293667793,
0.0355134941637516,
-0.0004766932688653469,
0.044129710644483566,
-0.014064498245716095,
0.01404446642845869,
-0.03242427483201027,
0.030573280528187752,
0.03652316704392433,
-0.04376928135752678,
-0.03444673866033554,
0.0004985960549674928,
0.01588517799973488,
0.07601834088563919,
0.0041823964565992355,
-0.029566895216703415,
-0.016701381653547287,
-0.04625887796282768,
0.009441652335226536,
-0.0017989152111113071,
0.03395487368106842,
-0.018132081255316734,
-0.03511126711964607,
0.002374397125095129,
-0.011547536589205265,
0.053187791258096695,
-0.015053021721541882,
0.019085049629211426,
0.020516909658908844,
-0.019733816385269165,
-0.02464509941637516,
-0.03138645365834236,
0.031844768673181534,
-0.026174096390604973,
-0.0004401706682983786,
0.02663281187415123,
-0.0012874267995357513,
-0.03149772062897682,
-0.004284488502889872,
-0.01332118734717369,
0.038453832268714905,
-0.022117547690868378,
-0.0405917689204216,
0.051729101687669754,
-0.020609620958566666,
-0.011180796660482883,
0.046999212354421616,
-0.018000900745391846,
-0.008274995721876621,
-0.011258178390562534,
0.0014549375046044588,
-0.011792546138167381,
0.011105087585747242,
-0.036102160811424255,
-0.011409323662519455,
-0.04369654878973961,
-0.0011556396493688226,
0.05782315880060196,
-0.018297821283340454,
0.049046825617551804,
0.007986465469002724,
-0.029466817155480385,
0.04134567454457283,
-0.04382118582725525,
0.005871742498129606,
-0.012650026008486748,
-0.016020942479372025,
0.05065901577472687,
-0.029656799510121346,
0.013331692665815353,
0.0018362596165388823,
0.029227884486317635,
-0.013444689102470875,
0.0016209202585741878,
0.03442329540848732,
-0.007404211908578873,
0.012297756969928741,
-0.031039468944072723,
-0.02893541194498539,
0.024092236533761024,
-0.059177763760089874,
0.0006164154037833214,
-0.03408045321702957,
0.009519515559077263,
0.05033287778496742,
-0.01095039676874876,
0.016248192638158798,
-0.05144914984703064,
-0.012650708667933941,
-0.05216975882649422,
-0.004348833579570055,
0.023679716512560844,
-0.011576452292501926,
-0.0027875802479684353,
0.009376663714647293,
0.05808122083544731,
-0.0065974220633506775,
0.027172299101948738,
-0.038204923272132874,
-0.03276517242193222,
0.0000810540295788087,
0.03717822581529617,
-0.031809002161026,
0.03126690909266472,
-0.026860743761062622,
-0.029573775827884674,
-0.017291927710175514,
-0.018094118684530258,
0.02033250965178013,
0.04984630271792412,
0.01684328354895115,
-0.001133254379965365,
0.049927450716495514,
-0.0001915003958856687,
0.031586989760398865,
-0.007843658328056335,
-0.013931146822869778,
0.11077488213777542,
0.049805883318185806,
0.04577259719371796,
-0.025436101481318474,
0.06229530647397041,
0.032116565853357315,
0.03952484950423241,
-0.020612988620996475,
-0.01026182807981968,
0.005305619444698095,
0.026141894981265068,
-0.018887754529714584,
0.008198186755180359,
-0.024394279345870018,
0.006666295696049929,
0.042361851781606674,
-0.05801958590745926,
-0.014621883630752563,
-0.010732480324804783,
0.017607761546969414,
0.006008650176227093,
0.0019136270275339484,
-0.09047152101993561,
0.038516122847795486,
0.01237205509096384,
-0.04829105734825134,
-0.02063460648059845,
-0.016228239983320236,
0.05567510426044464,
0.014377723447978497,
0.0015236218459904194,
0.017899872735142708,
0.05647353455424309,
0.007283101323992014,
-0.010553966276347637,
0.007016933988779783,
0.06165669858455658,
0.004023809917271137,
0.024868248030543327,
0.01483204122632742,
0.012851865962147713,
-0.004972812253981829,
-0.004843122325837612,
0.015064087696373463,
-0.07587476819753647,
-0.024024223908782005,
-0.008742911741137505,
0.021867454051971436,
0.0053610242903232574,
-0.0002847864234354347,
-0.014332903549075127,
0.01641848124563694,
0.010633155703544617,
-0.05034689977765083,
-0.025973578914999962,
0.036635011434555054,
0.001756124198436737,
-0.04283876717090607,
-0.06284425407648087,
-0.013540421612560749,
-0.013148477301001549,
-0.04444795101881027,
0.004690970294177532,
0.02225225605070591,
0.0013123775133863091,
-0.02108786068856716,
0.012184079736471176,
-0.02303481474518776,
-0.013800225220620632,
-0.020930640399456024,
0.025206921622157097,
0.00900183618068695,
-0.024128476157784462,
-0.0480693057179451,
-0.02741182968020439,
0.01307110395282507,
-0.0003470202209427953,
-0.0029008493293076754,
-0.02100060135126114,
-0.015575441531836987,
-0.0673324391245842,
0.020962556824088097,
0.02927825227379799,
0.017743511125445366,
-0.02222282811999321,
-0.0051397415809333324,
0.005358184687793255,
0.03155260905623436,
-0.008047142066061497,
-0.005926349200308323,
0.04251709580421448,
0.05067363381385803,
0.010596434585750103,
-0.0261396374553442,
0.0019113952293992043,
0.029514990746974945,
-0.06353913992643356,
-0.0010576187632977962,
0.005276049021631479,
0.0853809118270874,
0.015168971382081509,
-0.00866545271128416,
0.017580514773726463,
0.03241562098264694,
-0.020731691271066666,
-0.00030357501236721873,
0.00832738634198904,
-0.0027160693425685167,
0.005757554899901152,
0.011868514120578766,
0.020233692601323128,
0.004702994599938393,
-0.05139816924929619,
-0.023262761533260345,
0.01950763165950775,
-0.011584528721868992,
-0.0031710562761873007,
-0.014229567721486092,
0.02394004538655281,
-0.025861838832497597,
0.03074083849787712,
-0.027042342349886894,
-0.04004252329468727,
-0.030378248542547226,
-0.08667071908712387,
-0.009861611761152744,
0.020601904019713402,
-0.01568417251110077,
0.04512295871973038,
-0.013937398791313171,
-0.004665859509259462,
0.012826748192310333,
0.010006878525018692,
0.02054494246840477,
-0.06620470434427261,
-0.011749356053769588,
-0.018000228330492973,
0.02314230427145958,
-0.01731320098042488,
-0.10041850060224533,
0.06983312964439392,
-0.02629890851676464,
0.010483507998287678,
0.006958726793527603,
-0.004608506802469492,
0.03497932106256485,
0.020483722910284996,
0.012692241929471493,
0.009346324019134045,
0.016693009063601494,
0.026097401976585388,
0.00914386659860611,
-0.009078167378902435,
-0.04908692464232445,
0.019244495779275894,
0.038266491144895554,
0.0035297092981636524,
-0.01690635457634926,
0.010030543431639671,
-0.007108016405254602,
0.04097877815365791,
0.0314478799700737,
-0.0061472998932003975,
0.01524893008172512,
0.03267137333750725,
0.010492264293134212,
0.0014303536154329777,
0.012497848831117153,
-0.0013353500980883837,
0.0064935218542814255,
-0.07954293489456177,
0.03433772921562195,
-0.03496292605996132,
-0.00486579816788435,
-0.06056787818670273,
-0.02428634837269783,
-0.01368616335093975,
0.0011832742020487785,
-0.013984094373881817,
-0.029973939061164856,
-0.021004728972911835,
-0.008481238037347794,
-0.04580463841557503,
0.014644586481153965,
-0.01632111519575119,
-0.00629403768107295,
-0.039409954100847244,
-0.00782603770494461,
-0.020858315750956535,
0.028965849429368973,
0.024733228608965874,
0.02691633626818657,
0.00444234162569046,
0.03651123121380806,
-0.003974224906414747,
-0.04526194557547569,
0.0012365608708932996,
0.03979304060339928,
-0.024742702022194862,
-0.007566716987639666,
0.036088861525058746,
-0.04325965791940689,
0.0010839883470907807,
0.04532146081328392,
-0.03340843319892883,
0.005488527938723564,
0.007254322525113821,
-0.016658330336213112,
-0.01628849469125271,
0.05807718634605408,
-0.021880248561501503,
0.006305239629000425,
-0.035307202488183975,
-0.05568860471248627,
0.016042590141296387,
0.053494893014431,
0.01593845523893833,
-0.014639624394476414,
0.05302486568689346,
-0.007734384387731552,
-0.036066778004169464,
-0.007826420478522778,
-0.028876198455691338,
0.007459983695298433,
0.005125641822814941,
0.019854944199323654,
0.044317565858364105,
-0.040530912578105927,
0.006007052958011627,
-0.031168976798653603,
-0.00985422171652317,
0.0561264343559742,
-0.009643357247114182,
0.0032959156669676304,
-0.0009981280891224742,
0.009199516847729683,
-0.008040452376008034,
-0.011954293586313725,
-0.0035381007473915815,
0.008938435465097427,
-0.07734984904527664,
-0.034158170223236084,
0.004894017241895199,
0.01816561445593834,
-0.0007221520063467324,
-0.0492783822119236,
-0.03062116540968418,
0.030414657667279243,
0.01478494144976139,
-0.01901833340525627,
-0.006295663770288229,
-0.04131367430090904,
0.010240759700536728,
-0.07354915142059326,
0.05133634805679321,
0.015409819781780243,
-0.04790385439991951,
-0.04369880259037018,
-0.048042766749858856,
-0.021777739748358727,
0.02879275567829609,
0.09343741834163666,
0.038483329117298126,
-0.04351362958550453,
0.022540532052516937,
0.015736088156700134,
0.05552661418914795,
-0.040947187691926956,
0.029069317504763603,
0.003155546262860298,
-0.007433038670569658,
0.006486245431005955,
-0.02443733438849449,
-0.007405874319374561,
-0.015057699754834175,
0.024430619552731514,
-0.01658867672085762,
0.002316385041922331,
-0.04788120090961456,
-0.02765803225338459,
0.009759186767041683,
0.007680939044803381,
-0.03512312471866608,
0.07160131633281708,
0.004678129684180021,
0.0006125423824414611,
-0.004065253771841526,
-0.02910863235592842,
-0.07385636866092682,
0.042777881026268005,
-0.03773351386189461,
0.03540537878870964,
0.01771884225308895,
-0.01948338747024536,
0.03609578311443329,
0.0023160993587225676,
-0.047168128192424774,
0.023731248453259468,
-0.04813283681869507,
0.005000814329832792,
0.0866987407207489,
0.0034233788028359413,
-0.00449261162430048,
-0.011315015144646168,
0.005664351861923933,
-0.02220924198627472,
-0.006378490943461657,
-0.009196610189974308,
0.03353962302207947,
0.04375799000263214,
-0.013330798596143723,
-0.005305630154907703,
0.08653055876493454,
-0.00385291944257915,
0.0154871866106987,
-0.01279453281313181,
-0.007052585948258638,
-0.025970730930566788,
0.00026595930103212595,
-0.03169042617082596,
-0.014003834687173367,
-0.05612163990736008,
-0.003914163447916508,
-0.0014593646628782153,
0.09435835480690002,
-0.027114517986774445,
-0.011032767593860626,
-0.04523812234401703,
0.016984356567263603,
-0.05830119922757149,
-0.0055623240768909454,
0.030017388984560966,
0.022406816482543945,
-0.029102850705385208,
-0.0011194051476195455,
-0.0238497331738472,
-0.022428154945373535,
0.030471323058009148,
-0.016092898324131966,
0.042227692902088165,
-0.0327962189912796,
0.014538737013936043,
-0.03398680314421654,
0.02215924859046936,
-0.044277168810367584,
0.009390491992235184,
0.059054896235466,
0.011323518119752407,
-0.004416133277118206,
0.0037557827308773994,
-0.028379129245877266,
-0.038775380700826645,
0.04071102291345596,
-0.0276784747838974,
-0.04965920001268387,
-0.033124491572380066,
0.05288385599851608,
0.03341639041900635,
-0.0187818743288517
] |
<p>I have a (hopefully) quick question: is it possible to have a null Killing field $\xi ^ \mu$ such that the twist 1-form $\omega_{\mu} = \epsilon_{\mu\nu\alpha\beta}\xi^\nu \nabla^\alpha \xi^\beta \neq 0$ but the exterior derivative $(d \omega)_{\mu\nu} = 2\nabla_{[\mu}\omega_{\nu]} = 0$? Or does $(d \omega)_{\mu\nu} = 0$ always imply $\omega_{\mu} = 0$ for a null Killing field? </p>
| 10,764 |
[
-0.020920760929584503,
0.01185397244989872,
-0.000966578780207783,
-0.021579712629318237,
0.05985139682888985,
0.03150622546672821,
-0.04231535270810127,
-0.032601598650217056,
-0.027490120381116867,
-0.07858611643314362,
0.009382658638060093,
0.025369156152009964,
0.05182376503944397,
-0.007811958435922861,
0.0254390649497509,
-0.00540531100705266,
-0.03240387141704559,
0.004845449235290289,
-0.009796848520636559,
0.0011132361833006144,
-0.013839070685207844,
0.034750666469335556,
0.026160752400755882,
0.008181970566511154,
-0.024480048567056656,
-0.002966703847050667,
-0.016283253207802773,
0.004898411221802235,
-0.021086029708385468,
0.025740444660186768,
0.030462678521871567,
-0.03088056668639183,
0.015751518309116364,
0.02914370782673359,
-0.008498728275299072,
0.01937919855117798,
-0.022814832627773285,
-0.010677182115614414,
-0.025468066334724426,
-0.0008724682847969234,
-0.01870182529091835,
-0.018462521955370903,
-0.024062925949692726,
0.05531289055943489,
-0.039264120161533356,
-0.023879380896687508,
-0.004968857858330011,
0.00636106776073575,
0.07028583437204361,
-0.03805232793092728,
0.08877537399530411,
-0.0055060479789972305,
0.029515942558646202,
-0.011184871196746826,
0.003750366624444723,
-0.04397286847233772,
0.06992675364017487,
0.0540849007666111,
-0.017614617943763733,
-0.022118978202342987,
-0.032348111271858215,
-0.02340921014547348,
-0.005804494954645634,
-0.012552211061120033,
-0.006734840106219053,
0.07792475819587708,
0.012581711634993553,
-0.02979391999542713,
0.025562450289726257,
-0.010819821618497372,
-0.006422067992389202,
-0.021314028650522232,
-0.017290590330958366,
-0.012284016236662865,
-0.013568542897701263,
0.004136285744607449,
0.013197792693972588,
0.0007556774653494358,
0.036850228905677795,
0.01971544325351715,
-0.01712998002767563,
0.007210406940430403,
0.06382834166288376,
0.016591493040323257,
0.0038840705528855324,
-0.00577848544344306,
0.0660235583782196,
0.025148293003439903,
-0.000929085595998913,
0.033225562423467636,
0.01102227158844471,
-0.022507591173052788,
0.02101166918873787,
-0.04420056194067001,
-0.026786161586642265,
0.019913356751203537,
0.01026811171323061,
0.05381198599934578,
-0.008979080244898796,
-0.02410932071506977,
-0.05186222493648529,
-0.021250391378998756,
0.010776382870972157,
0.022997582331299782,
0.040363818407058716,
-0.02035171538591385,
-0.045583099126815796,
0.017672646790742874,
-0.06128225475549698,
0.018008491024374962,
-0.03235648572444916,
0.009875851683318615,
-0.032571516931056976,
-0.022667206823825836,
0.006434089038521051,
0.0023678706493228674,
-0.013683930970728397,
-0.054754238575696945,
0.00581808015704155,
0.08899927884340286,
0.05032744258642197,
-0.025075653567910194,
0.02290438301861286,
-0.031052859500050545,
-0.06601948291063309,
0.00004214869113638997,
0.0641225054860115,
0.007702606730163097,
-0.05105167254805565,
-0.045049868524074554,
-0.004957121331244707,
0.016699736937880516,
-0.009621316567063332,
0.02743096463382244,
0.022534361109137535,
-0.011385668069124222,
-0.08101040124893188,
-0.06800581514835358,
-0.010712036862969398,
-0.040166329592466354,
-0.005639656912535429,
-0.05944065749645233,
-0.03490481898188591,
0.012617449276149273,
0.08993390947580338,
0.01504907850176096,
-0.0024036208633333445,
0.012910338118672371,
0.018704062327742577,
-0.007846291176974773,
0.003248443827033043,
-0.009636146016418934,
-0.021392937749624252,
-0.04161441698670387,
-0.042667366564273834,
-0.04370449483394623,
0.04217701405286789,
0.008333821780979633,
-0.006330200005322695,
-0.021470053121447563,
0.09599373489618301,
-0.028430582955479622,
0.0342692956328392,
-0.008717638440430164,
-0.0282257329672575,
-0.03910815715789795,
0.07142744958400726,
0.007404080592095852,
0.014796337112784386,
0.026783490553498268,
0.0034987619146704674,
0.032982636243104935,
-0.01998070254921913,
0.05126505717635155,
0.05178188905119896,
-0.055785808712244034,
-0.0028359643183648586,
0.0034475845750421286,
0.03409634158015251,
0.02137657254934311,
-0.0024079459253698587,
-0.003051005769520998,
-0.008460410870611668,
0.002078734338283539,
-0.034160662442445755,
0.045459795743227005,
-0.016448169946670532,
0.01991851069033146,
0.004895243793725967,
-0.02857096865773201,
0.02806226909160614,
-0.03444214537739754,
0.044745009392499924,
0.058424029499292374,
-0.020706014707684517,
0.032567281275987625,
0.04429050534963608,
-0.0018964275950565934,
-0.03079979121685028,
-0.04387153312563896,
-0.0012628904078155756,
0.01709713786840439,
0.0033024789299815893,
-0.01311382744461298,
0.007561407517641783,
0.022329341620206833,
0.020560359582304955,
0.00903316680341959,
0.04790748655796051,
0.007396759930998087,
-0.02056654542684555,
-0.03673536330461502,
-0.018395740538835526,
0.035379037261009216,
-0.023632435128092766,
0.0604977123439312,
0.01782035641372204,
-0.005547550972551107,
-0.024667106568813324,
0.03014278970658779,
-0.053557660430669785,
0.04897370561957359,
0.07157457619905472,
-0.002300743944942951,
0.02602563053369522,
0.051563896238803864,
0.01137068122625351,
0.01765548251569271,
-0.00003786278102779761,
-0.014891507104039192,
-0.014210402965545654,
0.02907685749232769,
0.038900990039110184,
-0.010130494832992554,
-0.04641308635473251,
0.029147321358323097,
0.012200613506138325,
0.027279077097773552,
0.04782560467720032,
0.028231767937541008,
0.026435241103172302,
-0.038669053465127945,
0.0019027760718017817,
-0.0052365390583872795,
0.008610563352704048,
0.016116328537464142,
0.06122077256441116,
-0.013811069540679455,
0.01740078628063202,
0.00005385433178162202,
-0.02572278492152691,
0.029998058453202248,
-0.032658226788043976,
-0.04474952816963196,
0.027919720858335495,
0.01777510903775692,
0.053088460117578506,
0.01933554746210575,
0.04681861028075218,
0.06095471978187561,
-0.00434962147846818,
0.00599771598353982,
-0.015120618045330048,
0.02217462845146656,
0.03761882334947586,
0.018233971670269966,
0.02374863624572754,
-0.028577877208590508,
0.010586770251393318,
-0.046878401190042496,
-0.006864830385893583,
0.03445397689938545,
-0.005465770605951548,
0.00854253489524126,
0.0027036129031330347,
0.029057327657938004,
0.003640605602413416,
0.026353344321250916,
-0.004862245172262192,
-0.015052979812026024,
0.04167681187391281,
-0.0205160491168499,
0.005640744231641293,
0.04998110234737396,
-0.029428744688630104,
-0.012339157052338123,
-0.051821887493133545,
-0.01209349650889635,
0.0654023140668869,
0.011786838062107563,
0.0099038016051054,
0.025272324681282043,
-0.02921181358397007,
-0.011470792815089226,
-0.05470035597681999,
-0.03609628602862358,
-0.005341306794434786,
-0.009530222974717617,
-0.011821096763014793,
0.019058309495449066,
0.03384999558329582,
-0.016722602769732475,
0.015642734244465828,
-0.009022614918649197,
-0.05614261329174042,
-0.01659885048866272,
-0.005647858139127493,
0.03636785224080086,
-0.053086355328559875,
0.026734644547104836,
0.02333824336528778,
-0.015941213816404343,
0.025316152721643448,
-0.033074118196964264,
-0.02989196591079235,
0.02908836491405964,
0.004076956771314144,
-0.0031614440958946943,
0.022382225841283798,
-0.030432838946580887,
0.10119540989398956,
0.04419676586985588,
-0.03175291791558266,
-0.01882973313331604,
0.0010723447194322944,
-0.002659483812749386,
-0.041205257177352905,
-0.016804873943328857,
-0.038279447704553604,
-0.005965466611087322,
0.02639784850180149,
0.01157631166279316,
0.03096703812479973,
0.01824786141514778,
-0.007259097415953875,
-0.02275579236447811,
0.015466166660189629,
-0.00036280674976296723,
0.011154239065945148,
0.04765119031071663,
0.022598473355174065,
0.025328321382403374,
0.017556464299559593,
0.046556662768125534,
0.020848501473665237,
0.019994959235191345,
-0.03138398379087448,
0.02302560582756996,
0.02969571016728878,
0.007385462522506714,
-0.017265863716602325,
0.03307506814599037,
-0.0054946052841842175,
-0.013430888764560223,
-0.019542373716831207,
-0.008424201048910618,
0.054873693734407425,
-0.018167516216635704,
0.010266547091305256,
-0.0013631166657432914,
-0.02340746857225895,
-0.028860079124569893,
0.014865133911371231,
-0.006252138875424862,
-0.006965520326048136,
0.04155588150024414,
-0.025908716022968292,
-0.011129635386168957,
0.03666926547884941,
0.057832349091768265,
0.036761924624443054,
-0.0021152980625629425,
-0.026458874344825745,
0.0015641473000869155,
-0.06725601851940155,
0.008609805256128311,
0.025653338059782982,
0.034653130918741226,
0.017246229574084282,
0.02875552698969841,
0.014123434200882912,
0.036261942237615585,
-0.0015603374922648072,
0.013561071828007698,
-0.0438326895236969,
0.0130453547462821,
-0.0529882051050663,
-0.01729312352836132,
-0.03709093853831291,
-0.028059210628271103,
-0.005395382177084684,
-0.018917139619588852,
-0.021051928400993347,
-0.020017605274915695,
-0.011838224716484547,
-0.022090015932917595,
0.011556869372725487,
-0.036649189889431,
-0.06329577416181564,
0.015221717767417431,
0.09605956077575684,
0.005061676260083914,
-0.022022726014256477,
-0.009715770371258259,
0.02999807894229889,
-0.03919113054871559,
0.0006858886918053031,
-0.02996334806084633,
0.022086838260293007,
-0.033887915313243866,
0.02719765156507492,
0.027032682672142982,
0.007742434274405241,
-0.018379848450422287,
0.0223799180239439,
0.05318724736571312,
0.042761191725730896,
0.019885404035449028,
0.010588589124381542,
-0.026330603286623955,
-0.052297186106443405,
-0.01869126781821251,
0.0025519533082842827,
0.08225908875465393,
-0.00041881302604451776,
0.00025184176047332585,
0.022885426878929138,
0.001750121358782053,
-0.009253409691154957,
0.022164301946759224,
0.07163043320178986,
0.03847412392497063,
-0.010079181753098965,
-0.03823474049568176,
0.004335891455411911,
-0.01358488667756319,
0.004912473727017641,
-0.022415731102228165,
-0.02763260155916214,
-0.010075971484184265,
-0.037464965134859085,
-0.05319453775882721,
-0.02960832417011261,
-0.021673865616321564,
-0.010991036891937256,
0.026279278099536896,
-0.003551432630047202,
-0.010552295483648777,
0.01663939282298088,
0.03169804438948631,
0.0900089368224144,
0.06796287000179291,
0.02668522298336029,
0.023511847481131554,
-0.06910804659128189,
0.00486069917678833,
0.039430275559425354,
-0.00391737837344408,
0.014366096816956997,
-0.020583774894475937,
-0.012950394302606583,
-0.02020937390625477,
0.03874471038579941,
0.0011656936258077621,
0.054395511746406555,
0.047856055200099945,
-0.007409157697111368,
0.01126868650317192,
-0.026928875595331192,
-0.03335079550743103,
0.033792778849601746,
0.01248666737228632,
-0.007971215061843395,
-0.03429076820611954,
0.009447128511965275,
-0.005998210981488228,
0.04489929601550102,
0.004349361639469862,
0.027607271447777748,
0.041467227041721344,
-0.016883036121726036,
0.010903158225119114,
0.018750816583633423,
-0.022705527022480965,
-0.07511631399393082,
0.0038071905728429556,
0.03355296328663826,
-0.031012389808893204,
0.07557559013366699,
-0.008062709122896194,
-0.011627708561718464,
0.05516035482287407,
0.003164819674566388,
-0.011920969933271408,
0.029836256057024002,
-0.024489350616931915,
0.02699807472527027,
0.03188746050000191,
0.01588772051036358,
0.014839839190244675,
0.04281700775027275,
0.02973843738436699,
0.0096250856295228,
-0.040559593588113785,
0.010828668251633644,
-0.04162759706377983,
-0.004322348162531853,
-0.05318700149655342,
0.001906464109197259,
-0.03969002142548561,
0.0242561437189579,
-0.023045150563120842,
0.006090070120990276,
0.007260023150593042,
-0.042708300054073334,
-0.0028050043620169163,
0.04352584853768349,
0.02187226712703705,
-0.04930111765861511,
0.008527450263500214,
0.008402029983699322,
0.011071199551224709,
-0.016151268035173416,
0.0036693839356303215,
0.016005489975214005,
0.009888296015560627,
0.025160130113363266,
-0.031964898109436035,
0.00734976539388299,
-0.008862093091011047,
-0.0037111069541424513,
-0.0061370329931378365,
-0.030746573582291603,
0.03588651865720749,
-0.005607111845165491,
-0.012918276712298393,
0.024079805240035057,
-0.04758129641413689,
0.023803874850273132,
-0.0125605883076787,
-0.026652174070477486,
-0.0042771403677761555,
-0.03846126049757004,
0.03843492642045021,
0.049140334129333496,
0.02702280506491661,
-0.08467947691679001,
-0.005485616158694029,
0.0036445907317101955,
-0.031109226867556572,
-0.005501107312738895,
-0.02226676233112812,
-0.0029567608144134283,
-0.01807362586259842,
-0.03547781705856323,
0.01734142377972603,
0.03879962116479874,
-0.010973149910569191,
0.031211862340569496,
0.029262065887451172,
0.051016099750995636,
0.03784354776144028,
-0.01597083918750286,
-0.034210290759801865,
0.04378385469317436,
-0.030950119718909264,
0.009519769810140133,
0.040541671216487885,
0.06669624894857407,
-0.023072106763720512,
0.011449935846030712,
-0.02380603365600109,
-0.0343925878405571,
0.029220933094620705,
-0.01061881985515356,
0.003813511924818158,
0.023274892941117287,
0.007849696092307568,
0.03233491629362106,
-0.007148116361349821,
0.0035266035702079535,
-0.05272635444998741,
0.0101507268846035,
0.0026404217351228,
0.04408767819404602,
-0.0018787893932312727,
-0.044564664363861084,
0.009895686991512775,
-0.00013904206571169198,
0.0232121329754591,
-0.013305549509823322,
0.05688878521323204,
-0.013669919222593307,
-0.043380256742239,
-0.03593437746167183,
-0.016758935526013374,
0.0070925443433225155,
-0.022326897829771042,
0.008619707077741623,
0.020759643986821175,
0.03045623190701008,
-0.05113055557012558,
-0.029837803915143013,
-0.020347289741039276,
0.02028784155845642,
0.06981373578310013,
-0.033487193286418915,
0.013617646880447865,
0.013160845264792442,
0.028668515384197235,
-0.029745088890194893,
-0.03426884859800339,
0.005929604638367891,
0.001559112686663866,
0.024526525288820267,
0.06427240371704102,
-0.04417148232460022,
0.025643453001976013,
0.03413185477256775,
0.06385475397109985,
-0.044400282204151154,
0.021405024453997612,
0.012350698001682758,
0.019816936925053596,
0.05694448575377464,
0.014434642158448696,
-0.04705371707677841,
0.03706749528646469,
-0.03961176425218582,
0.054441824555397034,
0.010305975563824177,
-0.015577965416014194,
0.010999946855008602,
0.02581026405096054,
0.04389180988073349,
0.00660471897572279,
-0.05769870802760124,
-0.037429407238960266,
0.03329603746533394,
0.028161875903606415,
0.02553560584783554,
0.011546880006790161,
-0.011656836606562138,
0.08248703181743622,
-0.004117234610021114,
-0.0096385283395648,
-0.00921520683914423,
-0.029237497597932816,
0.0014479856472462416,
-0.046898726373910904,
-0.061551954597234726,
0.029915688559412956,
0.017920009791851044,
0.009398098103702068,
-0.01222189236432314,
0.004707681015133858,
0.018718957901000977,
0.01711232028901577,
-0.0030260891653597355,
0.014544215053319931,
0.04721364006400108,
-0.003161905100569129,
0.033159829676151276,
-0.028814364224672318,
0.013615380972623825,
0.1192835345864296,
0.05468697473406792,
0.045140985399484634,
-0.05513612926006317,
-0.009854892268776894,
-0.021658914163708687,
0.005807791370898485,
-0.032063622027635574,
0.013930847868323326,
-0.01650339737534523,
-0.020554199814796448,
-0.013304971158504486,
0.0679432600736618,
-0.01044077891856432,
-0.023676255717873573,
0.046705443412065506,
-0.016613932326436043,
-0.03676655888557434,
-0.012223003432154655,
0.0008913699421100318,
0.0009941819589585066,
-0.016386564821004868,
-0.036370061337947845,
0.041660405695438385,
0.02396935038268566,
0.013211325742304325,
-0.028550662100315094,
-0.034116365015506744,
0.016314633190631866,
-0.024887654930353165,
-0.05148056149482727,
-0.017657160758972168,
0.0003334293724037707,
0.003662250703200698,
-0.005298372823745012,
-0.016729626804590225,
0.015422044321894646,
-0.00217453739605844,
0.02569468505680561,
0.06371617317199707,
0.019524751231074333,
0.049420785158872604,
0.02513071708381176,
0.02125893533229828,
-0.029349323362112045,
-0.008223270997405052,
-0.014440000057220459,
0.032076653093099594,
-0.017468485981225967,
0.019236629828810692,
-0.019719816744327545,
-0.029142791405320168,
0.024815581738948822,
-0.024662623181939125,
-0.058113422244787216,
-0.0127179604023695,
0.015191261656582355,
-0.0017540123080834746,
0.003725982503965497,
0.0054092006757855415,
0.04948698356747627,
0.040676429867744446,
0.004629610572010279,
-0.017066698521375656,
-0.008065774105489254,
-0.012389641255140305,
0.004662594757974148,
0.07224050909280777,
0.0019774166867136955,
-0.05493408441543579,
-0.0170303788036108,
-0.047587279230356216,
-0.02081552892923355,
-0.0026278465520590544,
-0.00029590673511847854,
0.002209153724834323,
0.04507865756750107,
-0.004398054908961058,
-0.014165868051350117,
-0.009170395322144032,
-0.07923554629087448,
0.012046147137880325,
-0.05742977559566498,
-0.014941440895199776,
-0.017567001283168793,
0.0012708799913525581,
0.005856968928128481,
0.011257054284214973,
0.0044328863732516766,
-0.028235578909516335,
0.02671479992568493,
0.02318093553185463,
-0.014337144792079926,
-0.01563963107764721,
-0.05000700801610947,
0.014829535037279129,
-0.03419842571020126,
0.012772602960467339,
-0.023850176483392715,
-0.0037281697150319815,
0.01185773964971304,
0.034194208681583405,
0.015361816622316837,
0.018750779330730438,
-0.0254928320646286,
-0.029763037338852882,
0.006547290366142988,
-0.019676240161061287,
0.020366977900266647,
0.026015443727374077,
0.03674829378724098,
-0.04479038342833519,
-0.04197702184319496,
-0.020523790270090103,
0.0047011105343699455,
-0.01698199287056923,
0.027110066264867783,
-0.03067362681031227,
-0.02178039401769638,
-0.001996756996959448,
-0.005182525143027306,
-0.042856793850660324,
-0.02588493563234806,
-0.03136589378118515,
0.029028089717030525,
0.02546580880880356,
-0.04986117035150528,
0.0034144918899983168,
0.007936820387840271,
0.005723145324736834,
-0.06911473721265793,
-0.022233884781599045,
0.028462540358304977,
-0.0252365842461586,
0.02880423329770565,
0.025033211335539818,
0.014296897687017918,
0.04829498752951622,
0.004040490370243788,
-0.017016099765896797,
0.004043005872517824,
-0.05435683950781822,
-0.05175500363111496,
0.05081745609641075,
0.022470694035291672,
0.04508916661143303,
0.02138175070285797,
-0.024191701784729958,
-0.019077187404036522,
0.05301760882139206,
-0.0010196868097409606,
-0.003735274076461792,
0.009170143865048885,
-0.06067497655749321,
0.005287943407893181,
-0.032771941274404526,
0.002832557074725628,
-0.022675378248095512,
-0.016354789957404137,
0.029820282012224197,
-0.01807328127324581,
-0.008519630879163742,
-0.029411546885967255,
0.003094032173976302,
-0.0184466652572155,
0.04516778886318207,
0.0044154510833323,
0.03878004476428032,
-0.007642161566764116,
0.09230706095695496,
-0.03847086429595947,
0.04078999161720276,
0.0262224692851305,
0.01927352510392666,
-0.09735256433486938,
-0.011601652018725872,
0.04618089273571968,
0.03530768305063248,
0.04873139038681984,
-0.04242366924881935,
0.04657388851046562,
0.005019886419177055,
-0.04888927936553955,
-0.047400761395692825,
-0.02153238281607628,
-0.0063863531686365604,
-0.04613211005926132,
-0.027474358677864075,
-0.026400255039334297,
-0.0026323816273361444,
0.06100323051214218,
0.03988112136721611,
-0.009196567349135876,
-0.010802209377288818,
-0.015618857927620411,
-0.001804932951927185,
0.0021139204036444426,
0.04106774926185608,
-0.003769202623516321,
-0.02271922118961811,
0.024498870596289635,
-0.009493842720985413,
-0.043371450155973434,
0.014838126488029957,
-0.031920161098241806,
-0.03332273289561272,
0.004403865896165371,
0.004986666142940521,
0.044710129499435425,
-0.024635963141918182,
0.012905620969831944,
-0.01210776623338461,
-0.012890581972897053,
-0.01300969161093235,
0.0010749305365607142,
0.016784245148301125,
-0.059982504695653915,
0.023018470034003258,
0.008852868340909481,
-0.01913413219153881,
-0.02131827175617218,
0.02053711749613285,
-0.05593859404325485,
-0.0525595098733902,
-0.02779179997742176,
-0.006513398606330156,
0.0019402171019464731,
-0.014014924876391888,
0.005715363658964634,
-0.035037893801927567,
-0.003218434751033783,
0.016771867871284485,
0.03176029399037361,
-0.003776507219299674,
0.025445904582738876,
-0.016091609373688698,
-0.05046284571290016,
-0.008507747203111649,
0.04577616602182388,
-0.017254596576094627,
-0.042602673172950745,
0.015340953134000301,
-0.04257388040423393,
-0.004861744120717049,
-0.0029430475551635027,
-0.049979403614997864,
-0.01358684990555048,
0.03187846764922142,
-0.007974015548825264,
0.02259640581905842,
-0.025722909718751907,
-0.05311642214655876,
-0.03531573712825775,
-0.06880612671375275,
-0.007156761363148689,
-0.018650280311703682,
0.017854735255241394,
-0.0022653648629784584,
-0.008299518376588821,
-0.027269382029771805,
-0.026413315907120705,
0.02324393205344677,
-0.05029081180691719,
-0.015093040652573109,
0.038523364812135696,
0.010554325766861439,
-0.0005467053852044046,
-0.016455741599202156,
0.007872308604419231,
-0.02210315875709057,
-0.03512224555015564,
0.0012794501380994916,
0.00024004594888538122,
-0.003573926165699959,
0.030519479885697365,
0.011098464019596577,
0.0014067767187952995,
0.0007834011339582503,
-0.011581599712371826,
-0.0246537197381258,
0.019027292728424072,
-0.027963124215602875,
0.016521263867616653,
0.058410875499248505,
-0.0027745338156819344,
-0.006677523721009493,
-0.010544593445956707,
-0.005515849683433771,
-0.029180990532040596,
0.03424084559082985,
-0.017812708392739296,
-0.03514647111296654,
-0.04368950054049492,
0.0019876707810908556,
0.004437266383320093,
-0.0163587499409914,
0.0063732098788022995,
0.05777588114142418,
-0.04352071136236191,
-0.06356780230998993,
0.01262014452368021,
-0.012318558990955353,
0.003204428358003497,
0.02386939339339733,
-0.003465769812464714,
0.023784203454852104,
0.026195265352725983,
0.02704140916466713,
0.02311544492840767,
0.03301694989204407,
-0.004443952348083258,
-0.02374560944736004,
0.014288131147623062,
-0.015750300139188766,
0.009143012575805187,
-0.031240440905094147,
0.0713290423154831,
-0.000003846599156531738,
-0.07889260351657867,
0.005080643575638533,
0.012316837906837463,
0.014245506376028061,
-0.026905670762062073,
-0.01112136710435152,
0.05233815684914589,
-0.011659376323223114,
0.04209170490503311,
-0.04434426873922348,
-0.02499835193157196,
-0.03287576511502266,
0.037352193146944046,
0.0016696007223799825,
0.04848125949501991,
-0.022677404806017876,
-0.010316718369722366,
-0.02168138697743416,
-0.00912773609161377,
0.024885598570108414,
-0.06175003573298454,
-0.01892724819481373,
0.012301431968808174,
-0.004709399305284023,
-0.0028751844074577093,
-0.0493636429309845,
0.018532490357756615,
-0.03889475390315056,
-0.002213476225733757,
0.008268115110695362,
0.02252804860472679,
-0.029454689472913742,
-0.0011679459130391479,
-0.023377859964966774,
0.056033823639154434,
-0.025133701041340828,
-0.03136514872312546,
-0.014810794033110142,
-0.012536776252090931,
0.004560780245810747,
0.052045539021492004
] |
<p>Shall we consider photoelasticity a non-mathematical, or purely visual, proof of the existence of stresses in mechanical structures undergoing external loading?</p>
| 10,765 |
[
-0.037798359990119934,
0.005747971590608358,
-0.022196542471647263,
-0.04988633096218109,
0.019530439749360085,
0.015062132850289345,
-0.03304401785135269,
0.007487659342586994,
-0.00967088807374239,
-0.045401349663734436,
0.040370289236307144,
0.018904700875282288,
0.014111594296991825,
0.0283083263784647,
0.006856570951640606,
0.011362208053469658,
-0.0100567527115345,
-0.003029381623491645,
-0.01202852837741375,
-0.03309857100248337,
0.006203907076269388,
0.0007182000554166734,
0.003244376741349697,
-0.0059846374206244946,
0.013271217234432697,
0.004338536877185106,
0.021800680086016655,
-0.021123521029949188,
0.03225438669323921,
0.055082619190216064,
-0.020749974995851517,
-0.004046773072332144,
-0.018677745014429092,
0.04422125965356827,
0.018542015925049782,
0.011304132640361786,
-0.026954874396324158,
-0.022275162860751152,
0.019772538915276527,
-0.005004590377211571,
0.011512074619531631,
0.021609291434288025,
0.022224145010113716,
0.041527457535266876,
-0.015941444784402847,
0.017690792679786682,
-0.022352144122123718,
-0.006529577076435089,
-0.0026782089844346046,
-0.03908209130167961,
0.052527256309986115,
-0.022181278094649315,
0.014730233699083328,
0.03145837411284447,
-0.0300606656819582,
-0.006526711396872997,
0.042138323187828064,
0.06218872219324112,
-0.03571578860282898,
-0.05354736000299454,
-0.021287327632308006,
0.00023809396952856332,
-0.011654305271804333,
-0.02726033143699169,
-0.024199016392230988,
0.03825220465660095,
-0.006866180803626776,
-0.031918659806251526,
0.0445256307721138,
0.0031006683129817247,
-0.034852832555770874,
0.009518668986856937,
0.0701138824224472,
-0.019474631175398827,
-0.04208720475435257,
-0.005818618461489677,
0.011583510786294937,
-0.015330015681684017,
0.017414741218090057,
0.028365524485707283,
-0.0007492335280403495,
-0.011170926503837109,
-0.002485509729012847,
0.05524040758609772,
0.013508261181414127,
-0.024350043386220932,
0.0984221026301384,
-0.013534937985241413,
0.02415914088487625,
-0.0023709512315690517,
0.019011441618204117,
-0.008678882382810116,
0.0033420680556446314,
-0.01377229392528534,
-0.006431791931390762,
0.028075335547327995,
-0.002870457246899605,
0.05566269904375076,
0.016615601256489754,
-0.02521408721804619,
0.022604692727327347,
0.00212453817948699,
0.022187964990735054,
0.0367044173181057,
-0.011620309203863144,
-0.01666528731584549,
0.02670328877866268,
0.04302927851676941,
0.038416482508182526,
0.010057210922241211,
-0.07755287736654282,
0.020547104999423027,
-0.008650965988636017,
0.037403881549835205,
0.037608470767736435,
-0.02589506097137928,
0.005377653054893017,
-0.005364927463233471,
0.03493959456682205,
0.06449390202760696,
0.03709335997700691,
-0.03889692574739456,
0.013032001443207264,
-0.025276921689510345,
-0.07440291345119476,
0.03376734256744385,
0.04061637073755264,
-0.05251927301287651,
-0.03712517023086548,
0.004529197700321674,
0.019683169201016426,
-0.0032432072330266237,
-0.0201466865837574,
-0.0038120518438518047,
0.049438949674367905,
0.00007170208846218884,
-0.08303531259298325,
-0.07018812745809555,
0.03686981648206711,
0.017889874055981636,
-0.017074748873710632,
-0.04159223288297653,
0.043368756771087646,
0.05073035508394241,
0.05727594718337059,
-0.0029512213077396154,
0.013243176974356174,
0.003923887852579355,
0.06056457757949829,
-0.027857955545186996,
-0.007950229570269585,
-0.0016534485621377826,
0.02185164950788021,
-0.02743544615805149,
0.009290391579270363,
-0.09634409099817276,
-0.022360598668456078,
0.03631880134344101,
-0.0025831314269453287,
-0.05101015046238899,
0.05322839319705963,
-0.05256304517388344,
0.014213141053915024,
-0.021417930722236633,
-0.028449343517422676,
-0.031519126147031784,
0.07515116780996323,
-0.030397795140743256,
0.023082375526428223,
0.03608321398496628,
0.005042081233114004,
0.012456212192773819,
0.003242787905037403,
0.03797193616628647,
0.004113264847546816,
-0.04920472949743271,
0.0307005662471056,
0.03967716917395592,
0.017511902377009392,
0.0012294402113184333,
-0.026059197261929512,
-0.036685582250356674,
0.0011477811494842172,
0.012970122508704662,
0.01656963862478733,
0.055329564958810806,
0.004424414597451687,
-0.008678074926137924,
0.050998661667108536,
-0.056490473449230194,
0.007851061411201954,
-0.05926288664340973,
0.05144919455051422,
-0.01144616212695837,
-0.006275673862546682,
0.02809920348227024,
0.0024361545220017433,
-0.015733297914266586,
-0.03611744940280914,
-0.021854819729924202,
-0.006504604127258062,
0.041498832404613495,
0.013077374547719955,
-0.014712568372488022,
0.017636505886912346,
0.005881485063582659,
0.034516412764787674,
0.02449587732553482,
-0.008308276534080505,
-0.03543473407626152,
-0.03739355131983757,
0.04598189517855644,
-0.038266777992248535,
0.016436748206615448,
-0.014206401072442532,
-0.005722427740693092,
0.009329630993306637,
0.0006445575272664428,
-0.014871361665427685,
0.05467648431658745,
-0.023463835939764977,
0.04005717113614082,
0.04745756462216377,
0.003989720717072487,
0.0012934745755046606,
0.011130216531455517,
0.021031802520155907,
0.019519111141562462,
-0.018380625173449516,
-0.0014865526463836432,
-0.05150137096643448,
-0.006494840141385794,
0.046283017843961716,
0.04694565385580063,
-0.03749688342213631,
0.029745418578386307,
0.022022804245352745,
0.0621420182287693,
0.033822786062955856,
0.009693952277302742,
-0.024722952395677567,
-0.04309980571269989,
0.011190205812454224,
0.05747523903846741,
0.019999634474515915,
0.026693571358919144,
-0.014975872822105885,
0.0432945117354393,
0.036884475499391556,
0.008999616838991642,
0.019350215792655945,
0.022118384018540382,
-0.049752991646528244,
0.01006352063268423,
0.021862907335162163,
0.011034764349460602,
0.05649169906973839,
-0.01044553518295288,
0.02043929696083069,
0.027060095220804214,
-0.030782226473093033,
0.015484684146940708,
-0.021345797926187515,
-0.009369519539177418,
0.03273174539208412,
-0.024856770411133766,
-0.0516514852643013,
-0.02281847968697548,
0.04679250717163086,
-0.025303101167082787,
0.011166743002831936,
-0.05011782422661781,
-0.03359287977218628,
-0.015643633902072906,
-0.004784050863236189,
0.021633554250001907,
0.013629398308694363,
0.03125740587711334,
-0.05735364928841591,
-0.004678729921579361,
0.020939085632562637,
-0.0400235652923584,
0.012455579824745655,
0.010052250698208809,
-0.02961663156747818,
0.019445983693003654,
-0.040206827223300934,
-0.05463537946343422,
0.0239168219268322,
-0.019406823441386223,
0.016332142055034637,
0.008632098324596882,
-0.016018753871321678,
-0.034877002239227295,
-0.013968285173177719,
-0.03342333063483238,
-0.013521714136004448,
-0.039671123027801514,
-0.02041053958237171,
0.03198217228055,
-0.02170831337571144,
-0.03496873378753662,
-0.015639768913388252,
0.01498109195381403,
-0.0671413317322731,
-0.011147890239953995,
-0.009549668058753014,
0.005939430557191372,
-0.047931015491485596,
0.06606186926364899,
0.03517681732773781,
-0.06357108801603317,
-0.00434912508353591,
-0.03622232377529144,
-0.03936860337853432,
0.03455045819282532,
-0.006740708835422993,
0.039664026349782944,
-0.01433203648775816,
-0.05122767761349678,
0.056541722267866135,
0.006312665529549122,
-0.03735004737973213,
-0.03576330095529556,
-0.022243570536375046,
-0.0018543668556958437,
-0.009110613726079464,
-0.02547677420079708,
-0.01613982953131199,
0.015038195997476578,
0.055253766477108,
0.021652033552527428,
0.004555962514132261,
0.005485349800437689,
0.04538987576961517,
-0.028637157753109932,
-0.03290706127882004,
-0.016010746359825134,
0.005940489005297422,
-0.0027881967835128307,
0.02431817539036274,
-0.009598652832210064,
0.018056325614452362,
0.010271471925079823,
0.01714811660349369,
0.015748610720038414,
-0.06388893723487854,
0.09071843326091766,
0.0036209183745086193,
-0.00010947326518362388,
-0.031032782047986984,
0.027668379247188568,
0.006419382523745298,
0.024276170879602432,
-0.010556984692811966,
0.03504479303956032,
0.019161323085427284,
-0.016739575192332268,
-0.004862797912210226,
0.022782666608691216,
0.02941305935382843,
-0.019097333773970604,
-0.017177879810333252,
0.021717723459005356,
-0.026258153840899467,
0.04476778209209442,
-0.012807568535208702,
-0.008331469260156155,
0.01449848897755146,
0.014827044680714607,
0.053670089691877365,
0.04765084758400917,
-0.013586279936134815,
0.013474225997924805,
-0.022479914128780365,
-0.02468896470963955,
-0.016317423433065414,
0.01923041231930256,
0.0036449520848691463,
0.02781270444393158,
0.030992263928055763,
0.010711953043937683,
0.038137808442115784,
0.003329178085550666,
-0.09514934569597244,
-0.01080107968300581,
0.0010540285147726536,
0.021607303991913795,
-0.026096204295754433,
-0.009511511772871017,
-0.012250353582203388,
-0.03544493764638901,
-0.02403835766017437,
-0.04231744259595871,
0.015928814187645912,
-0.07704214751720428,
-0.020232917740941048,
-0.02849516272544861,
-0.04517409950494766,
0.016396915540099144,
-0.018758269026875496,
0.02616468071937561,
-0.039141036570072174,
0.005222369451075792,
0.06480423361063004,
-0.014050554484128952,
-0.006397299002856016,
-0.00795331597328186,
0.02567289210855961,
0.006218255963176489,
0.021934758871793747,
0.024979302659630775,
0.028520487248897552,
-0.0381142683327198,
-0.00144743244163692,
0.00990132987499237,
0.022527221590280533,
0.017199944704771042,
-0.005040546879172325,
-0.024954738095402718,
-0.014397462829947472,
-0.021921513602137566,
0.017452429980039597,
0.03156118467450142,
-0.0023149545304477215,
0.002634757896885276,
0.012910670600831509,
-0.018161598592996597,
-0.011150351725518703,
0.05319416522979736,
0.03947797045111656,
0.0234120674431324,
-0.038784459233284,
-0.04752253741025925,
-0.02269718423485756,
-0.03614971786737442,
-0.025735212489962578,
0.04734613001346588,
0.023141343146562576,
-0.017139703035354614,
0.027564283460378647,
0.020715681836009026,
-0.010766606777906418,
0.013068167492747307,
0.01988728530704975,
0.004338947590440512,
-0.01180720329284668,
0.029057113453745842,
0.008393347263336182,
0.03918519243597984,
0.03587448224425316,
0.054827041923999786,
0.033434025943279266,
-0.04627345874905586,
-0.1140049621462822,
0.016519196331501007,
0.052696507424116135,
0.0026323378551751375,
-0.02741691656410694,
-0.013054895214736462,
-0.024307087063789368,
-0.0513010136783123,
0.040665920823812485,
-0.033869266510009766,
-0.002606563037261367,
-0.016500117257237434,
0.029046615585684776,
-0.038001056760549545,
-0.002109566004946828,
-0.017461378127336502,
0.02395700104534626,
0.013713848777115345,
-0.007937629707157612,
-0.03640031814575195,
0.0158129520714283,
0.022875720635056496,
0.005969207733869553,
0.002773356158286333,
0.029461342841386795,
0.04219752177596092,
-0.0025461334735155106,
-0.048902880400419235,
0.027951287105679512,
-0.06286418437957764,
-0.054316144436597824,
0.022966619580984116,
0.020059145987033844,
-0.028924863785505295,
0.013753472827374935,
-0.01068666111677885,
-0.05545143410563469,
0.0517764687538147,
-0.011604064144194126,
0.006529497914016247,
0.04614297300577164,
-0.017908314242959023,
0.022305749356746674,
0.029607851058244705,
-0.015585081651806831,
0.02944466844201088,
0.07573842257261276,
-0.025754878297448158,
-0.016248062252998352,
0.014543973840773106,
0.00960184819996357,
-0.029485316947102547,
-0.007037078961730003,
-0.009683285839855671,
0.02165438048541546,
-0.020990299060940742,
0.025600675493478775,
-0.025181684643030167,
0.010901319794356823,
-0.0009986144723370671,
-0.026561807841062546,
-0.003277083858847618,
0.032332874834537506,
0.011029998771846294,
-0.014338385313749313,
-0.03329414501786232,
0.003491197479888797,
-0.0012626720126718283,
-0.03856480121612549,
-0.01397531945258379,
0.035496167838573456,
-0.009601210243999958,
0.023310916498303413,
0.012377933599054813,
0.014073374681174755,
-0.0467132069170475,
0.007228001486510038,
-0.0028442793991416693,
-0.04200015962123871,
0.030984243378043175,
-0.009940844029188156,
0.07390258461236954,
0.032137032598257065,
-0.04136565327644348,
0.02276073396205902,
0.012690011411905289,
-0.008767911233007908,
0.04982086643576622,
-0.02020864188671112,
0.018526922911405563,
0.029191501438617706,
-0.00015592819545418024,
-0.027437854558229446,
-0.06084582209587097,
0.011797935701906681,
0.052203066647052765,
-0.01876634545624256,
-0.016073614358901978,
0.013169893063604832,
-0.005582697223871946,
-0.036796990782022476,
0.02925446629524231,
0.04395253583788872,
-0.03403192758560181,
-0.006835410371422768,
-0.0033016116358339787,
-0.020306000486016273,
0.046552348881959915,
-0.03343471884727478,
-0.01565956138074398,
0.006482311058789492,
0.0042963228188455105,
-0.04252826049923897,
0.01592072658240795,
-0.008066823706030846,
-0.014713052660226822,
0.013141507282853127,
-0.017638377845287323,
-0.011019370518624783,
0.0047486936673521996,
0.018417777493596077,
0.03829368203878403,
0.021129898726940155,
0.013273950666189194,
-0.0178209375590086,
-0.04892866313457489,
0.04737696796655655,
-0.010802239179611206,
0.04139075055718422,
0.02153201214969158,
0.008765725418925285,
-0.010956353507936,
-0.03482935205101967,
0.026073239743709564,
0.022181125357747078,
-0.03224446624517441,
-0.003115687519311905,
0.07975038141012192,
-0.015948796644806862,
0.008130350150167942,
-0.001756511628627777,
-0.03133620694279671,
0.000927093205973506,
-0.016891928389668465,
0.02811647206544876,
0.007305385544896126,
0.009127125144004822,
-0.04480033367872238,
-0.021917708218097687,
-0.00149669055826962,
-0.012853743508458138,
0.06618879735469818,
-0.057212598621845245,
0.06488607078790665,
-0.008149341680109501,
-0.03585448116064072,
0.02453775331377983,
0.022540295496582985,
0.01068851351737976,
0.020179741084575653,
-0.0014495849609375,
0.053518641740083694,
-0.04234848544001579,
-0.008544730953872204,
0.011970053426921368,
0.03753836080431938,
-0.017113620415329933,
0.00013622721598949283,
-0.009635244496166706,
0.04012132063508034,
-0.004289462696760893,
-0.04644452780485153,
-0.06945445388555527,
0.05069122090935707,
-0.05060216411948204,
0.0270881038159132,
0.0068305195309221745,
-0.03573683649301529,
0.024801451712846756,
-0.011516920290887356,
0.025569994002580643,
0.007085172459483147,
-0.031210964545607567,
-0.03708106279373169,
0.037460800260305405,
-0.03759278357028961,
0.04721984639763832,
-0.003315441543236375,
-0.014947285875678062,
-0.004397429991513491,
0.022539427503943443,
0.034580767154693604,
-0.015499279834330082,
-0.06134061515331268,
-0.03185832500457764,
-0.028605887666344643,
0.005344688892364502,
0.054973751306533813,
0.0022948398254811764,
-0.022996123880147934,
0.0466616116464138,
-0.03564151003956795,
0.0037811053916811943,
0.0309425238519907,
0.035886529833078384,
-0.02717652916908264,
0.04477297142148018,
-0.04636728763580322,
0.03826591745018959,
-0.017407603561878204,
0.011749344877898693,
0.12490828335285187,
0.03952719271183014,
0.027806101366877556,
-0.03146011382341385,
0.040022578090429306,
-0.03609670326113701,
-0.016950959339737892,
-0.019253455102443695,
0.03692479804158211,
-0.0010268588084727526,
-0.013236790895462036,
-0.01644992269575596,
0.06315817683935165,
-0.029761111363768578,
-0.02240096405148506,
0.03546988591551781,
-0.03972046822309494,
-0.01770058274269104,
-0.0023740516044199467,
0.0005999035784043372,
-0.02406584843993187,
0.0021662632934749126,
-0.024605758488178253,
-0.0069042351096868515,
-0.019026951864361763,
-0.01817413419485092,
-0.012340012937784195,
-0.051306597888469696,
0.028444474563002586,
0.02114761248230934,
-0.03767501190304756,
0.0021551477257162333,
0.039527829736471176,
-0.03489816188812256,
-0.058178722858428955,
-0.0035258298739790916,
-0.017429331317543983,
0.02609403245151043,
0.04627741500735283,
-0.00833864789456129,
0.009390586987137794,
-0.01104113832116127,
-0.019739236682653427,
-0.010734121315181255,
-0.04351105913519859,
0.017470933496952057,
-0.03287584334611893,
0.03129494562745094,
-0.003689424367621541,
0.016104649752378464,
0.015242806635797024,
-0.0502108596265316,
-0.006070554256439209,
-0.06279712170362473,
-0.03268776088953018,
-0.00815847609192133,
0.003331300802528858,
-0.0031240726821124554,
-0.0349733792245388,
0.010762385092675686,
0.021054575219750404,
0.04171838238835335,
0.04533688351511955,
-0.018322553485631943,
0.0043442388996481895,
0.020014574751257896,
0.021420571953058243,
0.07567650079727173,
-0.02506081573665142,
-0.036089301109313965,
-0.049389805644750595,
-0.015142453834414482,
-0.030418414622545242,
-0.04283393174409866,
-0.0037898789159953594,
0.009317588992416859,
0.024479426443576813,
0.023484570905566216,
-0.009834721684455872,
-0.007672804873436689,
-0.019477302208542824,
-0.009671688079833984,
-0.010959267616271973,
-0.025289585813879967,
-0.011489318683743477,
0.02878587506711483,
0.047441285103559494,
0.048744045197963715,
-0.009465279057621956,
-0.009243454784154892,
-0.016773739829659462,
0.018909767270088196,
0.022928522899746895,
-0.053930338472127914,
-0.03057538904249668,
-0.014475376345217228,
0.02169625274837017,
0.00957309640944004,
-0.024024421349167824,
-0.026923768222332,
0.02646770514547825,
0.028359532356262207,
0.018891457468271255,
0.04139910265803337,
0.0022272635251283646,
-0.006114564836025238,
0.03497401997447014,
-0.016643673181533813,
0.0007590486784465611,
0.007572630885988474,
0.02036154270172119,
-0.062253620475530624,
-0.03791869059205055,
-0.019682282581925392,
-0.017131973057985306,
-0.0006204303936101496,
0.03676679730415344,
-0.007554640527814627,
-0.0015789474127814174,
-0.018302837386727333,
0.02669437788426876,
-0.07328890264034271,
-0.04486595839262009,
-0.030204666778445244,
-0.05914916470646858,
0.00856542494148016,
0.005742629524320364,
-0.027253353968262672,
0.01534190122038126,
-0.015946893021464348,
-0.0232299342751503,
0.037711840122938156,
0.04480689391493797,
0.01300931628793478,
0.021769892424345016,
0.030324451625347137,
-0.009772966615855694,
0.02646450698375702,
-0.011647260747849941,
-0.04575536772608757,
0.027226129546761513,
-0.014501660130918026,
-0.06459079682826996,
0.02284127101302147,
-0.03036952018737793,
0.020375436171889305,
-0.0045134155079722404,
0.0029739888850599527,
-0.003816117299720645,
0.027461286634206772,
-0.03271474689245224,
0.0189967080950737,
0.022385718300938606,
-0.0013133269967511296,
-0.03312798961997032,
-0.03951729089021683,
0.030225925147533417,
-0.02058308944106102,
0.000018232625734526664,
0.026343021541833878,
0.0314638577401638,
0.009205604903399944,
-0.02944152243435383,
0.05286763235926628,
-0.01889183558523655,
0.0008089377079159021,
0.009515311568975449,
0.022055359557271004,
0.028354430571198463,
0.013906100764870644,
-0.022797919809818268,
0.04134941101074219,
0.02228977344930172,
-0.012468880042433739,
-0.09901949763298035,
-0.01144931185990572,
0.0112046143040061,
0.012567932717502117,
0.026690764352679253,
-0.0294940285384655,
0.061828743666410446,
-0.02196238562464714,
-0.08249314874410629,
0.01149809267371893,
-0.03416086360812187,
-0.05888424068689346,
-0.0010642997222021222,
0.012179887853562832,
-0.0196990929543972,
0.05329090729355812,
0.016605952754616737,
0.062231943011283875,
0.007379928603768349,
0.05448594316840172,
0.009279265999794006,
0.016020620241761208,
0.015987910330295563,
0.02749008685350418,
-0.015913650393486023,
-0.024647662416100502,
0.07508044689893723,
0.02412361279129982,
-0.04267473891377449,
-0.006722158752381802,
0.022622747346758842,
0.033591605722904205,
0.007617573253810406,
0.024165108799934387,
-0.010305571369826794,
0.02405274100601673,
0.012649266049265862,
-0.0322539396584034,
-0.037251994013786316,
0.01748845726251602,
-0.022303393110632896,
0.02445674128830433,
-0.04924701526761055,
0.03144888952374458,
0.007893546484410763,
-0.04331456124782562,
-0.05175142362713814,
0.040920358151197433,
-0.035126421600580215,
-0.05078359320759773,
0.0003107654629275203,
0.011295533739030361,
-0.014438943937420845,
-0.024131430312991142,
0.03873801603913307,
-0.04777031019330025,
0.026958376169204712,
-0.02162967622280121,
0.029449816793203354,
-0.01764105260372162,
0.022033555433154106,
0.02486606501042843,
-0.04599439725279808,
-0.023662352934479713,
-0.02146134525537491,
-0.0172065831720829,
-0.07201123982667923,
0.011522959917783737,
0.021341770887374878,
-0.02065693400800228,
-0.010505090467631817,
-0.03400333225727081,
-0.04617255553603172,
0.01837373897433281,
0.01767798699438572,
0.023594697937369347,
0.03677328675985336,
-0.03323933482170105,
-0.04894524812698364,
-0.10454083979129791,
0.03393792733550072,
-0.008835215121507645,
-0.0289157647639513,
-0.020060349255800247,
-0.0031894876156002283,
-0.028272800147533417,
0.026427825912833214,
0.04585709795355797,
-0.02847612462937832,
-0.010842411778867245,
0.02175704948604107,
0.00964510627090931,
-0.015744201838970184,
-0.0052674561738967896,
0.008513140492141247,
-0.02961297705769539,
0.002861360553652048,
0.000965907471254468,
-0.03762532398104668,
-0.023430904373526573,
0.016297418624162674,
0.053533148020505905,
0.00786749366670847,
0.04198218882083893,
0.018703047186136246,
-0.036074768751859665,
0.061500344425439835,
0.0072715687565505505,
-0.03141989931464195,
0.0637674406170845,
-0.016210384666919708,
0.029543401673436165,
0.005643229000270367,
-0.04521849751472473,
-0.054219767451286316,
0.030161172151565552,
-0.03330127149820328,
0.010580198839306831,
-0.04156342148780823,
-0.0037322475109249353,
0.027711601927876472,
-0.03452692925930023,
0.01934860646724701,
0.02912934496998787,
-0.02381860464811325,
-0.016648123040795326,
-0.005408721510320902,
0.030076010152697563,
0.009405468590557575,
-0.015120371244847775,
0.048205360770225525,
0.030637670308351517,
-0.008709476329386234,
-0.016154123470187187,
0.008583798073232174,
0.06628449261188507,
0.004906788468360901,
0.005191010423004627,
0.04745956510305405,
-0.017812132835388184,
0.012976625002920628,
0.0281439907848835,
0.03103143908083439,
-0.0063494304195046425,
-0.03226100280880928,
0.0018152155680581927,
0.01719682849943638,
0.004816674627363682,
-0.010617021471261978,
0.005312788765877485,
0.08190792053937912,
-0.006691641639918089,
-0.003578648902475834,
-0.027056686580181122,
-0.005035897251218557,
0.02029232494533062,
0.030547630041837692,
0.058815810829401016,
0.02560078538954258,
-0.020628472790122032,
0.01976368948817253,
-0.019114529713988304,
0.028867574408650398,
0.0042259045876562595,
-0.0010250803316012025,
-0.0042891413904726505,
-0.0027272156439721584,
-0.014592445455491543,
-0.0038182551506906748,
-0.01489018090069294,
-0.05992584303021431,
0.0314205102622509,
0.03515880927443504,
0.04861823841929436,
0.0058427294716238976,
0.014185248874127865,
0.001977959182113409,
-0.041377902030944824,
0.04885948821902275,
-0.0584026537835598,
0.0018646782264113426,
0.02711610496044159,
0.01759650558233261,
0.04019331932067871,
0.005204486194998026
] |
<p>At a free massless Lagrangian
\begin{equation} L_0 = \frac 1 2 ( \partial \psi)^2 ,\end{equation}
add an interaction term \begin{equation} L_I = \frac 1 2 m^2 \psi^2\end{equation}
where m is small enough to converge its perturbation calculation. From these setup, is it possible to gain the same results as of the free massive Lagrangian? Please point me a book description or some internet site. Thanks.</p>
| 10,766 |
[
0.032910559326410294,
0.020085319876670837,
-0.005958267487585545,
-0.002318001352250576,
0.021280959248542786,
-0.01095336303114891,
-0.02941380813717842,
-0.050917983055114746,
0.01524361688643694,
-0.061097949743270874,
0.020480895414948463,
0.009962105192244053,
0.0676506832242012,
0.019452301785349846,
0.036105647683143616,
-0.009414564818143845,
-0.03855665400624275,
0.017958998680114746,
0.014720115810632706,
-0.0068605272099375725,
-0.014058210887014866,
0.03542130067944527,
0.029359618201851845,
-0.004027767572551966,
-0.04154350981116295,
0.018965885043144226,
-0.014229953289031982,
0.001087258686311543,
-0.030226964503526688,
0.08858844637870789,
-0.04330594465136528,
-0.00410371134057641,
0.005573692731559277,
0.02587435580790043,
0.005501126870512962,
0.0077819908037781715,
-0.044167909771203995,
-0.0499432273209095,
0.019978897646069527,
-0.012521017342805862,
-0.040753740817308426,
-0.048414599150419235,
0.006854662671685219,
0.0476185604929924,
0.01844424195587635,
0.004192945547401905,
0.009554161690175533,
-0.04397052153944969,
0.08152105659246445,
-0.040241409093141556,
0.04893859848380089,
0.02861926332116127,
0.043140195310115814,
0.012764821760356426,
-0.008610797114670277,
-0.02848636917769909,
0.077158622443676,
0.083597332239151,
0.009352758526802063,
-0.05574739724397659,
0.001584644429385662,
-0.04913586378097534,
0.017530394718050957,
-0.007858426310122013,
-0.043008383363485336,
0.019019287079572678,
-0.01789877377450466,
0.0001615641376702115,
0.029533913359045982,
-0.015043101273477077,
0.013054641894996166,
-0.02113388478755951,
0.03772006183862686,
-0.0029428957495838404,
0.00519186444580555,
-0.002740998985245824,
0.010095427744090557,
-0.001529012923128903,
-0.009208591654896736,
0.028972400352358818,
0.010410396382212639,
0.04300721734762192,
0.054184604436159134,
0.014463147148489952,
-0.0001850144035415724,
-0.0012443835148587823,
0.05518997460603714,
0.014999421313405037,
0.006912542507052422,
0.042287930846214294,
-0.021289685741066933,
-0.00073361856630072,
0.041538629680871964,
-0.02693009562790394,
-0.022680791094899178,
0.017341475933790207,
0.02902381867170334,
0.04929104447364807,
0.018666580319404602,
-0.004093610681593418,
-0.012434765696525574,
-0.02383793331682682,
-0.020429644733667374,
0.0570947602391243,
0.033232953399419785,
-0.013667797669768333,
-0.05979868397116661,
0.00518789142370224,
-0.011897755786776543,
-0.03419565036892891,
-0.015232774429023266,
-0.0039737108163535595,
-0.0014247619546949863,
-0.022425072267651558,
0.0036972796078771353,
-0.0655122920870781,
-0.009781298227608204,
-0.028469329699873924,
0.06640378385782242,
0.07388880103826523,
0.06262505054473877,
-0.020994141697883606,
0.018801022320985794,
-0.03886473551392555,
-0.0437643863260746,
0.02038521133363247,
0.04135742038488388,
-0.002032138407230377,
-0.04996607452630997,
0.018654560670256615,
0.05988113582134247,
-0.02617664262652397,
0.006552737671881914,
0.019472379237413406,
0.023185478523373604,
-0.04142947867512703,
-0.06527500599622726,
-0.017144815996289253,
0.005196291022002697,
-0.03254036232829094,
0.009008064866065979,
-0.05387360230088234,
-0.03939911350607872,
0.052697669714689255,
0.10139553993940353,
0.00972797442227602,
0.015569988638162613,
-0.02211827225983143,
0.03674128279089928,
0.014671633951365948,
-0.005602371878921986,
-0.03333278000354767,
-0.014730273745954037,
-0.047171834856271744,
0.0044815982691943645,
-0.08663936704397202,
0.02187122032046318,
0.03768393024802208,
-0.020381705835461617,
0.008550961501896381,
0.09283503890037537,
-0.007478248793631792,
0.005209735129028559,
0.016272980719804764,
-0.027764536440372467,
0.004925592802464962,
0.07130936533212662,
0.01118084229528904,
0.012120178900659084,
0.010941620916128159,
0.006427277345210314,
0.02367803268134594,
0.00982291903346777,
0.03006153553724289,
0.02838071994483471,
-0.036810487508773804,
-0.04380756989121437,
-0.033595919609069824,
0.022635919973254204,
0.008410600014030933,
0.005686170421540737,
-0.029126783832907677,
-0.04754135012626648,
0.0074701872654259205,
-0.012585903517901897,
0.03356277570128441,
0.0038851231802254915,
0.004708700813353062,
-0.017938919365406036,
-0.062258996069431305,
-0.0018908149795606732,
-0.07155730575323105,
0.010472524911165237,
0.046435657888650894,
-0.006107244174927473,
0.07103075087070465,
0.012758389115333557,
0.022936031222343445,
-0.009720295667648315,
-0.035371165722608566,
-0.027867712080478668,
0.023261243477463722,
-0.00008093072392512113,
0.001325265970081091,
0.04180823266506195,
0.0313575342297554,
0.0253512691706419,
0.023986387997865677,
0.02978603169322014,
-0.04785254970192909,
-0.05916135758161545,
0.038690291345119476,
-0.0043548657558858395,
0.042627956718206406,
-0.011066066101193428,
0.01065783016383648,
-0.0027668823022395372,
-0.0010943834204226732,
-0.0231759212911129,
0.023732053115963936,
-0.02564864046871662,
0.04368947073817253,
0.07248689234256744,
0.03552776575088501,
-0.011145144701004028,
0.029365956783294678,
0.02391914837062359,
0.020648818463087082,
-0.013126708567142487,
-0.02555530145764351,
-0.05728771537542343,
-0.02745174802839756,
0.03192465007305145,
0.04756003990769386,
-0.04213027283549309,
0.006864121183753014,
0.06546337157487869,
0.012366779148578644,
0.025151215493679047,
0.03366483747959137,
-0.032455239444971085,
-0.021686486899852753,
0.07060909271240234,
0.0426463857293129,
-0.015896271914243698,
-0.007025057449936867,
0.02723466232419014,
0.023761333897709846,
0.013407309539616108,
0.012355811893939972,
-0.022131945937871933,
0.032087091356515884,
-0.03424592316150665,
-0.022083893418312073,
-0.018326621502637863,
-0.008787757717072964,
0.025269964709877968,
-0.024124495685100555,
0.03296251222491264,
0.009432610124349594,
-0.01581779308617115,
-0.05066997930407524,
-0.051969945430755615,
-0.009517371654510498,
0.02448616549372673,
-0.015906156972050667,
-0.013124710880219936,
-0.04831402376294136,
0.006351885385811329,
-0.0582200363278389,
-0.00576731376349926,
0.015905603766441345,
0.001736838254146278,
-0.03735673800110817,
0.02760876528918743,
0.03777157887816429,
0.003977316431701183,
0.026358600705862045,
0.004889694508165121,
-0.03488526865839958,
0.029791709035634995,
-0.023588281124830246,
0.015895962715148926,
0.030132025480270386,
-0.04400080069899559,
0.004974410869181156,
-0.03626926243305206,
-0.023859553039073944,
0.03833623230457306,
-0.021371442824602127,
0.01970849744975567,
0.03967834264039993,
-0.018792012706398964,
-0.06195488199591637,
-0.01073988527059555,
-0.02511686459183693,
-0.024180198088288307,
-0.017962131649255753,
0.029802195727825165,
0.01581149362027645,
0.040005285292863846,
-0.037256646901369095,
-0.01189899817109108,
-0.0578802116215229,
-0.01028230506926775,
-0.02823307178914547,
0.01630176417529583,
0.03056221455335617,
-0.043202243745326996,
0.03603433817625046,
0.03704213351011276,
-0.01510750874876976,
0.041088368743658066,
-0.07418365776538849,
-0.016799474135041237,
0.03498650714755058,
0.01535213366150856,
0.024143870919942856,
-0.008786603808403015,
-0.034375905990600586,
0.08238112181425095,
0.004526806063950062,
-0.044446442276239395,
-0.04474281519651413,
-0.00042272437713108957,
-0.0032931503374129534,
-0.008787804283201694,
-0.004623947199434042,
-0.00428836839273572,
-0.015453493222594261,
0.02936694212257862,
0.01239156536757946,
-0.002982191741466522,
0.02240775339305401,
0.014603180810809135,
-0.0028259686660021544,
0.0031637081410735846,
0.007422374561429024,
0.011001966893672943,
0.048558495938777924,
-0.009799334220588207,
-0.047270942479372025,
0.00402789143845439,
0.012430348433554173,
0.01975717581808567,
-0.00012537158909253776,
-0.03516795486211777,
0.060363318771123886,
0.021739711984992027,
0.006397088058292866,
-0.022154485806822777,
0.048165690153837204,
-0.017858020961284637,
-0.00982549786567688,
-0.014639917761087418,
0.02942306362092495,
0.010859169997274876,
-0.018172863870859146,
0.00829711277037859,
0.043666012585163116,
0.03594034165143967,
-0.01318938285112381,
-0.05925609916448593,
-0.019982650876045227,
-0.005551627371460199,
0.025540567934513092,
-0.015538034029304981,
-0.0321098193526268,
0.022822096943855286,
0.02656768262386322,
-0.0015539907617494464,
-0.03309470787644386,
0.012748736888170242,
0.030331067740917206,
-0.04625680297613144,
-0.001540330471470952,
-0.004300439730286598,
0.06810561567544937,
-0.025987112894654274,
0.031539518386125565,
0.008558620698750019,
0.0007943466189317405,
0.019099000841379166,
0.017580730840563774,
-0.07522169500589371,
0.046496693044900894,
-0.04043033346533775,
-0.03871496766805649,
0.04871371015906334,
0.01396467536687851,
0.0052003213204443455,
-0.019714733585715294,
-0.013752598315477371,
-0.012447625398635864,
-0.010592494159936905,
-0.0501730740070343,
0.015150671824812889,
-0.052810657769441605,
-0.028516491875052452,
-0.02690129540860653,
0.030980810523033142,
-0.012138517573475838,
-0.0071962871588766575,
-0.01662585325539112,
0.007079153321683407,
-0.05370236933231354,
-0.016672398895025253,
-0.0052374969236552715,
-0.009327606298029423,
-0.011431250721216202,
0.029575232416391373,
0.03233446925878525,
0.049075644463300705,
-0.024925315752625465,
0.028485611081123352,
0.024223916232585907,
0.06494423747062683,
0.016690745949745178,
-0.004649336449801922,
0.007716136518865824,
-0.03897299990057945,
-0.03640612214803696,
0.024645989760756493,
0.06433034688234329,
-0.01504922192543745,
-0.03369474038481712,
0.021759673953056335,
0.011872109025716782,
-0.013151036575436592,
0.043268654495477676,
0.0420210175216198,
0.027340717613697052,
-0.018499573692679405,
-0.06743724644184113,
-0.016643133014440536,
0.009537299163639545,
-0.014087698422372341,
0.011345984414219856,
-0.02373788133263588,
-0.02317087911069393,
0.007652899716049433,
0.02606053277850151,
0.022148966789245605,
-0.04385382682085037,
-0.02720707096159458,
-0.00903110671788454,
0.00960706640034914,
-0.006071881391108036,
-0.002668241737410426,
0.0031307279132306576,
0.03901609405875206,
0.026431744918227196,
-0.022117778658866882,
0.018766975030303,
-0.06052720174193382,
-0.015231931582093239,
0.03532323241233826,
0.04184660315513611,
0.018011897802352905,
0.012831132858991623,
-0.0373629666864872,
-0.029052734375,
0.05906761810183525,
-0.021747788414359093,
0.008659983985126019,
0.010978007689118385,
0.024528898298740387,
0.009142318740487099,
-0.0019220220856368542,
-0.03742985427379608,
-0.0006578913307748735,
-0.016145238652825356,
-0.004995881114155054,
-0.05750468000769615,
0.0034165543038398027,
-0.0065529136918485165,
0.031055482104420662,
0.04066705331206322,
0.0945485308766365,
0.010280979797244072,
0.008850066922605038,
-0.00808135699480772,
0.004944162908941507,
-0.031073931604623795,
-0.07997462898492813,
-0.007009795401245356,
-0.008255725726485252,
-0.0587986595928669,
0.01937580294907093,
-0.027480032294988632,
-0.0436009056866169,
0.001800013706088066,
0.015518194995820522,
-0.026089191436767578,
-0.015381881967186928,
-0.03524668887257576,
0.03214642405509949,
0.026331663131713867,
-0.015549791045486927,
0.03659031540155411,
0.03561816364526749,
0.009861240163445473,
-0.01898270845413208,
-0.018522532656788826,
0.04056674614548683,
0.0021136028226464987,
0.0019813808612525463,
-0.04832583665847778,
-0.01719536818563938,
0.002932247007265687,
0.016018306836485863,
-0.030739974230527878,
0.029334669932723045,
-0.022815575823187828,
-0.021180247887969017,
-0.044225744903087616,
0.04715355113148689,
-0.005363565869629383,
0.0003189833660144359,
0.03363196551799774,
0.025347618386149406,
0.02414572797715664,
-0.03919549286365509,
0.02337123639881611,
-0.009302068501710892,
-0.0032775425352156162,
0.039707064628601074,
-0.02576718106865883,
0.05429831147193909,
-0.020757492631673813,
-0.020716197788715363,
0.017600245773792267,
-0.05796026811003685,
0.05011231079697609,
0.015930701047182083,
0.017265858128666878,
0.008106266148388386,
-0.04749733582139015,
-0.00783084612339735,
0.0015052355593070388,
-0.011819603852927685,
0.010757485404610634,
-0.046345580369234085,
0.0066250767558813095,
0.04411187022924423,
-0.0066244835034012794,
-0.10286924988031387,
-0.042789213359355927,
0.007778466213494539,
-0.016568420454859734,
-0.00843653455376625,
-0.027421297505497932,
-0.030710162594914436,
-0.039971448481082916,
-0.010789860039949417,
-0.00447068503126502,
0.02561534382402897,
-0.023418771103024483,
-0.0184035524725914,
-0.010756860487163067,
0.018938813358545303,
-0.0031285409349948168,
-0.005325592588633299,
-0.04517505690455437,
0.006182994693517685,
-0.01739092729985714,
-0.018613053485751152,
0.010379916988313198,
0.06587815284729004,
-0.013641116209328175,
-0.012178992852568626,
-0.010932743549346924,
-0.007037483621388674,
0.039857055991888046,
-0.0031412155367434025,
-0.03184632956981659,
0.05173696577548981,
0.028801485896110535,
0.03605251386761665,
-0.021215686574578285,
-0.03373527526855469,
0.008558946661651134,
0.04134514927864075,
0.014209264889359474,
-0.009548790752887726,
-0.020960019901394844,
-0.05203709751367569,
0.044947076588869095,
0.010085942223668098,
-0.01926465891301632,
0.010817373171448708,
0.05981633812189102,
-0.0046307798475027084,
-0.02107585221529007,
0.021405356004834175,
-0.01014149934053421,
-0.023957978934049606,
0.007443578448146582,
0.01930558867752552,
0.012414030730724335,
0.018973011523485184,
-0.0181990098208189,
-0.021300749853253365,
-0.027862144634127617,
0.015015280805528164,
0.05810683220624924,
0.011044830083847046,
0.012235431931912899,
0.011194000020623207,
-0.008923646062612534,
-0.013880820944905281,
-0.0034907241351902485,
-0.04287484288215637,
-0.010545714758336544,
-0.002591304248198867,
0.05597790330648422,
-0.043556053191423416,
-0.02205657958984375,
0.026263238862156868,
0.04757682606577873,
-0.03568827360868454,
0.03924538940191269,
0.013350946828722954,
0.028706036508083344,
0.010319922119379044,
-0.012263323180377483,
-0.019552748650312424,
0.055362481623888016,
-0.043210651725530624,
0.05002783238887787,
-0.001141982153058052,
-0.0008887929725460708,
0.012921647168695927,
0.040998756885528564,
0.027092715725302696,
-0.00751493638381362,
-0.04210282117128372,
-0.027801262214779854,
0.0232403427362442,
0.04219638183712959,
0.016491785645484924,
0.01730324514210224,
0.009752655401825905,
0.006843403447419405,
0.022340500727295876,
-0.0023690168745815754,
0.01634332910180092,
-0.060724347829818726,
-0.022530484944581985,
-0.03052626922726631,
-0.05808437988162041,
0.030571317300200462,
-0.007969596423208714,
-0.0008008645381778479,
0.03728058561682701,
-0.01624937355518341,
0.04373474791646004,
0.010836027562618256,
0.008407363668084145,
-0.014430745504796505,
0.0712587833404541,
0.013152798637747765,
0.032324571162462234,
0.010135043412446976,
-0.02120405063033104,
0.1043223887681961,
0.06910651922225952,
-0.0028879004530608654,
-0.08959899842739105,
0.022686012089252472,
-0.03451079502701759,
0.03055427595973015,
-0.056489359587430954,
0.023586593568325043,
-0.012686452828347683,
-0.05004206672310829,
-0.008987287059426308,
0.07176832854747772,
-0.04114329069852829,
0.009135250933468342,
0.07185234874486923,
-0.00466805649921298,
-0.06837276369333267,
0.012568272650241852,
-0.007763633970171213,
-0.02776239439845085,
0.004965726286172867,
-0.013076618313789368,
0.00640435004606843,
-0.017710231244564056,
0.029410526156425476,
-0.014763803221285343,
-0.015962690114974976,
0.04079226404428482,
0.013629085384309292,
-0.08485019952058792,
0.0017645817715674639,
-0.020770268514752388,
-0.016665281727910042,
-0.0015659916680306196,
-0.012623787857592106,
0.045004840940237045,
0.0014641003217548132,
0.030162271112203598,
0.05140681192278862,
0.021412743255496025,
0.0037408280186355114,
0.009590468369424343,
-0.027090832591056824,
0.005242753308266401,
0.004466377664357424,
-0.011276401579380035,
0.09362978488206863,
-0.008161207661032677,
-0.0038518435321748257,
0.02162390574812889,
0.023023391142487526,
-0.0164022333920002,
-0.003331831656396389,
-0.006047483999282122,
0.015862274914979935,
0.017782172188162804,
-0.032873909920454025,
0.03362737223505974,
-0.006471333559602499,
0.04376160353422165,
0.0026783146895468235,
-0.007643114309757948,
0.0030377437360584736,
-0.006605527829378843,
-0.019931674003601074,
-0.0037093451246619225,
0.024691520258784294,
-0.02139904908835888,
-0.007736138068139553,
-0.01768118515610695,
-0.02265160158276558,
-0.03604401648044586,
-0.04037566855549812,
0.014327015727758408,
0.008324666880071163,
0.035020094364881516,
-0.004756275098770857,
0.003788106143474579,
-0.03890739381313324,
-0.0777677372097969,
0.014479090459644794,
-0.01514621451497078,
0.005717050284147263,
0.002327792579308152,
-0.009998750872910023,
0.03316430374979973,
0.0084990868344903,
-0.027097651734948158,
-0.02218928188085556,
0.002388664521276951,
0.023070257157087326,
0.012599700130522251,
-0.037365421652793884,
-0.04243460297584534,
-0.0014126001624390483,
-0.049674034118652344,
0.015243683010339737,
-0.02783224731683731,
-0.02689957432448864,
0.011419670656323433,
0.01384417712688446,
0.016637243330478668,
0.014648495241999626,
0.0017550039337947965,
0.022382240742444992,
0.022016046568751335,
0.0020587050821632147,
-0.009524641558527946,
0.029349304735660553,
0.01896332949399948,
-0.003984019625931978,
-0.03721568360924721,
-0.01949474774301052,
0.014101964421570301,
0.01881941221654415,
0.010461877100169659,
-0.0400700606405735,
0.012379557825624943,
0.0151693569496274,
-0.006979597266763449,
-0.003564860438928008,
-0.004831858444958925,
-0.05409916117787361,
0.015402616001665592,
0.00013382641191128641,
0.004488587379455566,
-0.016059940680861473,
0.016580186784267426,
-0.03793373703956604,
-0.02148708514869213,
0.02701171115040779,
0.03171771019697189,
-0.05275864899158478,
-0.011857462115585804,
0.01848268136382103,
-0.005730448756366968,
0.040932547301054,
-0.010064051486551762,
-0.0348285473883152,
0.028282782062888145,
-0.052001263946294785,
-0.035086553543806076,
0.0016043944051489234,
0.0004990745801478624,
0.05184376612305641,
0.04617033898830414,
-0.04549179971218109,
-0.04750217869877815,
0.04975586384534836,
-0.023958222940564156,
-0.009441854432225227,
-0.007801217492669821,
-0.0534653440117836,
-0.027035389095544815,
-0.006489946506917477,
-0.0005859289085492492,
-0.017619814723730087,
-0.024411892518401146,
-0.012400749139487743,
0.04273726046085358,
-0.01864936761558056,
-0.004767142701894045,
-0.00007204738358268514,
0.001612373162060976,
0.029470471665263176,
0.013759991154074669,
-0.03952370956540108,
0.01632894016802311,
0.04208812490105629,
-0.01722601056098938,
0.002627624198794365,
-0.0036782545503228903,
0.005497426725924015,
-0.11903419345617294,
-0.027976064011454582,
-0.034882623702287674,
0.03334325924515724,
0.06977885961532593,
-0.04473947361111641,
0.014246544800698757,
0.006255121435970068,
-0.04083217680454254,
-0.010007711127400398,
-0.042824018746614456,
0.005178516730666161,
-0.007949186488986015,
0.0019009070238098502,
0.0019008733797818422,
0.0364859402179718,
0.06258999556303024,
0.011877283453941345,
0.013346238061785698,
-0.012368487194180489,
-0.0003169743868056685,
-0.01200284156948328,
0.005712362006306648,
0.008526217192411423,
0.005824005231261253,
-0.020476708188652992,
0.057151805609464645,
-0.018646689131855965,
-0.0468180775642395,
0.010761440731585026,
0.015946773812174797,
-0.003576038870960474,
-0.02701071836054325,
0.027099914848804474,
-0.016711080446839333,
0.02858959138393402,
-0.0014757815515622497,
0.015629835426807404,
0.01083007175475359,
0.017373032867908478,
0.016635775566101074,
0.01357367541640997,
-0.03628569096326828,
0.00556866405531764,
0.010615660808980465,
-0.03293825313448906,
-0.023227356374263763,
0.07751414179801941,
-0.005236366298049688,
-0.034844592213630676,
-0.044559333473443985,
-0.015958568081259727,
0.02824116125702858,
-0.024814264848828316,
0.019249500706791878,
-0.03193274885416031,
-0.004558466840535402,
0.03773488849401474,
0.01672363467514515,
-0.011747680604457855,
0.05611540749669075,
0.012526363134384155,
-0.013980912044644356,
0.018675953149795532,
0.0014158508274704218,
0.013112417422235012,
-0.05275687947869301,
-0.038290321826934814,
-0.006099019665271044,
-0.002673627343028784,
-0.019174132496118546,
-0.025558579713106155,
-0.030914701521396637,
0.018965400755405426,
-0.00826764851808548,
0.04788697883486748,
-0.028778133913874626,
-0.0027160164900124073,
-0.015350895933806896,
-0.05204596742987633,
0.03493645414710045,
-0.001592625048942864,
-0.012107303366065025,
-0.01685340516269207,
-0.0029796746093779802,
-0.012214389629662037,
-0.01719091460108757,
0.022682292386889458,
-0.023847198113799095,
-0.012098148465156555,
-0.005717057269066572,
0.013390922918915749,
0.015849776566028595,
-0.003518402576446533,
-0.011344710364937782,
-0.015986129641532898,
-0.019787747412919998,
-0.009056334383785725,
0.010437327437102795,
0.004198608919978142,
0.04522824287414551,
0.00785874854773283,
0.01224382221698761,
0.02164924144744873,
0.017938079312443733,
-0.04547019675374031,
0.0675596073269844,
0.0013201021356508136,
0.02723911963403225,
0.06923026591539383,
-0.0012134903809055686,
0.025132574141025543,
0.039919327944517136,
-0.06423082202672958,
-0.033540647476911545,
0.032433073967695236,
-0.048945579677820206,
-0.01748049259185791,
-0.015914298593997955,
0.004508414771407843,
-0.04839790612459183,
-0.032455138862133026,
0.04814649745821953,
0.04059911146759987,
0.009585125371813774,
-0.00045470017357729375,
0.05125167965888977,
0.0341954343020916,
0.024493498727679253,
0.02086590602993965,
0.004947689361870289,
0.01481623575091362,
0.02877526544034481,
0.028925640508532524,
0.035580798983573914,
0.008943725377321243,
-0.003411484882235527,
0.037138693034648895,
0.02312619239091873,
-0.011396604590117931,
0.03257499635219574,
0.010494128800928593,
0.019195502623915672,
-0.021143263205885887,
-0.027500417083501816,
0.026511017233133316,
-0.023966535925865173,
0.02042536437511444,
-0.015744922682642937,
-0.01441031415015459,
0.08521542698144913,
-0.04550756886601448,
0.027097351849079132,
-0.007571069523692131,
-0.005740164779126644,
0.012772714719176292,
-0.006940530147403479,
0.012172084301710129,
0.06411520391702652,
-0.00973306130617857,
-0.02583206817507744,
0.005896726157516241,
-0.022083748131990433,
0.007870719768106937,
-0.055180199444293976,
0.007552729453891516,
0.003533418755978346,
0.0068867322988808155,
-0.02272825688123703,
-0.0094833355396986,
-0.03491712361574173,
-0.03843643516302109,
0.018840402364730835,
0.05929639935493469,
0.0303332582116127,
-0.006727670319378376,
0.003074119333177805,
-0.04305550828576088,
0.07696830481290817,
-0.05680845305323601,
0.01925358548760414,
-0.014244727790355682,
0.0014394046738743782,
-0.020428508520126343,
-0.009366946294903755
] |
<p>Today I was doing my physics homework and there was a problem involving a space ship falling at 9.8 m/(s^2) to simulate gravity, and it asked how long would it take for the ship to reach to speed of light, and I calculated it to be just under a year. So if it takes less than a year to go to the speed of light at 9.8m/(s^2) to reach the speed of light and proximus centari is one light year away even with the consequences of relativity (which I understand in the abstract) why does it not take about six years to get to alpha centari, and why will it take Voyager (travelling at a much faster acceleration) so long, especially in space where there is no friction?</p>
<p>Thank you.</p>
| 10,767 |
[
0.010758800432085991,
-0.043585434556007385,
-0.04614648595452309,
-0.01596376858651638,
0.03441251069307327,
0.005807018373161554,
-0.03603054955601692,
0.0003628304984886199,
-0.004638319835066795,
-0.02873431146144867,
0.004312661476433277,
0.07222842425107956,
0.06352883577346802,
0.02665242925286293,
0.00877511128783226,
0.011461621150374413,
-0.0196862630546093,
-0.014210466295480728,
-0.01955094002187252,
-0.04752800613641739,
0.033622149378061295,
-0.007708013989031315,
-0.007422575261443853,
-0.002870704047381878,
-0.039272941648960114,
0.00639135017991066,
0.019137077033519745,
-0.002998366253450513,
0.007042329758405685,
0.024079617112874985,
0.006998669356107712,
-0.0076211607083678246,
0.010591531172394753,
0.037793830037117004,
0.018194135278463364,
0.004220978356897831,
-0.03179604187607765,
-0.01908116042613983,
-0.0043406435288488865,
0.016649378463625908,
-0.022806018590927124,
-0.009109456092119217,
-0.014032985083758831,
0.06930850446224213,
0.0010498681804165244,
0.012306669726967812,
0.04458099976181984,
-0.003983011469244957,
0.05715060979127884,
-0.032892804592847824,
0.03770749643445015,
-0.02208840474486351,
0.060911037027835846,
-0.001744434586726129,
0.0013807271607220173,
-0.02238549292087555,
0.07166152447462082,
0.09877239912748337,
-0.008901462890207767,
-0.011196979321539402,
0.0008320723427459598,
0.022591372951865196,
-0.03274499252438545,
-0.00398694071918726,
0.00269572576507926,
0.02163022756576538,
-0.041829802095890045,
-0.007848870009183884,
0.03610618785023689,
0.00525605259463191,
0.020334992557764053,
0.0088649308308959,
0.027232641354203224,
-0.0062484219670295715,
-0.010458570905029774,
-0.0529550276696682,
0.011269996874034405,
0.01433849148452282,
0.028843535110354424,
0.03190833702683449,
-0.005938923452049494,
0.018048126250505447,
0.055840447545051575,
0.026103906333446503,
0.009268325753509998,
-0.018425609916448593,
0.031387921422719955,
-0.02136552892625332,
-0.006785350851714611,
0.036135267466306686,
-0.013278525322675705,
0.04426541551947594,
-0.0005339568597264588,
0.03388921543955803,
0.009347930550575256,
0.032207001000642776,
-0.0027615034487098455,
0.043528683483600616,
0.005589613225311041,
-0.025764668360352516,
0.01562606915831566,
-0.02092370204627514,
0.017372548580169678,
0.014726086519658566,
0.01908963918685913,
-0.012763733975589275,
-0.06385171413421631,
0.0058381822891533375,
-0.051258452236652374,
-0.019125770777463913,
-0.004739454481750727,
0.0015765733551234007,
0.02903827652335167,
0.001858755829744041,
0.025007452815771103,
-0.03540439531207085,
-0.009848617017269135,
-0.010409894399344921,
0.05493013560771942,
0.029488129541277885,
0.010796811431646347,
-0.02084658108651638,
0.03299236670136452,
-0.012294984422624111,
-0.045346472412347794,
0.026994843035936356,
0.0005858955555595458,
-0.03780074417591095,
-0.008568414486944675,
-0.021642493084073067,
0.02225765772163868,
-0.03398680314421654,
0.013134852983057499,
-0.01866396702826023,
0.02867083251476288,
0.013350360095500946,
-0.10026494413614273,
-0.10198213160037994,
0.03678346425294876,
0.007038585375994444,
0.011521250009536743,
-0.07828398793935776,
0.03785893693566322,
0.011189652606844902,
0.07424136251211166,
-0.012478250078856945,
0.011346103623509407,
-0.004080051090568304,
0.028861094266176224,
0.024991577491164207,
-0.025259695947170258,
-0.0005075745284557343,
-0.017560767009854317,
-0.04458983987569809,
0.02165534906089306,
-0.0949295312166214,
0.00950369518250227,
0.010807712562382221,
0.009023529477417469,
-0.036147382110357285,
0.05637093633413315,
-0.023241624236106873,
-0.0028183660469949245,
-0.0008724037907086313,
0.0020856717601418495,
-0.029143022373318672,
0.10322379320859909,
0.05170362442731857,
0.01673111505806446,
0.05552007630467415,
0.02653108909726143,
0.043648622930049896,
-0.016864070668816566,
0.01903189718723297,
0.052698563784360886,
-0.04782054200768471,
-0.0009697411442175508,
0.002336577046662569,
-0.01492099929600954,
-0.003548952052369714,
-0.019464947283267975,
-0.04478330910205841,
-0.012234048917889595,
0.011087645776569843,
0.023910412564873695,
0.06288441270589828,
-0.0026817522011697292,
0.013470103964209557,
-0.008227799087762833,
-0.018262963742017746,
-0.015882529318332672,
-0.054894447326660156,
0.024372193962335587,
0.025658106431365013,
0.0034535021986812353,
0.018625596538186073,
-0.004965540487319231,
0.02313530072569847,
-0.0331442654132843,
-0.025368154048919678,
-0.006305735558271408,
0.018668221309781075,
0.014014300890266895,
-0.03598899766802788,
0.02823837287724018,
0.06771456450223923,
0.07115251570940018,
-0.008713774383068085,
0.007051599211990833,
-0.007492102682590485,
-0.007600803859531879,
0.037519097328186035,
-0.0018251790897920728,
0.006212467793375254,
-0.01505398377776146,
0.014555311761796474,
0.0223983321338892,
-0.012518548406660557,
-0.008099920116364956,
0.03787645697593689,
-0.004757723771035671,
0.09534897655248642,
0.02447795867919922,
-0.008387050591409206,
0.016005413606762886,
0.0179998017847538,
-0.022603197023272514,
0.009449416771531105,
0.007418176159262657,
-0.018079610541462898,
-0.01966177113354206,
-0.002038924489170313,
0.020479779690504074,
0.01940598525106907,
-0.030494412407279015,
-0.0020138719119131565,
0.04192741587758064,
0.03549261763691902,
0.02937224693596363,
0.018802460283041,
-0.018633585423231125,
-0.0003785377193707973,
0.012766549363732338,
0.011538906954228878,
-0.005070679821074009,
0.0013246395392343402,
0.03899272531270981,
0.01551857776939869,
-0.013731176033616066,
-0.03768257051706314,
-0.024375567212700844,
0.04897467792034149,
0.013340223580598831,
0.021941324695944786,
0.00726608419790864,
-0.024782205000519753,
0.07199867814779282,
-0.04136275127530098,
0.009531891904771328,
0.0512421540915966,
0.01101381704211235,
0.028637854382395744,
-0.043804991990327835,
0.005497064907103777,
0.027091756463050842,
0.01109572034329176,
-0.01513539906591177,
-0.026758626103401184,
0.030029207468032837,
-0.015429383143782616,
0.023866262286901474,
-0.029930049553513527,
-0.0060350471176207066,
-0.0024940473958849907,
0.007543337065726519,
0.04718856140971184,
0.0030717761255800724,
0.032717231661081314,
0.009970170445740223,
-0.028461424633860588,
0.011111080646514893,
-0.033033717423677444,
-0.008815568871796131,
0.008413609117269516,
-0.04416680708527565,
0.02203916572034359,
-0.014082802459597588,
-0.049164049327373505,
0.05047784000635147,
-0.009350097738206387,
0.006156763527542353,
0.018454233184456825,
-0.019850697368383408,
-0.07347927242517471,
-0.023323925212025642,
-0.03116767853498459,
-0.0321173332631588,
-0.011598530225455761,
0.03185552731156349,
0.036810874938964844,
-0.005384259391576052,
-0.03139377757906914,
0.05254669114947319,
-0.07536277174949646,
-0.020189806818962097,
-0.017921052873134613,
-0.006045189686119556,
0.023606834933161736,
-0.058365799486637115,
0.013227447867393494,
-0.003805991029366851,
-0.04234388470649719,
0.017126690596342087,
-0.0234957467764616,
-0.029316693544387817,
0.011429360136389732,
0.001775554963387549,
0.06023091822862625,
-0.0025619466323405504,
-0.02151281014084816,
0.04844379425048828,
0.03275167942047119,
-0.00015818674000911415,
-0.06389570236206055,
0.01706976816058159,
-0.028398996219038963,
0.00850713811814785,
0.006651632022112608,
0.03276192769408226,
-0.021188270300626755,
-0.00019097203039564192,
-0.012757456861436367,
0.01691739447414875,
0.043289732187986374,
-0.017714593559503555,
0.0009638459305278957,
-0.019378477707505226,
-0.004147032741457224,
0.00033220258774235845,
-0.0015150179388001561,
0.034654401242733,
-0.034436002373695374,
0.0202386025339365,
0.001344451680779457,
0.041693467646837234,
0.0038969824090600014,
-0.04519631713628769,
0.04545154795050621,
-0.008390752598643303,
0.03333238884806633,
-0.016746366396546364,
-0.006587091833353043,
-0.010488352738320827,
0.003030954161658883,
0.012673311866819859,
0.00791175477206707,
0.006604728288948536,
-0.008015094324946404,
-0.016906721517443657,
-0.000052107468945905566,
0.016073517501354218,
-0.0023663591127842665,
-0.022961007431149483,
-0.027464577928185463,
-0.012037470936775208,
0.008653193712234497,
-0.07303600013256073,
0.0024607982486486435,
0.057306140661239624,
0.023323459550738335,
0.04075229540467262,
-0.009963060729205608,
-0.048518940806388855,
0.0050980509258806705,
-0.05409771576523781,
-0.020114336162805557,
0.003657807130366564,
0.04640363156795502,
-0.020303349941968918,
0.033706724643707275,
0.020743606612086296,
0.014727964997291565,
0.02000129036605358,
-0.0005443934351205826,
-0.07811731845140457,
0.023872891440987587,
-0.06644336134195328,
-0.058107104152441025,
0.03516731783747673,
0.0033517649862915277,
-0.04841800406575203,
-0.03418184071779251,
-0.0061075626872479916,
0.003632559673860669,
-0.008966969326138496,
-0.06252171844244003,
0.017252303659915924,
-0.03719550371170044,
-0.007019248325377703,
-0.03900178521871567,
-0.017835643142461777,
0.025420943275094032,
-0.006140964571386576,
0.019665200263261795,
0.04403466731309891,
-0.03993311896920204,
-0.022964781150221825,
0.0025547107215970755,
-0.02540787123143673,
0.05493069067597389,
0.024088069796562195,
0.032529786229133606,
0.005116347223520279,
-0.046373698860406876,
-0.015071667730808258,
0.03302386403083801,
0.01053557638078928,
0.03964022547006607,
-0.02587530016899109,
-0.04839979484677315,
-0.04325602948665619,
-0.030308542773127556,
0.024624045938253403,
0.03142741695046425,
0.020587487146258354,
0.02040671557188034,
-0.003704338101670146,
0.008097851648926735,
-0.0023178057745099068,
0.005319361574947834,
0.06015792861580849,
-0.014722228981554508,
-0.006769050378352404,
-0.018439074978232384,
-0.031048959121108055,
-0.05950412526726723,
-0.03571073338389397,
0.008762631565332413,
-0.002765117911621928,
-0.03574651479721069,
-0.002137916162610054,
-0.002252759877592325,
-0.019839907065033913,
-0.011781119741499424,
0.007861276157200336,
-0.005057996138930321,
-0.007761583663523197,
0.02671268954873085,
-0.011680183000862598,
-0.0072291637770831585,
0.027642082422971725,
0.0588437020778656,
-0.016287727281451225,
0.01965470239520073,
-0.05331147089600563,
-0.00019879559113178402,
0.02175193652510643,
0.07375497370958328,
-0.02064261958003044,
-0.00383569672703743,
-0.08448899537324905,
-0.028721408918499947,
0.03724193200469017,
-0.03336483612656593,
0.025613470003008842,
-0.009150899946689606,
-0.0017328269314020872,
-0.008520753122866154,
-0.04061949625611305,
-0.02873247303068638,
0.029199276119470596,
-0.005613315850496292,
0.0016565186670050025,
-0.013835289515554905,
0.016002271324396133,
0.019238626584410667,
-0.018880795687437057,
0.06790231913328171,
0.05183568224310875,
0.010396157391369343,
0.007080815266817808,
0.0023197787813842297,
0.0014042271068319678,
-0.047660257667303085,
-0.049097977578639984,
-0.005097947549074888,
-0.011839780025184155,
-0.036380209028720856,
0.003907401114702225,
-0.040093984454870224,
-0.055982865393161774,
0.03708445653319359,
0.029395177960395813,
-0.01008959487080574,
-0.017664900049567223,
-0.004220193717628717,
0.015328440815210342,
0.051967281848192215,
0.0026084682904183865,
0.05408551171422005,
0.029453588649630547,
-0.008402413688600063,
-0.010707441717386246,
-0.03428030014038086,
0.012622041627764702,
-0.00818929634988308,
-0.016393952071666718,
-0.009538001380860806,
-0.017852220684289932,
0.0029743886552751064,
0.0591043084859848,
-0.03988177701830864,
-0.026835056021809578,
-0.012298071756958961,
-0.003739716252312064,
0.013064762577414513,
0.028316283598542213,
0.026481179520487785,
0.00944952480494976,
-0.01287439651787281,
0.0022109788842499256,
-0.004948403220623732,
-0.02313959412276745,
0.02842370979487896,
0.032106779515743256,
-0.034903958439826965,
0.018696459010243416,
-0.005970016587525606,
-0.024396611377596855,
0.0021202932111918926,
-0.02201763167977333,
0.021704139187932014,
-0.035056035965681076,
0.04129605367779732,
-0.02832949161529541,
-0.007515348959714174,
0.050534334033727646,
-0.06298036128282547,
-0.032110124826431274,
-0.03560059890151024,
-0.015276270918548107,
0.06498459726572037,
-0.05774547532200813,
-0.0018385756993666291,
0.018998848274350166,
0.003771008225157857,
-0.07667069137096405,
-0.050715122371912,
0.044541530311107635,
0.016429433599114418,
-0.00948287919163704,
-0.01255002710968256,
0.0005250117974355817,
-0.03908697888255119,
-0.022179942578077316,
-0.02841758541762829,
0.06462176889181137,
0.0020709687378257513,
-0.011996148154139519,
-0.014299600385129452,
0.011639193631708622,
0.04002190753817558,
-0.006341324187815189,
0.0021193113643676043,
0.03238369897007942,
-0.014476891607046127,
-0.004690379370003939,
-0.04790354520082474,
0.10145062208175659,
-0.026741359382867813,
-0.06966012716293335,
-0.026011036708950996,
-0.02375061623752117,
0.014054840430617332,
-0.038818083703517914,
0.019980670884251595,
0.04544339329004288,
0.014261399395763874,
-0.0069726440124213696,
0.02711457945406437,
0.043186068534851074,
-0.004770930856466293,
0.014857105910778046,
0.006961641367524862,
-0.015707284212112427,
0.0016032649436965585,
-0.008581598289310932,
0.050043199211359024,
-0.004877927713096142,
0.04064818099141121,
-0.020877763628959656,
0.02162816748023033,
-0.027476778253912926,
-0.01943068951368332,
0.030367013067007065,
0.03051024116575718,
-0.03475586697459221,
-0.02489250712096691,
-0.02309015579521656,
0.00517417024821043,
-0.0431089885532856,
-0.03902484476566315,
-0.0025167022831737995,
0.005120004061609507,
0.0013280240818858147,
0.0689195990562439,
-0.020460011437535286,
0.02535880357027054,
-0.01968645304441452,
-0.0045722732320427895,
-0.030667347833514214,
-0.02618574909865856,
-0.062035754323005676,
-0.0029632742516696453,
0.02352851815521717,
0.02417956106364727,
-0.005473290104418993,
-0.047309622168540955,
0.039269786328077316,
0.04618718847632408,
-0.0020269567612558603,
0.008604736998677254,
0.03332982957363129,
0.014626295305788517,
0.00444069504737854,
0.007751613389700651,
-0.04115903005003929,
0.01511619333177805,
-0.011979222297668457,
0.05342963710427284,
0.01238359697163105,
0.012464513070881367,
0.03572586551308632,
-0.008152504451572895,
0.0103021040558815,
-0.060868535190820694,
-0.016558874398469925,
-0.029464494436979294,
-0.015353329479694366,
0.034241605550050735,
0.01749815233051777,
-0.008850912563502789,
0.0062395622953772545,
0.02452125772833824,
0.03301608934998512,
0.03530850633978844,
-0.007282718550413847,
-0.04320567473769188,
-0.040017470717430115,
-0.043869972229003906,
-0.028590839356184006,
0.06596522778272629,
0.025045981630682945,
-0.03995242342352867,
-0.03625555709004402,
-0.016220517456531525,
0.00919104740023613,
-0.0002635100681800395,
0.041330017149448395,
0.0036612160038203,
0.10896365344524384,
0.015261463820934296,
0.01341693289577961,
-0.05231301859021187,
-0.0027444581501185894,
0.08533156663179398,
0.027263980358839035,
-0.028355013579130173,
-0.021965699270367622,
0.04112499952316284,
-0.03507409244775772,
0.03132576867938042,
-0.04851480573415756,
0.03919770196080208,
0.0015955204144120216,
-0.0074433800764381886,
0.04040534049272537,
0.03264777362346649,
-0.021058978512883186,
-0.001692192628979683,
0.03787818178534508,
-0.042669061571359634,
-0.014255684800446033,
-0.02947651781141758,
0.008965972810983658,
-0.0063443672843277454,
0.030765455216169357,
0.0019754415843635798,
0.015793874859809875,
-0.026907149702310562,
0.006186682730913162,
-0.005731138866394758,
-0.017020994797348976,
0.017321037128567696,
0.015983806923031807,
-0.07821599394083023,
0.009419616311788559,
0.03549438342452049,
-0.04021257162094116,
-0.05188758298754692,
0.03057774342596531,
0.013367576524615288,
-0.030985860154032707,
0.026885339990258217,
-0.0041349828243255615,
-0.022283410653471947,
0.022854166105389595,
0.0076361107639968395,
-0.0121038518846035,
-0.03634658455848694,
0.03964884206652641,
-0.03961065411567688,
0.07913791388273239,
-0.014448877424001694,
-0.016131585463881493,
0.020610813051462173,
0.009167348966002464,
-0.01015026681125164,
-0.05600353330373764,
-0.03275458142161369,
-0.006952193100005388,
-0.013818382285535336,
0.02183406427502632,
-0.009979011490941048,
-0.0035919148940593004,
0.018473826348781586,
-0.009725900366902351,
0.03460445627570152,
-0.022420592606067657,
0.021807368844747543,
0.021409327164292336,
-0.02365943416953087,
-0.008077346719801426,
-0.05255185440182686,
-0.01908188872039318,
-0.00992592517286539,
0.008609326556324959,
-0.05194816738367081,
0.012451034039258957,
0.019604304805397987,
0.03140166774392128,
0.01350579783320427,
-0.020632026717066765,
-0.02678649127483368,
-0.04343139007687569,
-0.00720797386020422,
0.030401436612010002,
0.005787461064755917,
-0.02990388125181198,
-0.03168876841664314,
-0.0005297945463098586,
0.05097660422325134,
0.03408535569906235,
-0.05058332532644272,
0.003197535639628768,
-0.05526956170797348,
0.03231101483106613,
0.03348635882139206,
-0.022700535133481026,
0.012018708512187004,
-0.0037362640723586082,
0.003955288790166378,
-0.0018821656703948975,
-0.022866753861308098,
0.03887392580509186,
0.030211191624403,
-0.004596542567014694,
-0.013984940014779568,
0.02243877947330475,
-0.005527051165699959,
0.033033039420843124,
0.020240221172571182,
-0.010274609550833702,
-0.021999714896082878,
-0.0011033931514248252,
0.032399293035268784,
-0.01836794801056385,
-0.026821324601769447,
-0.023652777075767517,
-0.013208648189902306,
0.010946575552225113,
0.0070764366537332535,
-0.010459054261446,
0.06386245042085648,
-0.027148865163326263,
0.019279491156339645,
-0.07856468111276627,
0.03253309801220894,
-0.042783644050359726,
0.0640307366847992,
-0.015562216751277447,
-0.008580061607062817,
-0.011130833998322487,
0.03234901651740074,
-0.037194911390542984,
-0.026994967833161354,
0.01745743304491043,
0.0176975280046463,
0.025734800845384598,
-0.01549308281391859,
0.009246475994586945,
-0.0014310277765616775,
0.046109169721603394,
-0.043428149074316025,
-0.011601819656789303,
0.019636245444417,
-0.05420321226119995,
-0.07863765209913254,
0.04136386886239052,
-0.006707903929054737,
0.027979625388979912,
0.018849704414606094,
-0.013195307925343513,
-0.021124912425875664,
0.08596736192703247,
-0.04877285659313202,
-0.025809606537222862,
0.0022972652222961187,
-0.006651048082858324,
-0.01868145354092121,
0.004288957919925451,
-0.0021976749412715435,
-0.04459141194820404,
0.006037103943526745,
0.03402714803814888,
0.013298857025802135,
-0.03409472852945328,
0.03841078653931618,
-0.05160612612962723,
0.007051476743072271,
-0.020515937358140945,
0.05160526558756828,
0.008289895951747894,
0.036743927747011185,
0.062192730605602264,
-0.03223070874810219,
0.06355607509613037,
0.029590245336294174,
-0.010800972580909729,
-0.07937436550855637,
0.017445024102926254,
-0.01133382972329855,
0.02092907391488552,
0.05597499758005142,
-0.060961853712797165,
0.023982707411050797,
0.037928398698568344,
-0.03861859068274498,
0.024038521572947502,
-0.03913310542702675,
-0.0332442969083786,
-0.013527538627386093,
-0.0016499474877491593,
0.020717017352581024,
0.048151563853025436,
0.044467050582170486,
-0.0062220958061516285,
0.02134677581489086,
0.01684727519750595,
-0.019847802817821503,
-0.04346821457147598,
0.0037673551123589277,
0.059630073606967926,
-0.026742881163954735,
0.01982356235384941,
0.03858926147222519,
-0.005180415231734514,
0.007763464003801346,
0.03003634698688984,
-0.0015954624395817518,
0.039123959839344025,
0.014188183471560478,
0.007843627594411373,
-0.002526454161852598,
-0.006422940641641617,
0.026261502876877785,
-0.02695181407034397,
-0.02016574516892433,
0.05155138671398163,
0.014221674762666225,
0.006114426534622908,
0.006472778972238302,
0.008510549552738667,
0.014492811635136604,
-0.02022673189640045,
-0.028167428448796272,
0.023681316524744034,
0.007687869016081095,
0.021701276302337646,
0.049741022288799286,
0.007082429248839617,
0.016646865755319595,
-0.04018022492527962,
-0.028004568070173264,
-0.050444480031728745,
-0.0013647211017087102,
0.012379176914691925,
-0.0071173463948071,
-0.01744329370558262,
-0.023461880162358284,
-0.015172083862125874,
-0.0073705934919416904,
-0.01251451950520277,
-0.005745994858443737,
0.027585480362176895,
-0.0372534915804863,
-0.014938502572476864,
-0.011028682813048363,
-0.027744930237531662,
0.016710858792066574,
-0.015254938043653965,
-0.03382306173443794,
0.03711191937327385,
0.022044489160180092,
0.02217218466103077,
0.0028006848879158497,
0.014606903307139874,
-0.021595992147922516,
-0.06824111938476562,
0.060435064136981964,
-0.020449552685022354,
-0.015993086621165276,
-0.036391694098711014,
-0.024516696110367775,
-0.04485009238123894,
0.008778819814324379,
0.05467098206281662,
-0.02250593714416027,
-0.009310168214142323,
-0.002423048485070467,
-0.03307071700692177,
-0.0020515003707259893,
-0.05800704285502434,
0.013922175392508507,
0.0005154654500074685,
-0.053562890738248825,
-0.020592568442225456,
-0.014320890419185162,
-0.004562885966151953,
-0.031352363526821136,
-0.002927422523498535,
-0.008375344797968864,
0.04721247777342796,
0.04472079873085022,
-0.042636845260858536,
0.04487426206469536,
0.026957901194691658,
0.007791032548993826,
0.06805223971605301,
-0.007707398850470781,
0.039562903344631195,
0.04699665307998657,
-0.004735088907182217,
-0.027433980256319046,
0.030489115044474602,
-0.029047571122646332,
-0.016264820471405983,
-0.007428937591612339,
-0.008908235467970371,
0.008857888169586658,
-0.06778719276189804,
0.024408405646681786,
0.049310747534036636,
-0.025222335010766983,
0.008322572335600853,
0.052430521696805954,
0.010197021067142487,
0.038181278854608536,
-0.020347515121102333,
0.03294368460774422,
0.023799410089850426,
0.009905717335641384,
-0.010276265442371368,
0.0019229351310059428,
0.023511435836553574,
0.008139516226947308,
0.05342043191194534,
0.07165051996707916,
0.011657284572720528,
0.019281014800071716,
-0.0079257907345891,
0.051556702703237534,
-0.035101741552352905,
-0.0221653264015913,
-0.031918589025735855,
-0.030086491256952286,
0.0017279915045946836,
0.035430654883384705,
-0.005509538110345602,
0.08270740509033203,
-0.06592127680778503,
0.035403743386268616,
0.0429726243019104,
-0.01471152063459158,
-0.03544960543513298,
-0.0005766844842582941,
-0.005425732582807541,
0.02174588479101658,
0.0013987899292260408,
-0.010418593883514404,
-0.0003908298967871815,
0.01172691211104393,
0.055232539772987366,
0.009651359170675278,
0.018298210576176643,
-0.010015331208705902,
-0.045913342386484146,
-0.008087442256510258,
0.010161629877984524,
0.009157720021903515,
-0.01849830523133278,
0.02236209250986576,
0.0329744927585125,
0.002018038649111986,
0.0004143438709434122,
0.0050125084817409515,
0.009955788031220436,
0.0605376772582531,
-0.0671391412615776,
-0.021646136417984962,
-0.03334953635931015,
0.003881472395732999,
-0.03560794144868851,
-0.007574707269668579
] |
<p>Let me preface this by saying that I have a very limited knowledge of optics -- basically, I know enough to be dangerous. So I have a square Fresnel lens that measures about 10.5 inches on a side. The focal length is about 11.5 inches. I'm trying to find a presumably-smaller glass collimating lens that will take the light from the Fresnel lens and convert it to a beam with an indefinite focal length (or at least, a focal length of a few feet). I don't care about image preservation, I just mainly want to transfer some focused light from point A to point B with a minimum of loss. I basically need to know what kind of lens to buy and where to place it. I've tried single and double convex and concave lenses and seemed to have the most luck with single convex, but wasn't able to get much of a beam past a couple of inches out. The attached picture shows kind of what I am looking for (lens on left represents Fresnel lens, lens on right represents collimating lens).</p>
<p>Any help you could give me with this would be great. </p>
<p><img src="http://i.stack.imgur.com/fWk1M.png" alt="enter image description here"></p>
| 10,768 |
[
-0.03881466016173363,
-0.0242746751755476,
-0.0023356578312814236,
-0.029327427968382835,
0.0532003752887249,
0.004528686869889498,
-0.03229379281401634,
-0.04076525568962097,
-0.01324408408254385,
-0.03038106858730316,
0.05460932478308678,
0.07589207589626312,
0.04806051775813103,
0.027637461200356483,
0.03014525957405567,
-0.0010489124106243253,
-0.01588975265622139,
-0.01278683077543974,
-0.048535313457250595,
-0.04522237181663513,
-0.010776590555906296,
0.005014576483517885,
-0.009560243226587772,
0.032165054231882095,
-0.030255910009145737,
0.026416294276714325,
0.018058866262435913,
-0.0018594908760860562,
0.0012792741181328893,
0.062813900411129,
-0.01667735166847706,
-0.03447651118040085,
0.0022185142152011395,
0.03263559192419052,
-0.012698705308139324,
-0.007665212266147137,
-0.015897048637270927,
-0.012561921030282974,
-0.02009928971529007,
-0.0028650432359427214,
-0.016983849927783012,
-0.009041029959917068,
-0.003930998034775257,
0.059852126985788345,
-0.02064555138349533,
-0.014425995759665966,
-0.02200290746986866,
-0.03812217339873314,
0.03038998506963253,
-0.0868639275431633,
0.051436085253953934,
0.01636560447514057,
0.07667865604162216,
0.030110985040664673,
-0.023666467517614365,
0.0021000956185162067,
0.06411531567573547,
0.07402592152357101,
-0.028662344440817833,
-0.0517914779484272,
-0.030849460512399673,
-0.004143441561609507,
-0.036931362003088,
-0.022266030311584473,
-0.020844966173171997,
-0.03210601955652237,
-0.019702710211277008,
-0.0057152011431753635,
0.01065243873745203,
-0.021949099376797676,
0.028316913172602654,
0.05021374672651291,
0.07263117283582687,
-0.008443106897175312,
-0.006207247730344534,
-0.032438185065984726,
0.0034514006692916155,
0.030547112226486206,
0.06516401469707489,
0.03447683900594711,
0.005673127248883247,
0.03263131529092789,
0.008757720701396465,
0.01586180180311203,
0.008778643794357777,
-0.016440358012914658,
0.07176092267036438,
-0.002998991869390011,
-0.011671383865177631,
0.022717872634530067,
-0.029441123828291893,
0.009755812585353851,
0.04210123419761658,
0.03426980972290039,
-0.019446413964033127,
0.0187559574842453,
-0.019962113350629807,
0.0537329763174057,
0.017975429072976112,
-0.03745242580771446,
0.03571363538503647,
-0.006983242463320494,
-0.026913875713944435,
0.06394429504871368,
0.011958453804254532,
-0.016565954312682152,
0.009292146191000938,
0.010902524925768375,
0.017596619203686714,
0.02128688432276249,
-0.0452413447201252,
0.023535996675491333,
0.008439190685749054,
0.03635789453983307,
0.0339396670460701,
-0.03329641371965408,
-0.02671913243830204,
0.007083789445459843,
0.051122698932886124,
0.07755543291568756,
0.06514593958854675,
-0.006539073307067156,
0.03375748172402382,
-0.04164961725473404,
-0.05725758522748947,
0.01999017596244812,
0.006443821359425783,
0.005308513529598713,
-0.003952514845877886,
0.018320458009839058,
0.04306148365139961,
0.02004941925406456,
0.02806800603866577,
-0.047446705400943756,
-0.005564916413277388,
-0.03318573534488678,
-0.054390404373407364,
-0.06084360554814339,
0.03429384157061577,
0.046436917036771774,
-0.0021770677994936705,
-0.07609338313341141,
0.004123358055949211,
0.025140460580587387,
0.06286609917879105,
0.0217987559735775,
0.005634763743728399,
-0.016516515985131264,
0.036262959241867065,
-0.05015484616160393,
-0.019214216619729996,
0.02981163188815117,
-0.0019633143674582243,
0.018581513315439224,
0.01791602000594139,
-0.04264036938548088,
0.02190423384308815,
0.05851561948657036,
0.019261589273810387,
-0.04419883340597153,
0.051354069262742996,
0.016730407252907753,
-0.005312848836183548,
0.005154246464371681,
-0.0000011098534287157236,
-0.040279172360897064,
0.06757035851478577,
0.02635250613093376,
-0.03361149877309799,
0.022742323577404022,
-0.009801897220313549,
0.027238141745328903,
0.023196684196591377,
-0.020748881623148918,
0.05695607140660286,
-0.012174369767308235,
0.004917140118777752,
-0.0030163417104631662,
0.0028713992796838284,
0.04887767508625984,
0.004845676943659782,
-0.02355552837252617,
-0.021024473011493683,
0.006511265411973,
0.013824938796460629,
0.08219540119171143,
-0.010610551573336124,
-0.029442939907312393,
0.005130998324602842,
-0.03730153292417526,
-0.0250916238874197,
-0.014172807335853577,
-0.009245587512850761,
0.010724341496825218,
0.010312632657587528,
0.010678780265152454,
0.01027046050876379,
0.033200062811374664,
0.014864991419017315,
-0.02701455168426037,
-0.011115551926195621,
0.0030583797488361597,
0.037319082766771317,
0.017996490001678467,
0.0487964004278183,
0.0657106563448906,
0.053682900965213776,
0.013426678255200386,
-0.012998879887163639,
-0.027674777433276176,
0.026631193235516548,
-0.006643699016422033,
-0.020379826426506042,
-0.0036838373634964228,
0.0058711920864880085,
0.021004632115364075,
-0.014576424844563007,
0.03371632844209671,
0.013615541160106659,
-0.0004068049311172217,
-0.006091082468628883,
0.04099743068218231,
0.03675008937716484,
-0.005623971112072468,
-0.0008800597861409187,
0.011828293092548847,
0.023937754333019257,
0.03781096264719963,
0.0004039230407215655,
-0.03730252757668495,
-0.055998966097831726,
0.03679012134671211,
0.00887359119951725,
0.007267097011208534,
-0.04806627333164215,
0.005536423530429602,
0.02026498317718506,
0.01111533585935831,
0.04328656941652298,
0.06275415420532227,
-0.04591650143265724,
-0.010864264331758022,
-0.028247402980923653,
0.01021197997033596,
-0.018644513562321663,
0.028647959232330322,
0.0035425513051450253,
0.011365929618477821,
0.026318034157156944,
-0.02864934876561165,
-0.027732115238904953,
0.008063288405537605,
-0.004928090609610081,
-0.004647295456379652,
-0.00910679716616869,
0.004619651008397341,
0.04546739161014557,
-0.025909340009093285,
0.004493887536227703,
0.03220897167921066,
-0.0046598115004599094,
0.010165889747440815,
-0.03537699952721596,
-0.02776714414358139,
0.021762417629361153,
0.03942674398422241,
0.012461302801966667,
0.009276882745325565,
0.002000800333917141,
-0.0488395020365715,
0.01792355626821518,
-0.03998963534832001,
0.019544200971722603,
-0.03213487192988396,
0.0067779854871332645,
0.000287258269963786,
0.04221540689468384,
0.005860055796802044,
-0.04304550588130951,
-0.05046042054891586,
-0.0009533900301903486,
-0.07208365201950073,
-0.008239966817200184,
-0.006059100851416588,
-0.02875625714659691,
-0.010015079751610756,
-0.01796133443713188,
-0.010768366977572441,
0.058639928698539734,
0.01553911529481411,
0.015667589381337166,
-0.002224019495770335,
0.022275490686297417,
-0.06041796877980232,
-0.007920138537883759,
-0.00693243695423007,
0.013077466748654842,
-0.011863554827868938,
0.007644319906830788,
0.014068959280848503,
0.021466175094246864,
-0.05785198137164116,
0.0010040109045803547,
-0.08400338888168335,
0.005143331363797188,
-0.01738888770341873,
0.015555529855191708,
-0.011499308049678802,
-0.04410255327820778,
0.015351944603025913,
-0.012248980812728405,
-0.017805157229304314,
0.05902983620762825,
-0.04167959839105606,
-0.04375150427222252,
0.013008173555135727,
0.03433792293071747,
-0.009106628596782684,
-0.004498215392231941,
-0.006823444273322821,
0.06862030178308487,
0.031138353049755096,
-0.036637790501117706,
-0.05414367839694023,
0.016986798495054245,
0.002181771444156766,
-0.0024142886977642775,
-0.001554783433675766,
0.019616609439253807,
-0.013684278354048729,
0.0477764867246151,
-0.013156579807400703,
0.005937758833169937,
0.040939684957265854,
0.04052942991256714,
-0.010634643025696278,
0.008761107921600342,
0.002515824744477868,
-0.013222129084169865,
0.034847699105739594,
0.017127547413110733,
-0.060193322598934174,
0.032846592366695404,
-0.02296084724366665,
0.02070634625852108,
0.0161361712962389,
-0.03909387066960335,
-0.010304044000804424,
0.004249934572726488,
-0.011323712766170502,
0.007386000361293554,
-0.006668526213616133,
0.017104262486100197,
-0.0018737968057394028,
0.008040009997785091,
0.010287626646459103,
0.06905527412891388,
-0.023135092109441757,
-0.011014287360012531,
0.010396403260529041,
0.03497207164764404,
0.01315101608633995,
-0.028673894703388214,
-0.013178586959838867,
0.01613200642168522,
0.005081864073872566,
0.037539299577474594,
-0.026839686557650566,
0.046600956469774246,
0.045320238918066025,
0.030000878497958183,
-0.005905314348638058,
0.004510539583861828,
0.02670728601515293,
-0.03053184226155281,
-0.0001499299833085388,
-0.03438646346330643,
0.044282060116529465,
0.031797509640455246,
0.030843514949083328,
0.06603576987981796,
0.0166865736246109,
0.02920030802488327,
0.018121855333447456,
-0.09000338613986969,
0.04140632972121239,
-0.0074775549583137035,
-0.013440189883112907,
-0.02444867417216301,
0.010060975328087807,
-0.05736099183559418,
-0.011312974616885185,
-0.02127249166369438,
-0.01974077709019184,
0.03449022024869919,
-0.010179021395742893,
0.01551619078963995,
-0.021611344069242477,
-0.01567230187356472,
-0.03856293857097626,
0.00760327372699976,
-0.011282403953373432,
-0.04161125794053078,
0.026116322726011276,
-0.0145859494805336,
-0.008232307620346546,
0.01216471754014492,
0.006369240116328001,
0.029408976435661316,
-0.0011402701493352652,
0.0410221628844738,
0.009007634595036507,
0.04027431830763817,
-0.03491556644439697,
0.011335638351738453,
0.006593900267034769,
0.01824304088950157,
-0.03164221718907356,
-0.015516718849539757,
-0.0450456365942955,
-0.04035978391766548,
-0.025123082101345062,
0.00038165695150382817,
0.017340993508696556,
-0.006849557626992464,
0.004815842490643263,
0.05708567425608635,
-0.030236026272177696,
-0.03574443608522415,
0.000948645465541631,
0.04820265993475914,
0.0014755766605958343,
-0.01882180944085121,
-0.03516315296292305,
-0.03882458433508873,
-0.028613634407520294,
0.008960029110312462,
0.08176642656326294,
0.04347212240099907,
-0.015034222044050694,
-0.023416927084326744,
0.06977367401123047,
-0.002268156735226512,
-0.020480500534176826,
0.03146505355834961,
-0.0470513179898262,
-0.00006292677426245064,
-0.008426971733570099,
0.019340982660651207,
0.01880527287721634,
0.04146956279873848,
0.03473643958568573,
0.035372816026210785,
0.03295839577913284,
-0.08104264736175537,
-0.002044723369181156,
0.018916038796305656,
0.055004820227622986,
0.002973644295707345,
0.0016170131275430322,
-0.039174553006887436,
-0.03999648615717888,
0.04392945393919945,
-0.057752590626478195,
0.01602945849299431,
-0.028388602659106255,
0.009650551714003086,
0.011744855903089046,
-0.032590363174676895,
-0.028342632576823235,
-0.010723501443862915,
-0.04375867545604706,
-0.0006568411481566727,
-0.006595420651137829,
-0.0013511325232684612,
-0.01808728277683258,
0.014784698374569416,
0.0006518976879306138,
0.05840415880084038,
0.02446325495839119,
-0.011168892495334148,
0.03383973240852356,
0.02254035323858261,
0.0032295442651957273,
-0.033561691641807556,
-0.011868591420352459,
0.009018327109515667,
-0.04765304550528526,
0.039598021656274796,
-0.03279857710003853,
-0.009826520457863808,
0.050963401794433594,
-0.012898938730359077,
-0.04317383095622063,
0.03368045389652252,
-0.036948222666978836,
-0.0000304271379718557,
0.04148167744278908,
0.021266687661409378,
0.039690736681222916,
0.029795248061418533,
-0.020990446209907532,
-0.0012947560753673315,
-0.03462143987417221,
0.0695074275135994,
-0.02670186385512352,
-0.008397306315600872,
-0.019257359206676483,
0.03194748982787132,
-0.04550331085920334,
0.05165005102753639,
-0.04629436507821083,
0.029974309727549553,
-0.004654897842556238,
-0.04143204912543297,
0.03264196962118149,
0.03518841788172722,
0.0005810331203974783,
0.013994352892041206,
0.012326310388743877,
0.02396465465426445,
0.019605303183197975,
-0.01890777423977852,
0.008340217173099518,
-0.007388672791421413,
0.02999678999185562,
0.02256709337234497,
-0.02628113143146038,
-0.0020852640736848116,
-0.03903764486312866,
-0.020713914185762405,
-0.012157506309449673,
-0.06864986568689346,
0.103909432888031,
-0.015034155920147896,
0.03325115516781807,
0.037256352603435516,
-0.07655023783445358,
-0.04038791358470917,
-0.00936026033014059,
-0.009535153396427631,
0.055372804403305054,
-0.08957149088382721,
0.017204584553837776,
0.01487033162266016,
-0.0028539402410387993,
-0.03272470086812973,
-0.014720851555466652,
0.002155307913199067,
0.020327283069491386,
-0.012275425717234612,
-0.041917815804481506,
0.027871977537870407,
-0.018215125426650047,
-0.013691795989871025,
-0.03093714639544487,
0.043562065809965134,
-0.043091803789138794,
-0.018464701250195503,
0.007882668636739254,
0.0032312592957168818,
0.02800600603222847,
-0.004562736488878727,
-0.002064655302092433,
0.022257978096604347,
0.007429597899317741,
-0.04251444712281227,
0.01248946227133274,
0.03678866848349571,
-0.05202874541282654,
-0.057718876749277115,
-0.005072727799415588,
-0.0235450379550457,
0.054470472037792206,
-0.013171117752790451,
0.0421006940305233,
0.015057122334837914,
0.049739472568035126,
-0.02068992145359516,
0.020579857751727104,
0.03517814353108406,
0.0055922213941812515,
-0.011005847714841366,
-0.048370882868766785,
0.009968879632651806,
-0.011739598587155342,
-0.037318166345357895,
0.018882354721426964,
-0.00014573970111086965,
0.05514976754784584,
-0.013217102736234665,
0.03191506117582321,
0.006283486261963844,
0.01434116717427969,
0.03962525352835655,
-0.00656858179718256,
0.004129946231842041,
-0.0250636488199234,
0.0561976358294487,
0.015036176890134811,
0.021974364295601845,
-0.04304974526166916,
-0.03877948224544525,
-0.036122098565101624,
-0.0040982626378536224,
0.06060299649834633,
-0.041366394609212875,
0.037493087351322174,
0.0361265167593956,
-0.011206816881895065,
-0.000992201967164874,
-0.008727865293622017,
0.004301024600863457,
0.017479034140706062,
0.01779862679541111,
0.027032626792788506,
-0.015554516576230526,
-0.0015399660915136337,
-0.0071916766464710236,
0.04431604593992233,
0.03136448934674263,
0.021913999691605568,
0.015619853511452675,
0.0704687312245369,
-0.016959792003035545,
-0.06113346666097641,
-0.05410592630505562,
0.024022653698921204,
-0.050317879766225815,
0.05249467119574547,
0.028248589485883713,
-0.04502807930111885,
0.02101634070277214,
0.010637609288096428,
0.0044753216207027435,
-0.0429806150496006,
-0.03120727650821209,
-0.01311960443854332,
0.0038884615059942007,
0.016443882137537003,
-0.035763584077358246,
-0.03353744000196457,
0.000006918611234141281,
0.02511594630777836,
0.026014745235443115,
0.017944859340786934,
-0.04956062510609627,
-0.06348095089197159,
-0.0250217467546463,
-0.05170974135398865,
-0.05449865385890007,
0.018488507717847824,
-0.014416958205401897,
-0.030182059854269028,
-0.0066452547907829285,
-0.037760499864816666,
-0.02231523208320141,
0.016100864857435226,
0.0017839616630226374,
-0.0023611090146005154,
0.021800488233566284,
-0.009262077510356903,
0.029663579538464546,
0.024719078093767166,
0.015288158319890499,
0.1174803078174591,
0.04045552387833595,
-0.02137858048081398,
-0.03465716540813446,
0.005550205707550049,
-0.03207162767648697,
0.010111765004694462,
-0.027900582179427147,
0.023862691596150398,
-0.05234454572200775,
-0.0017002407694235444,
0.021707141771912575,
0.034246016293764114,
0.0004294977698009461,
0.0038515725173056126,
0.03641378507018089,
-0.012576064094901085,
-0.03126561641693115,
0.05816783010959625,
0.0025252578780055046,
0.011865108273923397,
0.010769839398562908,
-0.02238789014518261,
0.040946122258901596,
-0.026964789256453514,
-0.027259446680545807,
-0.04535653069615364,
-0.006998919881880283,
0.023006770759820938,
0.018343588337302208,
0.01387588120996952,
-0.026128074154257774,
-0.0029250860679894686,
-0.001186623820103705,
-0.029051054269075394,
0.03578682988882065,
0.04162796586751938,
0.0014425743138417602,
-0.00013082318764645606,
-0.001196086872369051,
0.007580897305160761,
0.019065892323851585,
0.05702429264783859,
-0.006930286530405283,
-0.051332537084817886,
-0.027311084792017937,
-0.017133193090558052,
0.04700212553143501,
0.005110999569296837,
0.01267495471984148,
-0.01850990578532219,
0.02347470074892044,
0.04086702689528465,
-0.0675300732254982,
-0.020552508533000946,
0.018337802961468697,
0.002706907456740737,
0.011182564310729504,
-0.020567579194903374,
0.02345898561179638,
0.04346796125173569,
0.0005248322268016636,
-0.019647404551506042,
0.015497992746531963,
0.013779719360172749,
-0.03665093705058098,
-0.017031224444508553,
0.03765270859003067,
-0.016551243141293526,
-0.04899907484650612,
-0.0393998958170414,
0.030099257826805115,
0.012823676690459251,
-0.003224026644602418,
0.026600457727909088,
0.030785297974944115,
0.01627163216471672,
0.025116771459579468,
0.0049094404093921185,
-0.01279823761433363,
-0.06307071447372437,
0.009387176483869553,
-0.02244107984006405,
-0.019529996439814568,
-0.02889426425099373,
0.009581627324223518,
0.03508371859788895,
0.042568009346723557,
-0.017692985013127327,
0.004653058014810085,
-0.03604394942522049,
-0.011626256629824638,
0.040018633008003235,
-0.021751340478658676,
-0.05820957198739052,
0.006929442286491394,
0.0017096302472054958,
-0.008073410019278526,
-0.01316478755325079,
0.05052849277853966,
0.02670586295425892,
-0.011366581544280052,
0.025311904028058052,
0.011790374293923378,
-0.04748160392045975,
0.032857008278369904,
0.0036343184765428305,
-0.029824301600456238,
0.037516649812459946,
-0.040860615670681,
0.03184008598327637,
-0.013830534182488918,
-0.0233614444732666,
-0.028478674590587616,
-0.01484357938170433,
0.005768889095634222,
0.005619467701762915,
0.002090719062834978,
0.01295680832117796,
-0.014279321767389774,
0.016633570194244385,
-0.036473266780376434,
-0.004773514345288277,
-0.02188316360116005,
0.011876557022333145,
0.0027336999773979187,
0.022904278710484505,
-0.020260106772184372,
0.04121904820203781,
-0.01183998305350542,
-0.058913957327604294,
-0.003306133672595024,
-0.009355321526527405,
-0.028714461252093315,
0.012158687226474285,
-0.01673712208867073,
0.007280322257429361,
0.06992603838443756,
-0.01938304677605629,
-0.006061013787984848,
0.026137052103877068,
-0.028659427538514137,
0.007646388374269009,
0.03172154352068901,
0.01841636560857296,
0.01533451583236456,
0.015818895772099495,
-0.015642238780856133,
0.00017992168432101607,
0.05624402314424515,
0.04187309741973877,
-0.0533059798181057,
-0.016152475029230118,
-0.031121831387281418,
0.06637267768383026,
-0.043997686356306076,
-0.010740459896624088,
-0.05024408921599388,
0.0031312364153563976,
0.026833904907107353,
0.00011604669998632744,
0.008752510882914066,
0.008889272809028625,
-0.018894163891673088,
-0.025289129465818405,
-0.042449336498975754,
-0.01938522420823574,
-0.004212065599858761,
0.020662425085902214,
0.011927722953259945,
-0.07954955846071243,
0.028998123481869698,
0.05973517522215843,
-0.011149084195494652,
-0.07965026795864105,
0.003893180750310421,
-0.011013821698725224,
0.009178834035992622,
0.020968344062566757,
-0.09251321852207184,
0.014068960212171078,
0.026168152689933777,
-0.07045050710439682,
-0.002360934391617775,
0.005442971829324961,
-0.06309190392494202,
-0.05119270086288452,
0.018116937950253487,
0.0164056234061718,
0.019218020141124725,
-0.026691041886806488,
0.063031867146492,
0.01405024528503418,
0.011712322942912579,
-0.028696944937109947,
-0.015109874308109283,
-0.006037895567715168,
0.002004516776651144,
-0.004493600223213434,
0.002144901780411601,
0.03869856521487236,
-0.004642259795218706,
-0.030178241431713104,
0.054263725876808167,
-0.015445259399712086,
0.020564036443829536,
0.02306467480957508,
0.020875301212072372,
-0.019490119069814682,
0.03570552170276642,
-0.0011300017358735204,
0.010915013961493969,
0.005332781933248043,
-0.03433239832520485,
0.023475445806980133,
0.012214860878884792,
-0.0029347604140639305,
0.029314765706658363,
0.04815925285220146,
-0.030513746663928032,
-0.038503870368003845,
0.03472791239619255,
-0.039520036429166794,
0.007076504174619913,
-0.008610818535089493,
-0.03051130101084709,
0.03574274107813835,
-0.027168171480298042,
-0.02915244922041893,
-0.03634662181138992,
-0.02479471080005169,
0.015384338796138763,
-0.018388817086815834,
0.01884605921804905,
0.02235472947359085,
-0.04004330560564995,
-0.03375270217657089,
0.006676942575722933,
-0.005651689600199461,
-0.023908017203211784,
-0.015503374859690666,
-0.026791192591190338,
0.02450714074075222,
0.019298044964671135,
0.012350023724138737,
0.000108657157397829,
-0.03948266804218292,
0.020134883001446724,
-0.043132152408361435,
0.00882828887552023,
0.051165349781513214,
0.039595093578100204,
-0.039967719465494156,
-0.07919556647539139,
0.0008775322348810732,
-0.005464593879878521,
-0.017460621893405914,
-0.013166965916752815,
-0.03944862261414528,
-0.006868247874081135,
0.027016840875148773,
0.053319051861763,
-0.024197528138756752,
0.03489907830953598,
0.0008238774025812745,
-0.0013678910909220576,
0.02809886261820793,
-0.06645213067531586,
0.018034370616078377,
0.019941074773669243,
-0.03792443871498108,
-0.026616236194968224,
0.014964890666306019,
-0.008912505581974983,
0.010822500102221966,
0.031892579048871994,
-0.0021174908615648746,
0.017225049436092377,
-0.02268737554550171,
-0.017974209040403366,
0.007821902632713318,
-0.030157605186104774,
-0.017269140109419823,
0.05877280235290527,
-0.020441938191652298,
-0.030280252918601036,
-0.0026674941182136536,
-0.0413547120988369,
0.014915154315531254,
0.0043934304267168045,
-0.09113103896379471,
0.019059844315052032,
-0.01974022015929222,
-0.017298854887485504,
0.03477444499731064,
-0.07185989618301392,
0.019589733332395554,
0.005632513202726841,
-0.06524398177862167,
-0.019530916586518288,
0.046488258987665176,
0.021634262055158615,
0.004345741122961044,
0.013684138655662537,
0.004687812179327011,
-0.029574759304523468,
-0.0007243491127155721,
-0.00926295481622219,
0.02514779008924961,
-0.006531445775181055,
0.009862883016467094,
0.016173209995031357,
0.01499027106910944,
0.009444557130336761,
0.018091635778546333,
-0.048760317265987396,
0.03394433110952377,
-0.010698261670768261,
-0.03486702963709831,
0.0034148951526731253,
-0.014260930940508842,
-0.019088344648480415,
-0.0032869905699044466,
-0.016538040712475777,
0.06392472982406616,
-0.018436728045344353,
0.007684577722102404,
-0.03795062378048897,
-0.003627261845394969,
-0.02237243950366974,
0.049709878861904144,
0.011507428251206875,
0.035622596740722656,
-0.02493097074329853,
-0.001658013672567904,
-0.002403323305770755,
-0.002971476875245571,
0.025712618604302406,
-0.04026331752538681,
0.02046721987426281,
0.002059456193819642,
-0.0024963333271443844,
-0.009249992668628693,
-0.015816939994692802,
0.006326224189251661,
-0.016629278659820557,
-0.01227822620421648,
0.04662606120109558,
-0.03366140276193619,
0.01307961717247963,
-0.0014705830253660679,
0.02641305699944496,
0.04185166582465172,
-0.06862220913171768,
0.020879361778497696,
-0.0015610473928973079,
0.007831503637135029,
-0.007364095188677311,
0.05423658341169357
] |
<p>At the end of spontaneous symmetry breaking I get these mass terms:</p>
<p>$$W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp i W_{\mu}^{2} \bigr )$$</p>
<p>$$\mathcal{L}_{mass}=\frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{+}{W^{\mu}}^{-} + \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+}$$</p>
<p>So I have $$M_{W^+}=g \frac{v}{2} \quad M_{W^-}=g \frac{v}{2} $$</p>
<p>Is it right? Or there are too many terms and it is enough:</p>
<p>$$\mathcal{L}_{mass}= \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+} $$</p>
| 10,769 |
[
-0.004056381061673164,
-0.016830913722515106,
-0.020546747371554375,
-0.00712610874325037,
0.020106783136725426,
0.029703853651881218,
-0.03196568042039871,
-0.047467149794101715,
0.008461354300379753,
-0.030191125348210335,
0.03457709029316902,
0.01312311552464962,
0.06526108831167221,
-0.006038922816514969,
0.027825063094496727,
0.026473697274923325,
-0.00545619847252965,
-0.005136237479746342,
0.027569634839892387,
-0.01525032613426447,
-0.02724580653011799,
0.008802277967333794,
-0.01800086535513401,
-0.024791698902845383,
-0.009248118847608566,
0.04696708545088768,
0.029916705563664436,
0.02285628393292427,
-0.005984151735901833,
0.023421332240104675,
-0.0045743403024971485,
-0.020857855677604675,
0.019627029076218605,
0.010570108890533447,
0.030660822987556458,
0.01902349479496479,
-0.02959844470024109,
-0.03976001963019371,
0.031934890896081924,
0.010655484162271023,
-0.03137798607349396,
0.02905311994254589,
-0.0324876569211483,
0.040844205766916275,
-0.009855416603386402,
-0.010559884831309319,
-0.00035923224641010165,
-0.016939563676714897,
0.06683988124132156,
-0.03938177973031998,
0.06688680499792099,
0.0411505363881588,
0.06832064688205719,
-0.004716650582849979,
-0.030442818999290466,
-0.020028699189424515,
0.045463696122169495,
0.09380046278238297,
0.04192391410470009,
-0.041170910000801086,
-0.007596761919558048,
-0.03353378176689148,
0.031646959483623505,
0.012426032684743404,
-0.007645134348422289,
0.05048355087637901,
0.006854214705526829,
0.014477844350039959,
0.013989248313009739,
0.0025479798205196857,
0.04584117606282234,
-0.02543112449347973,
0.04630272462964058,
-0.009165792725980282,
0.028066745027899742,
0.009721018373966217,
0.013939951546490192,
0.03465351462364197,
-0.01597915031015873,
0.01967686042189598,
-0.01708761230111122,
0.025126075372099876,
0.00849439762532711,
0.04223666340112686,
-0.022165466099977493,
-0.007083663251250982,
0.07334666699171066,
0.0021162808407098055,
-0.015457686968147755,
0.05800538882613182,
0.01675611361861229,
0.01727714017033577,
0.060037579387426376,
-0.016379408538341522,
-0.020068392157554626,
0.050994131714105606,
-0.015637047588825226,
0.02329537644982338,
-0.002152594504877925,
0.02557753399014473,
-0.014753162860870361,
-0.00721929082646966,
0.001979188062250614,
0.05734633281826973,
-0.02736133150756359,
-0.003181986976414919,
-0.052927229553461075,
-0.020407313480973244,
-0.022058092057704926,
-0.015536446124315262,
-0.038092777132987976,
-0.004076450597494841,
0.008570602163672447,
-0.0066987997852265835,
-0.026325946673750877,
-0.023055987432599068,
-0.00046894868137314916,
-0.0001764098124112934,
0.05497993528842926,
0.0701051726937294,
0.05025698244571686,
-0.02702062763273716,
0.021768884733319283,
-0.007346657104790211,
-0.03985605761408806,
0.007931351661682129,
0.03253523260354996,
0.004911906085908413,
-0.05476514250040054,
0.02417374774813652,
0.06745113432407379,
-0.004871947690844536,
0.01087235938757658,
-0.01498305331915617,
0.04260724037885666,
-0.020919330418109894,
-0.07039637118577957,
-0.05369691178202629,
0.035627830773591995,
-0.03732168301939964,
0.02351757138967514,
-0.08663217723369598,
-0.03418901935219765,
0.019455263391137123,
0.12559844553470612,
-0.012731608003377914,
0.03151767700910568,
0.007261531427502632,
0.03492075204849243,
-0.016350315883755684,
-0.014749429188668728,
0.00843653455376625,
-0.0067661055363714695,
-0.012982584536075592,
-0.01585853286087513,
-0.049108363687992096,
-0.0038161007687449455,
0.06109919399023056,
0.025866325944662094,
0.037903863936662674,
0.06493352353572845,
-0.009845361113548279,
0.039947252720594406,
0.04153694212436676,
-0.005341439042240381,
-0.013918041251599789,
0.03183149918913841,
0.021909506991505623,
0.008494232781231403,
0.014840259216725826,
0.04351438954472542,
0.03108617477118969,
-0.03934480622410774,
0.00944568496197462,
0.05631550773978233,
-0.03993181511759758,
-0.0008203067118301988,
-0.07201416790485382,
0.029387906193733215,
0.006340936757624149,
-0.04531560838222504,
-0.06897599250078201,
-0.00862532202154398,
0.005294975824654102,
0.033337224274873734,
0.0018702356610447168,
-0.019657902419567108,
0.033824991434812546,
-0.00036777486093342304,
-0.04103215038776398,
-0.05838169530034065,
-0.03512191027402878,
0.009319886565208435,
0.015684673562645912,
-0.050553034991025925,
0.008155066519975662,
-0.0006412661750800908,
0.018017873167991638,
0.03363427147269249,
-0.021060407161712646,
-0.007683455944061279,
0.055925238877534866,
0.004122985061258078,
0.001654064399190247,
0.018899787217378616,
0.05668625980615616,
0.009197823703289032,
-0.004740436561405659,
0.03935704752802849,
-0.004654747433960438,
-0.01140323095023632,
0.026722868904471397,
0.018820663914084435,
0.0022914677392691374,
-0.02255455031991005,
-0.02647637017071247,
0.009567731991410255,
0.012070182710886002,
-0.012608930468559265,
0.039847232401371,
-0.013266723603010178,
0.05737999826669693,
0.043642375618219376,
0.00455086212605238,
0.0022714100778102875,
0.024373739957809448,
0.002483517164364457,
0.04707799851894379,
-0.04188969358801842,
-0.002286376431584358,
-0.043685123324394226,
-0.006198206916451454,
0.019099315628409386,
0.013289098627865314,
-0.032839588820934296,
0.021046966314315796,
0.034653641283512115,
0.017420338466763496,
0.04410649091005325,
0.01238510012626648,
-0.03975773602724075,
-0.042854804545640945,
0.031985048204660416,
0.046977702528238297,
0.023039232939481735,
0.01881309784948826,
0.023494156077504158,
0.007331195753067732,
0.004045527428388596,
-0.03551381453871727,
-0.015122263692319393,
0.028805840760469437,
-0.05249207094311714,
-0.02149944007396698,
-0.027020461857318878,
-0.00904647447168827,
0.04995519295334816,
-0.026168473064899445,
0.05685903877019882,
0.05057651922106743,
0.013207796961069107,
-0.02446051687002182,
-0.06256954371929169,
-0.017344219610095024,
-0.007273583207279444,
0.008977237157523632,
-0.027930354699492455,
-0.023110108450055122,
0.009689685888588428,
-0.04360252246260643,
-0.0002860547974705696,
-0.005323486402630806,
-0.013854221440851688,
-0.020602701231837273,
-0.0029213158413767815,
0.03691941127181053,
0.0037285611033439636,
0.061475079506635666,
-0.05130297318100929,
-0.04144909605383873,
0.01955425553023815,
-0.026384754106402397,
0.022877614945173264,
0.02407793141901493,
-0.04728304594755173,
0.005219316575676203,
-0.04339219629764557,
-0.02727349102497101,
0.01839975267648697,
0.02995024435222149,
0.0047592902556061745,
0.02726251445710659,
-0.010772899724543095,
-0.03594175726175308,
-0.03642446920275688,
-0.03816717863082886,
0.015143152326345444,
-0.024845276027917862,
-0.006774082779884338,
0.034382760524749756,
0.026512565091252327,
-0.040598314255476,
-0.01944870501756668,
-0.03133421018719673,
-0.046648863703012466,
-0.012505828402936459,
0.013607539236545563,
0.019874123856425285,
-0.019165685400366783,
0.04081923887133598,
0.030105797573924065,
-0.022009706124663353,
0.0047646514140069485,
-0.056415386497974396,
-0.02928694523870945,
0.031986821442842484,
-0.03385411947965622,
0.04511597752571106,
0.023898834362626076,
-0.04528474807739258,
0.09799831360578537,
0.04505610838532448,
0.004568723030388355,
-0.031334906816482544,
0.019614215940237045,
0.0026641618460416794,
-0.05949907749891281,
0.00793983694165945,
-0.00010394536366220564,
-0.000896706769708544,
0.051403727382421494,
0.028913799673318863,
0.04814055562019348,
0.02065425179898739,
-0.004830832127481699,
-0.04008708894252777,
0.009378412738442421,
0.01394239254295826,
-0.02886079251766205,
0.06565598398447037,
-0.017332976683974266,
-0.003124392358586192,
0.0010826380457729101,
-0.011826300993561745,
0.019603069871664047,
0.025626080110669136,
-0.048898011445999146,
0.0641760304570198,
-0.0013098514173179865,
0.0076887295581400394,
-0.012444439344108105,
0.041050467640161514,
0.03611302375793457,
-0.05518763139843941,
-0.01897871121764183,
-0.02130056358873844,
0.020446859300136566,
-0.014179114252328873,
0.001679948647506535,
0.06087817624211311,
-0.015374827198684216,
-0.022917168214917183,
-0.030495930463075638,
-0.018141936510801315,
-0.032320864498615265,
0.0048072487115859985,
0.01528073102235794,
-0.03568523749709129,
0.04869475215673447,
0.057136356830596924,
0.029088091105222702,
-0.04778621345758438,
-0.025714244693517685,
-0.01705321855843067,
-0.06718353927135468,
0.023662419989705086,
-0.026053164154291153,
0.019058194011449814,
-0.01960037462413311,
0.02492145076394081,
0.06431812793016434,
0.01895274594426155,
0.03392968326807022,
0.00820444617420435,
-0.07204069197177887,
0.03800278156995773,
-0.010410635732114315,
-0.010818644426763058,
0.009538454934954643,
-0.021481722593307495,
-0.014446502551436424,
-0.06688687205314636,
-0.03951956331729889,
-0.0008305940427817404,
-0.02890321984887123,
-0.02424333244562149,
0.03036326728761196,
-0.04641519486904144,
-0.009376546368002892,
0.004438481293618679,
0.001478715566918254,
0.06283202022314072,
-0.02332218736410141,
-0.02845260687172413,
0.0523151271045208,
-0.0255704578012228,
0.0037842525634914637,
-0.04012555629014969,
0.017886096611618996,
0.018537748605012894,
0.03033224307000637,
0.03573201596736908,
0.037939853966236115,
-0.05133281275629997,
0.0018302439711987972,
0.014399547129869461,
0.011540396139025688,
0.022894499823451042,
0.008112807758152485,
-0.013324064202606678,
-0.033560413867235184,
-0.022388260811567307,
0.034312695264816284,
0.017476191744208336,
0.01437930017709732,
0.0028993855230510235,
0.04335950314998627,
-0.005663486197590828,
-0.026195140555500984,
0.037255797535181046,
0.06153738498687744,
-0.04665715619921684,
-0.03222540020942688,
-0.061537016183137894,
-0.013952329754829407,
0.018640905618667603,
-0.022014396265149117,
0.007301256060600281,
-0.03391526639461517,
-0.041257672011852264,
0.011477652005851269,
0.023441256955266,
0.03711940720677376,
-0.044411901384592056,
0.03241840377449989,
-0.011430311016738415,
0.02110103890299797,
0.025729190558195114,
-0.006126867141574621,
0.008327479474246502,
0.030240893363952637,
0.004801734816282988,
0.013518277555704117,
-0.003128289943560958,
-0.09343849867582321,
0.002800246700644493,
0.019840015098452568,
0.05737635865807533,
0.004178100731223822,
-0.018338847905397415,
-0.03754584118723869,
-0.019278528168797493,
0.045285508036613464,
-0.02381684072315693,
0.03175973892211914,
0.018967293202877045,
0.014039494097232819,
0.014088533818721771,
-0.037069130688905716,
-0.04807897284626961,
0.009009184315800667,
-0.028025250881910324,
-0.007158319465816021,
-0.06502168625593185,
0.0006628939881920815,
-0.023348301649093628,
0.02686626836657524,
0.030748622491955757,
0.04237755015492439,
0.007650474086403847,
-0.01665233075618744,
-0.007193338125944138,
0.002275206847116351,
-0.03937501832842827,
-0.095024973154068,
-0.004743426572531462,
0.0026017827913165092,
-0.03532245755195618,
0.017169227823615074,
-0.019380884245038033,
-0.0622389018535614,
0.03668348491191864,
0.04702698811888695,
0.018377719447016716,
-0.02648352086544037,
-0.037664324045181274,
0.06390056759119034,
0.05173175781965256,
-0.01168088335543871,
0.058332838118076324,
0.02793077379465103,
-0.003270469605922699,
0.02322923205792904,
-0.04271244630217552,
0.024744683876633644,
-0.02784089185297489,
0.03190140798687935,
-0.02932634763419628,
-0.018977869302034378,
-0.0470396913588047,
0.024189606308937073,
-0.02092563919723034,
0.010538545437157154,
-0.021708894520998,
-0.043046146631240845,
0.017329463735222816,
0.01567850634455681,
0.02338881976902485,
-0.01722421683371067,
0.01631263643503189,
0.03387138992547989,
0.0071564847603440285,
-1.7103533878071175e-7,
0.020894819870591164,
0.001768335234373808,
-0.012033077888190746,
0.02451227232813835,
0.019951440393924713,
0.0014870790764689445,
-0.006253370083868504,
-0.04113230109214783,
-0.012527157552540302,
-0.07401401549577713,
0.010833976790308952,
0.006464553065598011,
-0.01145327277481556,
-0.003954428248107433,
-0.04723431169986725,
-0.04570036008954048,
-0.021600669249892235,
-0.007433731574565172,
-0.01491895318031311,
-0.0011206031776964664,
0.0027856500819325447,
0.03523578867316246,
0.0106191486120224,
-0.08656787872314453,
-0.030574409291148186,
-0.0077817789278924465,
-0.010931297205388546,
-0.013725930824875832,
0.008040675893425941,
-0.021379346027970314,
-0.038369033485651016,
-0.04601166397333145,
0.016763662919402122,
0.026217376813292503,
-0.029596295207738876,
-0.007026518229395151,
0.014855455607175827,
0.027820151299238205,
0.01206247229129076,
-0.002549616852775216,
-0.019858630374073982,
-0.019032549113035202,
0.006029641255736351,
-0.00862839724868536,
0.026164108887314796,
0.062483321875333786,
-0.020745251327753067,
-0.0450875498354435,
-0.006540257483720779,
-0.003085800912231207,
0.03658602386713028,
0.020047925412654877,
-0.006581353954970837,
0.029568281024694443,
0.012994060292840004,
0.01007537916302681,
-0.04665789380669594,
0.01549355499446392,
-0.024190133437514305,
0.038516391068696976,
0.030116381123661995,
0.03181760385632515,
-0.026178650557994843,
-0.019499270245432854,
0.021191133186221123,
-0.005369352176785469,
0.0216506477445364,
-0.038026709109544754,
0.03493514657020569,
-0.029321245849132538,
-0.023193299770355225,
0.015099438838660717,
-0.018437953665852547,
-0.03200506046414375,
0.002214212203398347,
-0.007518442813307047,
0.013705157674849033,
0.024439126253128052,
-0.018351657316088676,
-0.00993261393159628,
-0.042773839086294174,
0.012239417992532253,
0.07632222026586533,
-0.0013490079436451197,
0.02552526257932186,
0.007168375421315432,
-0.004134037531912327,
0.027443692088127136,
-0.030925597995519638,
-0.014208883047103882,
0.03252324089407921,
0.022419853135943413,
0.046449385583400726,
-0.060490597039461136,
-0.01741930842399597,
0.01742679439485073,
0.05595294013619423,
-0.026439307257533073,
0.020252490416169167,
0.043689511716365814,
-0.026657573878765106,
-0.028931602835655212,
0.004682001657783985,
-0.03982405364513397,
0.063217394053936,
-0.02005966752767563,
0.056048452854156494,
-0.02290848083794117,
0.022769341245293617,
0.03268260136246681,
0.011882631108164787,
0.0007899785414338112,
-0.014102479442954063,
-0.025933152064681053,
-0.040168337523937225,
0.007901374250650406,
0.031076597049832344,
-0.029805555939674377,
0.019906911998987198,
0.03110225684940815,
0.0280767735093832,
0.02795955166220665,
0.03513207286596298,
-0.007108266931027174,
-0.0656401515007019,
-0.011912771500647068,
-0.012727618217468262,
-0.0532166063785553,
0.02962638810276985,
-0.03620791807770729,
-0.006359784863889217,
0.004192023538053036,
-0.014239586889743805,
0.023561131209135056,
0.0003138466563541442,
0.07491324841976166,
-0.018712321296334267,
0.04726478457450867,
0.0156866405159235,
0.017650241032242775,
0.006878067273646593,
0.009791583754122257,
0.13144069910049438,
0.0512404590845108,
-0.019268367439508438,
-0.03914589807391167,
0.02561153657734394,
-0.013254525139927864,
0.009977633133530617,
-0.034596703946590424,
0.029664168134331703,
-0.04578022658824921,
-0.020423144102096558,
-0.04072761535644531,
0.04730677232146263,
-0.012298458255827427,
0.004352336749434471,
0.04021722450852394,
-0.008896342478692532,
-0.0704820305109024,
-0.015787212178111076,
0.016127988696098328,
-0.005247113760560751,
0.02634829841554165,
0.004056754522025585,
0.03799990937113762,
-0.002588748000562191,
0.00834146048873663,
-0.027811456471681595,
-0.017571955919265747,
0.012034393846988678,
0.008396841585636139,
-0.03640645369887352,
-0.0061332653276622295,
0.0015152194537222385,
-0.005730676464736462,
-0.019830165430903435,
0.0023846589028835297,
0.015130123123526573,
-0.01528104767203331,
0.021006513386964798,
0.03885894641280174,
-0.02571943774819374,
0.01478637382388115,
0.023928692564368248,
0.014591020531952381,
-0.03441338241100311,
-0.0052804588340222836,
0.00017746044613886625,
0.08020651340484619,
0.026473786681890488,
-0.014463297091424465,
0.02642904222011566,
-0.019060101360082626,
0.004904794506728649,
-0.06098509952425957,
-0.0194514449685812,
0.026078365743160248,
0.03280181810259819,
-0.027327701449394226,
-0.00010145278793061152,
-0.04383791983127594,
0.028706654906272888,
0.009047098457813263,
-0.00006821996066719294,
-0.026309682056307793,
0.0019103515660390258,
-0.0193018838763237,
0.0014265583595260978,
0.020199134945869446,
-0.013375310227274895,
-0.021530771628022194,
-0.003801899729296565,
-0.02224363200366497,
-0.03519356995820999,
-0.039528489112854004,
0.017029279842972755,
0.021416693925857544,
0.04524509981274605,
-0.014890125021338463,
-0.020183933898806572,
-0.038585059344768524,
-0.08647268265485764,
0.01585046760737896,
0.010309481993317604,
-0.023741532117128372,
0.003404407761991024,
-0.013081242330372334,
-0.011515256017446518,
0.006932344753295183,
-0.06582221388816833,
-0.0004292288504075259,
0.013218771666288376,
0.05422697216272354,
-0.012433404102921486,
-0.04059838503599167,
-0.04472355172038078,
0.05573657900094986,
-0.017103087157011032,
-0.007104073651134968,
-0.017399534583091736,
0.029509175568819046,
-0.0116506926715374,
0.006830987986177206,
0.031175553798675537,
0.017394645139575005,
0.0036380242090672255,
-0.0011434435145929456,
0.02359122782945633,
-0.015912562608718872,
-0.00021487184858415276,
0.03787657618522644,
-0.021331269294023514,
-0.0013091717846691608,
-0.019374527037143707,
0.0004641385457944125,
0.016971709206700325,
0.0062231156043708324,
0.003442412940785289,
-0.058466263115406036,
0.016876235604286194,
-0.016741888597607613,
-0.0019693635404109955,
-0.007523176725953817,
-0.0016683570574969053,
-0.027942396700382233,
0.01848411187529564,
0.0190120842307806,
-0.03843381628394127,
-0.020075727254152298,
0.02340143360197544,
0.006374555639922619,
0.007767778821289539,
0.03773703798651695,
0.06705960631370544,
-0.0076180496253073215,
-0.03706498444080353,
0.013499253429472446,
-0.0076687573455274105,
0.04322861507534981,
0.019306307658553123,
-0.014900925569236279,
0.017249176278710365,
-0.023175690323114395,
-0.03402738645672798,
0.052175939083099365,
0.035974711179733276,
0.024989407509565353,
0.007061818148940802,
-0.017665598541498184,
-0.012584014795720577,
0.0877891406416893,
-0.015945743769407272,
0.006203196942806244,
0.008411417715251446,
-0.04642944782972336,
-0.009549728594720364,
-0.03654837980866432,
0.00143242662306875,
0.019290102645754814,
0.020673463121056557,
0.01373906061053276,
0.012536702677607536,
-0.02946941927075386,
-0.00043998684850521386,
-0.012868953868746758,
-0.05776529386639595,
0.0679897665977478,
0.02816096507012844,
0.01672668568789959,
0.0033785949926823378,
0.05980266258120537,
0.01542058028280735,
0.013233614154160023,
-0.01094048097729683,
0.00016189651796594262,
-0.0628499984741211,
-0.03297852352261543,
0.0004447032988537103,
0.012842947617173195,
0.052183691412210464,
-0.05332798883318901,
0.013480289839208126,
0.0150959687307477,
-0.03414550796151161,
-0.03306564316153526,
-0.03406801074743271,
-0.01539439707994461,
-0.03228471800684929,
-0.03790196403861046,
-0.02799071930348873,
0.03313189372420311,
0.030261417850852013,
0.05087161436676979,
0.022300494834780693,
-0.013674509711563587,
-0.014833980239927769,
-0.05091260001063347,
-0.02066449448466301,
0.036018915474414825,
0.014535888098180294,
-0.040649596601724625,
0.05135778337717056,
-0.014773383736610413,
-0.04223291203379631,
-0.01235576719045639,
-0.011504373513162136,
0.021884286776185036,
0.01589207537472248,
0.04134557768702507,
-0.001685091177932918,
0.040744271129369736,
0.007747521623969078,
-0.0008715683361515403,
0.041101694107055664,
-0.01992790214717388,
0.024887440726161003,
0.016522562131285667,
-0.031938690692186356,
0.00615479052066803,
-0.0019598687067627907,
-0.03305880352854729,
-0.036369480192661285,
0.052835870534181595,
-0.04340466484427452,
-0.0005977359833195806,
-0.02868529036641121,
0.02381419762969017,
0.022028570994734764,
-0.06295810639858246,
0.03352723270654678,
-0.04188881441950798,
0.015142643824219704,
0.016009552404284477,
0.029404163360595703,
-0.029469480738043785,
-0.02545580081641674,
-0.0015879892744123936,
-0.0030475135426968336,
-0.02853425219655037,
0.013867655768990517,
-0.01652970351278782,
-0.02460458315908909,
-0.018261250108480453,
0.008428364060819149,
0.02775244601070881,
0.006891573779284954,
-0.008375258184969425,
-0.04179869219660759,
0.026659181341528893,
-0.00751773314550519,
0.009764419868588448,
-0.029369313269853592,
-0.0185761209577322,
-0.006320175714790821,
-0.06739409267902374,
0.006932584568858147,
0.020503677427768707,
0.005602863151580095,
-0.01058217417448759,
-0.017329994589090347,
0.018551992252469063,
0.02100870944559574,
0.021111125126481056,
0.013688878156244755,
-0.029660608619451523,
0.037338148802518845,
0.03407905250787735,
0.010801444761455059,
-0.044382814317941666,
-0.024633748456835747,
-0.010088540613651276,
0.017201194539666176,
-0.012352777644991875,
0.013229385018348694,
0.00534804118797183,
0.02820056863129139,
0.01713564060628414,
-0.011335932649672031,
-0.005640057381242514,
-0.001637756242416799,
-0.02952648140490055,
0.017203906551003456,
-0.04114583879709244,
-0.04069400206208229,
0.08003462105989456,
0.0015246541006490588,
0.014668549410998821,
0.047067008912563324,
-0.02925037033855915,
-0.013660933822393417,
0.009813359007239342,
-0.03154795616865158,
-0.033447373658418655,
-0.0203291866928339,
-0.020432129502296448,
0.03856373950839043,
-0.01977146789431572,
0.013748237863183022,
0.012680117972195148,
-0.0412973091006279,
-0.021457931026816368,
0.015686066821217537,
0.024288184940814972,
0.03073250502347946,
0.007387880235910416,
0.0085704755038023,
0.0443328358232975,
-0.005508294329047203,
0.025111617520451546,
0.058589715510606766,
0.015346054919064045,
0.027081552892923355,
-0.006986469961702824,
-0.000030403587516047992,
-0.027740435674786568,
-0.010659223422408104,
-0.00012518423318397254,
-0.020175864920020103,
-0.032227661460638046,
-0.004910044837743044,
-0.022804303094744682,
0.017030077055096626,
0.028682786971330643,
-0.010254083201289177,
-0.024211430922150612,
0.07362820953130722,
-0.013234281912446022,
0.01819571666419506,
-0.03664800524711609,
0.01934841275215149,
-0.019887221977114677,
0.04980923607945442,
-0.025245923548936844,
0.03718842566013336,
0.002515374682843685,
-0.027073923498392105,
-0.03145644813776016,
-0.006067389622330666,
0.034250129014253616,
-0.10067881643772125,
-0.004288829397410154,
-0.0011123468866571784,
-0.015415482223033905,
0.006622000597417355,
-0.03315115347504616,
-0.011874418705701828,
-0.043749336153268814,
0.032362036406993866,
0.030339961871504784,
-0.03027571551501751,
-0.02618776448071003,
-0.010455930605530739,
-0.0304101649671793,
0.04635130986571312,
-0.011955153197050095,
-0.004859738517552614,
-0.03582948073744774,
-0.018491258844733238,
-0.0014304621145129204,
-0.030391931533813477
] |
<p>It would really help me with an idea I have if I could see how something such as a symmetric field could collapse to something asymmetric. I know that if $x$ occures before $y$ is symmetric, then $y$ occurs before $x$, which doesn't make sense if we take time to be asymmetric (only flowing in one direction). Is there a relationship between energy in the universe being symmetric, and the production of anti-matter asymmetric? </p>
<p>I am mostly interested in the collapse of the wavefunction, and a search to find if this collapse is asymmetric I am left with the thought that I might have to specify what the symmetry/asymmetry would be in respect to, that being said, is there some sort of "field" whether physical or purely abstract which is symmetric and if a "disturbance" (observation?) happens, there is a collapse to an asymmetric field such as the collapse of the wavefunction? Maybe I have it all wrong?</p>
<ul>
<li>Digging deeper, what I am looking for examples of, especially of quantum systems is that of "symmetry breaking". I also found the answered question concerning spontaneous symmetry breaking in Quantum mechanics here: <a href="http://physics.stackexchange.com/questions/29311/what-is-spontaneous-symmetry-breaking-in-quantum-systems">spontaneous symmetry breaking in Quantum Systems</a>, and while I have some background in physics and pure math, I hope to get a much more canonical answer so as to understand more the foundations. \</li>
</ul>
| 10,770 |
[
-0.032281294465065,
-0.02446470409631729,
-0.003848073538392782,
-0.03131250664591789,
0.0427502803504467,
-0.012275236658751965,
-0.03316494822502136,
-0.03010612167418003,
0.03203003108501434,
-0.037161633372306824,
0.030860835686326027,
0.010301530361175537,
0.017813634127378464,
0.01980285532772541,
0.050324391573667526,
0.03280460461974144,
0.010234510526061058,
-0.05512456223368645,
-0.024281371384859085,
-0.014721594750881195,
-0.010177656076848507,
0.022221282124519348,
-0.014093715697526932,
0.024413082748651505,
-0.021222634240984917,
0.020225565880537033,
0.01870885118842125,
0.01073935441672802,
0.0020505094435065985,
0.07269095629453659,
-0.038277383893728256,
-0.02544260211288929,
-0.05205005034804344,
0.010253983549773693,
0.03058641217648983,
-0.01027436088770628,
0.02145426720380783,
-0.05613104626536369,
0.0152934230864048,
0.024104483425617218,
-0.03628164529800415,
0.018579699099063873,
-0.02636965736746788,
0.04392875358462334,
-0.04964422062039375,
-0.004648223984986544,
-0.013725985772907734,
0.004271364770829678,
0.04454560577869415,
-0.04561939835548401,
0.07664165645837784,
-0.014528858475387096,
0.05539529770612717,
0.0014291128609329462,
-0.00873560830950737,
0.001721876673400402,
0.08466120064258575,
0.05713212862610817,
0.02189432829618454,
-0.061951834708452225,
-0.030155355110764503,
-0.0219332966953516,
-0.010617918334901333,
-0.030288036912679672,
-0.06410243362188339,
0.04260818287730217,
-0.008354873396456242,
-0.026726871728897095,
0.006333407945930958,
-0.027579179033637047,
-0.027366863563656807,
0.014455312862992287,
0.038861535489559174,
-0.005345067009329796,
0.01389413233846426,
-0.01701202243566513,
0.02340162917971611,
-0.002015867969021201,
0.01667102798819542,
0.020002009347081184,
0.034819114953279495,
0.025186579674482346,
-0.021402036771178246,
0.03712058067321777,
-0.007396656088531017,
0.007835661061108112,
0.07231935113668442,
-0.019240181893110275,
-0.008071036078035831,
0.02389541268348694,
0.008201651275157928,
-0.016387877985835075,
0.04318300262093544,
-0.012217153795063496,
-0.04165343567728996,
0.004070935770869255,
0.003566557075828314,
0.036145392805337906,
0.014163967221975327,
-0.008740764111280441,
0.0020395289175212383,
-0.03569481521844864,
0.011909018270671368,
0.08543221652507782,
0.015993034467101097,
-0.04129590094089508,
-0.03933163359761238,
0.06075255200266838,
-0.02478068135678768,
-0.008013108745217323,
-0.025662031024694443,
-0.002613774733617902,
0.021533481776714325,
-0.0022644344717264175,
0.012269187718629837,
0.008334665559232235,
-0.002945501822978258,
-0.043665509670972824,
0.07189428061246872,
0.07102278620004654,
0.07374895364046097,
-0.007328807841986418,
0.039955105632543564,
-0.020571865141391754,
-0.05795951187610626,
0.00021240732166916132,
0.015305629931390285,
-0.0068009886890649796,
-0.038374967873096466,
0.00842767208814621,
-0.00460650073364377,
-0.034553248435258865,
0.005395420826971531,
-0.04885657876729965,
0.06950682401657104,
-0.04217364266514778,
-0.10069536417722702,
-0.058748453855514526,
0.021712498739361763,
0.02389499545097351,
-0.01064956746995449,
-0.057782623916864395,
-0.01599607616662979,
0.040097277611494064,
0.07906284928321838,
-0.028843989595770836,
-0.012077010236680508,
0.023242682218551636,
0.04669582471251488,
0.04408129304647446,
-0.005142080131918192,
-0.01390981674194336,
0.020421508699655533,
-0.0240964125841856,
-0.024482354521751404,
-0.029918570071458817,
0.00007218147948151454,
0.04937285557389259,
0.00028362678131088614,
-0.0014113415963947773,
0.06933257728815079,
-0.01744333654642105,
0.014090403914451599,
0.03359677270054817,
-0.0034995998721569777,
-0.012531568296253681,
0.10540378838777542,
0.021949689835309982,
-0.03476332873106003,
0.0394209660589695,
0.0037206716369837523,
0.01944732666015625,
-0.013648463413119316,
0.02514595165848732,
0.025259390473365784,
-0.042826708406209946,
0.00608653062954545,
-0.016837934032082558,
-0.0007320000440813601,
-0.019520046189427376,
-0.03148263320326805,
-0.011183143593370914,
-0.02979971282184124,
-0.0023492705076932907,
0.008089733310043812,
0.051835086196660995,
-0.0029840972274541855,
-0.01377157773822546,
0.01076649408787489,
-0.041909269988536835,
-0.03619607165455818,
-0.04446844384074211,
0.0013173605548217893,
-0.008670004084706306,
-0.02060873433947563,
0.02259823866188526,
0.01577947288751602,
0.014079293236136436,
-0.052234988659620285,
-0.0407148040831089,
0.017792141065001488,
0.018758494406938553,
0.010693734511733055,
-0.0036402149125933647,
0.015200653113424778,
0.039460133761167526,
0.0006876275292597711,
0.006566241849213839,
0.03537469357252121,
-0.012214642949402332,
-0.021581072360277176,
0.017596062272787094,
-0.018130982294678688,
-0.009219344705343246,
-0.02061346173286438,
0.005536785814911127,
0.011461800895631313,
0.0045715030282735825,
0.00834843423217535,
0.015420721843838692,
-0.04589712992310524,
0.061867620795965195,
0.02074917033314705,
0.00948726013302803,
-0.003689961275085807,
0.04759994521737099,
0.02990584634244442,
0.002848843578249216,
-0.009870333597064018,
-0.039291683584451675,
-0.042471885681152344,
-0.00344946444965899,
0.03929898515343666,
0.011402911506593227,
-0.03930601105093956,
0.033892661333084106,
0.012667241506278515,
0.031219806522130966,
0.03302556276321411,
0.0007808340014889836,
-0.04123861715197563,
-0.04119940847158432,
0.001632160972803831,
0.0022099711932241917,
0.018323989585042,
0.023800572380423546,
0.013682776130735874,
-0.01647299714386463,
0.031825363636016846,
0.00857447274029255,
-0.02158002182841301,
0.012792489491403103,
-0.0006276179337874055,
0.014065411873161793,
-0.025392869487404823,
-0.05622531846165657,
0.018787140026688576,
-0.003621818032115698,
0.01876961626112461,
0.025568630546331406,
-0.026336703449487686,
0.020792074501514435,
-0.055651646107435226,
0.005691576283425093,
0.007901931181550026,
-0.0020473599433898926,
-0.006630240939557552,
-0.03156087175011635,
-0.0012634136946871877,
0.013483918271958828,
-0.020508190616965294,
-0.001244627870619297,
-0.03468126803636551,
-0.00987034011632204,
-0.058419276028871536,
0.028693359345197678,
-0.004296072293072939,
0.029679425060749054,
-0.06359054148197174,
-0.031221169978380203,
0.014513885602355003,
-0.029331840574741364,
0.03959864377975464,
0.021746383979916573,
-0.04195667430758476,
0.023712359368801117,
-0.08121302723884583,
-0.017669325694441795,
0.01878315769135952,
-0.017256198450922966,
0.04020068049430847,
0.008822574280202389,
-0.013367700390517712,
-0.045672543346881866,
-0.022455811500549316,
-0.04202526435256004,
-0.00006829557969467714,
-0.03632896766066551,
0.017928747460246086,
0.041178710758686066,
-0.02566993422806263,
-0.03145705163478851,
-0.011667822487652302,
-0.017808128148317337,
-0.02594989538192749,
-0.035644594579935074,
0.0023163259029388428,
0.0213759858161211,
-0.009637807495892048,
0.0197468139231205,
0.02603970281779766,
-0.04501337930560112,
0.012710588052868843,
-0.05566830560564995,
-0.04988659918308258,
0.003623706754297018,
0.009712365455925465,
0.04272894933819771,
0.00005853174297953956,
-0.020049532875418663,
0.07226677983999252,
0.035270169377326965,
-0.01639404334127903,
-0.018488116562366486,
0.025798669084906578,
0.009056094102561474,
-0.01957962103188038,
0.025401558727025986,
-0.005443283822387457,
0.0003893635584972799,
0.07355814427137375,
0.022717861458659172,
0.05287601798772812,
-0.009206404909491539,
0.016998382285237312,
-0.07665731757879257,
-0.013375614769756794,
0.021849993616342545,
0.05002207309007645,
0.01295143086463213,
-0.005765797104686499,
-0.03129823878407478,
0.016500364989042282,
-0.0018005305901169777,
0.001311351777985692,
0.0064904820173978806,
-0.045981042087078094,
0.06932062655687332,
-0.009495407342910767,
0.0073656197637319565,
-0.05234505236148834,
0.036915604025125504,
-0.016415417194366455,
-0.018808243796229362,
0.008075106889009476,
0.010231412947177887,
0.037370696663856506,
0.0008361656800843775,
0.01785932295024395,
0.008261789567768574,
0.02214016392827034,
-0.04363096505403519,
-0.01861286163330078,
-0.00007689599442528561,
-0.005065282806754112,
0.03312790393829346,
-0.0005138752749189734,
-0.0014547000173479319,
0.053572848439216614,
0.0730869323015213,
0.01759936660528183,
0.00020519479585345834,
-0.032783981412649155,
-0.015805983915925026,
-0.0270176213234663,
0.0049542211927473545,
-0.02660091035068035,
0.04167892038822174,
0.0019189767772331834,
0.05962956324219704,
0.06836144626140594,
0.01101800985634327,
-0.0020980658009648323,
-0.01907353103160858,
-0.07094337791204453,
0.03226292505860329,
-0.0375538095831871,
0.0259841438382864,
-0.00445640878751874,
0.021394925191998482,
0.030827846378087997,
-0.02909853309392929,
-0.041873518377542496,
-0.024184351786971092,
0.0012202751822769642,
-0.06081228703260422,
-0.010199076496064663,
-0.04484349489212036,
-0.06336577981710434,
-0.01945478841662407,
0.045332033187150955,
0.05062786117196083,
-0.05880715698003769,
0.01381014846265316,
0.015848182141780853,
-0.046423330903053284,
-0.0013398079900071025,
-0.016699695959687233,
0.005673458334058523,
0.02053241617977619,
0.004306710325181484,
0.0335732139647007,
0.019147440791130066,
-0.010402758605778217,
-0.0003506129141896963,
0.038003526628017426,
0.06615959852933884,
-0.010534212924540043,
0.03125472739338875,
0.004913913551717997,
-0.047797154635190964,
-0.00017702461627777666,
-0.011291458271443844,
0.010678602382540703,
0.017444102093577385,
0.035736750811338425,
0.007110370323061943,
0.06013723462820053,
-0.03337655961513519,
0.04551684856414795,
0.042911551892757416,
-0.01667480356991291,
-0.0017848467687144876,
-0.015930145978927612,
-0.00973274651914835,
-0.022421114146709442,
-0.002852303208783269,
-0.012183192186057568,
-0.018686629831790924,
-0.022535469383001328,
0.03469298034906387,
0.04018566757440567,
0.015879642218351364,
-0.044170018285512924,
-0.00526266498491168,
0.005827005952596664,
0.020021138712763786,
0.022131018340587616,
0.013437064364552498,
0.020380917936563492,
0.056433647871017456,
0.05980692058801651,
0.013435148634016514,
-0.008246130309998989,
-0.0548771433532238,
-0.008128681220114231,
0.04348999261856079,
0.031910575926303864,
0.002546701580286026,
-0.0127954026684165,
-0.03492632135748863,
-0.04852451756596565,
0.0390862300992012,
-0.014624999836087227,
0.04081639647483826,
0.003665890311822295,
-0.02995666302740574,
-0.007708034943789244,
-0.027797412127256393,
-0.02966245636343956,
0.03643240034580231,
-0.010072572156786919,
-0.004700887482613325,
-0.03364826738834381,
-0.0037919734604656696,
-0.04039311036467552,
-0.018945159390568733,
-0.01697271317243576,
-0.0029495626222342253,
-0.009157774969935417,
0.01146485935896635,
-0.016326110810041428,
0.021045073866844177,
-0.008729199878871441,
-0.0906495749950409,
0.021010421216487885,
0.013601621612906456,
-0.026116225868463516,
0.04845847561955452,
0.002656528726220131,
-0.020359555259346962,
0.04399624094367027,
-0.0032044174149632454,
-0.004326286260038614,
0.01749674789607525,
-0.05127133056521416,
0.054666917771101,
0.015868332237005234,
0.013725591823458672,
0.03182605654001236,
0.04726019874215126,
-0.012128908187150955,
-0.018228458240628242,
-0.0025607014540582895,
0.028762299567461014,
-0.05502753332257271,
0.04106384515762329,
-0.05730747804045677,
-0.01271082740277052,
-0.05048641934990883,
0.07390717417001724,
-0.04074384272098541,
-0.035936590284109116,
-0.008488242514431477,
-0.015475901775062084,
0.025000978261232376,
0.009024308994412422,
0.02891540341079235,
-0.015482147224247456,
-0.004885471425950527,
0.022390302270650864,
-0.0031019141897559166,
-0.012663621455430984,
-0.0012739489320665598,
-0.004175011534243822,
-0.021222801879048347,
0.021100305020809174,
-0.0004093311436008662,
0.020447302609682083,
-0.05112123861908913,
-0.07044415175914764,
0.021915670484304428,
-0.010692722164094448,
0.0207449272274971,
-0.01807243935763836,
0.00017149279301520437,
0.021132877096533775,
-0.05175406485795975,
-0.022262955084443092,
0.046986375004053116,
-0.012928467243909836,
-0.024401897564530373,
-0.013554173521697521,
-0.00283799902535975,
0.004762823693454266,
0.017380036413669586,
-0.12529204785823822,
-0.009822339750826359,
0.030324604362249374,
-0.016057487577199936,
-0.011353954672813416,
-0.019049623981118202,
-0.023488415405154228,
-0.022686878219246864,
-0.028735371306538582,
0.02551913820207119,
0.012659122236073017,
-0.05580732226371765,
0.0004195916117168963,
-0.0010432645212858915,
0.007387480698525906,
-0.005617334973067045,
-0.03868397697806358,
-0.009035115130245686,
-0.018230387941002846,
-0.03050347790122032,
0.022252630442380905,
0.01548667624592781,
0.06764833629131317,
-0.020161034539341927,
-0.009485399350523949,
-0.01902255415916443,
-0.014007346704602242,
0.01403044443577528,
-0.03121507726609707,
-0.01714346557855606,
0.001289309118874371,
-0.0022010686807334423,
-0.021659843623638153,
-0.03402533009648323,
0.006385709159076214,
0.00850361492484808,
0.024861309677362442,
0.010294996201992035,
-0.030130617320537567,
-0.0029297282453626394,
-0.05500541254878044,
0.022543461993336678,
-0.0003827942709904164,
-0.0004793265834450722,
0.02490910515189171,
0.031898174434900284,
-0.01272252481430769,
-0.019656585529446602,
-0.00702103553339839,
-0.020626351237297058,
0.02409486100077629,
-0.0038413156289607286,
-0.024321436882019043,
-0.0032141010742634535,
-0.010400716215372086,
-0.031320374459028244,
-0.05288740620017052,
-0.006121345795691013,
0.015073321759700775,
0.048594433814287186,
-0.010240512900054455,
0.02444855496287346,
0.037056904286146164,
0.010044986382126808,
-0.014578723348677158,
-0.05559038743376732,
0.01786687970161438,
0.005605517886579037,
0.025088271126151085,
0.04113999381661415,
-0.045028943568468094,
0.011234273202717304,
0.012610482051968575,
0.07421309500932693,
-0.03303839638829231,
0.04217175766825676,
0.04333392530679703,
0.03759725019335747,
0.03843587264418602,
-0.02731229178607464,
-0.03395719453692436,
0.04388975352048874,
-0.05570847541093826,
0.015247832983732224,
-0.024382559582591057,
0.019016826525330544,
0.023718807846307755,
0.02812502719461918,
0.02172975242137909,
-0.021588994190096855,
-0.019641311839222908,
-0.06322009116411209,
0.013452394865453243,
0.01990451104938984,
0.01737399771809578,
0.0007246665772981942,
0.033988140523433685,
0.029772527515888214,
-0.0029396468307822943,
-0.011125082150101662,
0.01771104335784912,
-0.06490907818078995,
-0.021795347332954407,
-0.02536129020154476,
-0.017966365441679955,
0.03424099087715149,
-0.005217838566750288,
-0.016884051263332367,
0.01160265039652586,
-0.01785224862396717,
0.031833354383707047,
-0.004618623293936253,
0.03247704729437828,
-0.026526175439357758,
0.015750760212540627,
0.0007605067803524435,
0.06393849849700928,
-0.012341944500803947,
0.006747452076524496,
0.11252033710479736,
0.06291859596967697,
0.03168707340955734,
-0.024649059399962425,
0.024317411705851555,
-0.00460145203396678,
0.031200941652059555,
0.007309552747756243,
0.0006984745268709958,
0.005989470053464174,
-0.004112199414521456,
0.0045373341999948025,
0.08432687819004059,
0.012480107136070728,
-0.004369066096842289,
0.04687506705522537,
-0.080083929002285,
-0.02657455764710903,
-0.024066468700766563,
0.042210958898067474,
-0.005849516950547695,
0.020612506195902824,
-0.048413801938295364,
0.02362813428044319,
-0.026858221739530563,
-0.0275175292044878,
-0.020373957231640816,
-0.03778092563152313,
0.006507351528853178,
-0.0001649866026127711,
-0.014974942430853844,
0.007788587361574173,
0.002034655539318919,
-0.02717428281903267,
-0.07109827548265457,
-0.008420484140515327,
0.02933925949037075,
-0.010098903439939022,
0.04732340946793556,
0.0340832956135273,
0.009434095583856106,
-0.013618766330182552,
-0.00020155713718850166,
0.005841259378939867,
-0.06234842538833618,
-0.01772065833210945,
0.004948650952428579,
0.06310205161571503,
-0.01645166426897049,
0.016515519469976425,
-0.038018763065338135,
-0.025912754237651825,
0.0303658377379179,
-0.013654432259500027,
-0.04551428183913231,
-0.011303047649562359,
0.017644686624407768,
-0.02966996841132641,
-0.002135662594810128,
-0.028240501880645752,
0.017316460609436035,
-0.01798248291015625,
0.004566728137433529,
-0.0015937694115564227,
0.0032898413483053446,
0.03608546778559685,
-0.008854136802256107,
0.032406050711870193,
0.022312425076961517,
-0.00419742614030838,
-0.007306073792278767,
-0.024765677750110626,
-0.025836344808340073,
-0.02501205913722515,
0.04713500291109085,
-0.029018152505159378,
0.046329353004693985,
-0.0021795255597680807,
0.005436289124190807,
-0.0018977639265358448,
-0.055601805448532104,
0.033601775765419006,
-0.0378943607211113,
-0.019229231402277946,
0.004298515617847443,
0.01684308983385563,
0.0281972773373127,
0.036433517932891846,
-0.05706111714243889,
0.008547329343855381,
0.015623818151652813,
0.0031311889179050922,
0.006157632451504469,
0.0005262704216875136,
-0.03225475549697876,
0.026035400107502937,
-0.023922502994537354,
-0.009937227703630924,
-0.03617905452847481,
-0.009226985275745392,
0.03331752121448517,
-0.00394670432433486,
0.015289447270333767,
0.04209703207015991,
-0.01788802444934845,
-0.031336598098278046,
0.04853416234254837,
-0.021202804520726204,
0.011365553364157677,
0.006605545990169048,
0.04118972644209862,
-0.022303473204374313,
-0.06092314422130585,
0.02496919594705105,
0.0038384285289794207,
-0.014917489141225815,
0.009599769487977028,
-0.023302866145968437,
0.011821286752820015,
-0.014283672906458378,
0.021899141371250153,
-0.061135075986385345,
-0.009463218040764332,
-0.06159752607345581,
-0.024648157879710197,
0.032180193811655045,
-0.03593306988477707,
0.002172537613660097,
0.056109536439180374,
0.02852216735482216,
-0.018023958429694176,
0.03507104516029358,
0.05295111984014511,
-0.005059945862740278,
0.0154299046844244,
0.05579026788473129,
0.019351890310645103,
0.027878226712346077,
0.04477108642458916,
-0.006368416361510754,
0.02811232954263687,
-0.03507806360721588,
-0.04713086038827896,
0.05475909262895584,
-0.015464096330106258,
0.012654315680265427,
0.02037738636136055,
0.0087813725695014,
-0.024577707052230835,
0.030819838866591454,
0.007246834691613913,
0.010749643668532372,
0.0167764350771904,
-0.015805350616574287,
-0.010559877380728722,
-0.02901208959519863,
0.04206417500972748,
-0.013418813236057758,
-0.038669403642416,
0.049454689025878906,
0.030675619840621948,
0.006088754627853632,
-0.0055862171575427055,
0.016620885580778122,
0.0023456793278455734,
0.03801500052213669,
0.0032688849605619907,
-0.006319054868072271,
0.0025023079942911863,
0.06871640682220459,
-0.03626162186264992,
0.04780114069581032,
0.03161952644586563,
0.027690034359693527,
-0.09228403866291046,
0.008645448833703995,
0.018787696957588196,
0.01316833682358265,
0.008510613813996315,
-0.03836052864789963,
0.037005919963121414,
0.04271938279271126,
-0.055429838597774506,
0.03216220438480377,
-0.022486712783575058,
-0.009470426477491856,
-0.0072387889958918095,
-0.012694921344518661,
-0.03983421251177788,
0.05498350039124489,
0.011307395994663239,
0.05557640269398689,
0.02555021643638611,
0.0460207536816597,
-0.011265202425420284,
-0.035357750952243805,
-0.02874508872628212,
0.04410551115870476,
-0.008406000211834908,
-0.014025215990841389,
0.09610199928283691,
-0.003627119353041053,
-0.02920566312968731,
0.006408073473721743,
-0.03252400830388069,
-0.028526902198791504,
-0.007864018902182579,
-0.004479303956031799,
-0.009303370490670204,
-0.004528206307440996,
0.0009530090028420091,
0.025269964709877968,
0.015604736283421516,
0.023927995935082436,
0.05444797873497009,
0.038471683859825134,
0.014635474421083927,
0.02406158670783043,
-0.013451614417135715,
-0.04312129691243172,
-0.0011561264982447028,
0.021026886999607086,
-0.020297635346651077,
-0.006919811014086008,
0.0101488521322608,
0.005143058020621538,
0.013385255821049213,
-0.01223932858556509,
0.029447928071022034,
-0.01842108555138111,
-0.03702225163578987,
0.015644323080778122,
0.0435970164835453,
-0.015879252925515175,
0.0518028624355793,
-0.01131038274616003,
-0.010844927281141281,
0.025413641706109047,
0.010183676145970821,
0.009264525026082993,
-0.04985294118523598,
-0.004310067743062973,
-0.012996271252632141,
-0.007342048920691013,
0.026788724586367607,
-0.01942760869860649,
-0.031710293143987656,
0.024298688396811485,
0.000984442187473178,
0.01628277078270912,
-0.023967145010828972,
-0.04291882365942001,
-0.0070471083745360374,
-0.0952051430940628,
0.012947332113981247,
-0.015419086441397667,
0.038116782903671265,
-0.03254152089357376,
-0.006872763857245445,
0.008236175402998924,
0.0034068741369992495,
0.03160063549876213,
0.0020563427824527025,
-0.0272133257240057,
0.062179338186979294,
-0.0036595601122826338,
0.013328218832612038,
-0.03572744131088257,
-0.011502503417432308,
-0.02419222891330719,
0.014698616228997707,
0.01335940696299076,
-0.03674134984612465,
0.006986288353800774,
0.01764334924519062,
0.022885268554091454,
-0.00508390087634325,
0.008734520524740219,
0.0031325966119766235,
-0.047916654497385025,
0.07458829134702682,
-0.02642069198191166,
-0.01384758297353983,
0.0756673738360405,
0.00240781856700778,
0.0008801200310699642,
0.048355832695961,
-0.012135797180235386,
-0.04147883132100105,
-0.00652185408398509,
-0.04480014368891716,
-0.03879968449473381,
0.0003702616086229682,
-0.021916473284363747,
0.02604834735393524,
-0.011568977497518063,
-0.005939677823334932,
0.02538386546075344,
-0.03448302671313286,
-0.02001373842358589,
0.046480488032102585,
0.008392715826630592,
0.05616838485002518,
-0.00152147829066962,
-0.0006515296990983188,
0.022756660357117653,
0.019351668655872345,
-0.00906434841454029,
0.029929449781775475,
0.019411129876971245,
0.02683255448937416,
0.022703958675265312,
0.019734805449843407,
-0.011938081122934818,
0.013629943132400513,
0.017467541620135307,
0.00945368967950344,
-0.01867523044347763,
0.007040827069431543,
0.03455282002687454,
0.01647142507135868,
0.02870718017220497,
-0.013665071688592434,
-0.02441481314599514,
0.06484759598970413,
0.017614740878343582,
0.02703547663986683,
-0.02567349374294281,
0.014002826996147633,
-0.020257843658328056,
-0.012179555371403694,
0.0011009927839040756,
0.03482132405042648,
-0.03729759156703949,
-0.009010490030050278,
-0.04349954053759575,
0.02227545529603958,
0.01025477796792984,
-0.04721895977854729,
0.022617600858211517,
-0.00787345226854086,
-0.025918850675225258,
0.007987900637090206,
-0.02700752578675747,
-0.022089144214987755,
-0.04559985175728798,
0.0330466665327549,
0.036288175731897354,
0.026114722713828087,
0.012369513511657715,
-0.005080771632492542,
-0.03777676820755005,
0.060983482748270035,
-0.06556227803230286,
-0.019230658188462257,
-0.030091429129242897,
0.01907452382147312,
-0.03773074224591255,
-0.016300596296787262
] |
<p>Did the geocentric theorists also use the fact that the earth had an axis tilt? Or was their explanation of some other kind?</p>
| 10,771 |
[
-0.044313035905361176,
-0.020453274250030518,
-0.028994079679250717,
0.012315133586525917,
0.06323876976966858,
0.020208902657032013,
-0.009433460421860218,
0.003556701820343733,
-0.009595384821295738,
-0.03183051571249962,
-0.021368827670812607,
0.02127542719244957,
0.030925657600164413,
0.003949049394577742,
0.029158098623156548,
-0.002122914418578148,
-0.0059906779788434505,
0.011180019937455654,
-0.00826659332960844,
-0.05205486714839935,
-0.018251607194542885,
-0.009915759786963463,
-0.04634927585721016,
0.01642608642578125,
-0.00215463456697762,
0.01649419404566288,
0.053090114146471024,
-0.016315016895532608,
0.01791556365787983,
0.043515078723430634,
0.02034374326467514,
0.027036622166633606,
0.0015386182349175215,
0.017902743071317673,
0.042625490576028824,
-0.04106086492538452,
0.016070568934082985,
-0.00005049735773354769,
-0.0026833347510546446,
0.06514155864715576,
-0.03437233343720436,
0.01371782273054123,
-0.01782580092549324,
0.020237009972333908,
-0.01533692516386509,
0.03704885393381119,
-0.03240303695201874,
-0.009592900052666664,
0.037936728447675705,
-0.03675359487533569,
0.0543111115694046,
-0.04570556804537773,
-0.028706829994916916,
0.004529127851128578,
-0.0010836810106411576,
0.030166052281856537,
0.07358092814683914,
0.030011892318725586,
-0.03538001701235771,
-0.06118176504969597,
-0.0339621864259243,
-0.017400728538632393,
0.01078625675290823,
-0.030205680057406425,
-0.014034689404070377,
-0.004840550944209099,
0.01566319167613983,
-0.04194793477654457,
0.04322849586606026,
0.009806822054088116,
-0.014861227944493294,
0.049291156232357025,
0.012028804048895836,
-0.026498882099986076,
-0.01510881818830967,
-0.04247872158885002,
-0.0003155110462103039,
-0.00996658205986023,
0.036227498203516006,
0.006841949187219143,
0.0032453974708914757,
-0.004320349544286728,
0.0283672958612442,
0.036088135093450546,
-0.006869557313621044,
0.027492370456457138,
0.05506182461977005,
0.004476689267903566,
-0.006919750012457371,
0.033994778990745544,
0.01253596879541874,
0.018174560740590096,
0.02164251171052456,
-0.02259061671793461,
-0.04792601242661476,
0.04438260570168495,
0.0017902025720104575,
0.023634854704141617,
0.04493332281708717,
-0.007132823579013348,
0.008681477047502995,
-0.01726272888481617,
0.009374711662530899,
0.075437031686306,
0.021317850798368454,
-0.003952092956751585,
-0.05090160667896271,
0.02009829878807068,
-0.03069034032523632,
0.00966203585267067,
0.008993325755000114,
0.01086715143173933,
-0.01143771130591631,
-0.020092152059078217,
0.03461170569062233,
0.009769161231815815,
0.005051966290920973,
-0.016931161284446716,
0.04625349119305611,
0.055089931935071945,
0.03897576406598091,
-0.006293139886111021,
0.009640134871006012,
-0.011009500361979008,
-0.05660705268383026,
0.0038619302213191986,
0.007416774984449148,
-0.002720748307183385,
0.000773870327975601,
0.017489753663539886,
0.023872895166277885,
-0.009634287096560001,
-0.03679327294230461,
0.026363497599959373,
0.038055118173360825,
0.00281134364195168,
-0.08410653471946716,
-0.05788162350654602,
0.07082163542509079,
0.01161617785692215,
-0.006581644527614117,
-0.056776173412799835,
-0.003634685417637229,
-0.009493716061115265,
0.07302851974964142,
0.010747617110610008,
-0.02611674927175045,
-0.02045411802828312,
0.024147434160113335,
-0.016592370346188545,
-0.0253008846193552,
-0.016803769394755363,
0.0012645561946555972,
-0.05234145745635033,
-0.023859085515141487,
-0.08809851109981537,
-0.018570082262158394,
0.011034748516976833,
0.0146252466365695,
-0.030052559450268745,
0.036467816680669785,
-0.001230626367032528,
-0.00789138488471508,
0.0012567633530125022,
-0.031880490481853485,
-0.021799327805638313,
0.06970738619565964,
0.0019456782611086965,
-0.014489608816802502,
0.031017569825053215,
-0.008410834707319736,
0.06067122891545296,
0.04009036719799042,
0.03676725551486015,
0.00731262331828475,
-0.039090946316719055,
0.004074149299412966,
0.023840004578232765,
0.01345251128077507,
0.009370546787977219,
-0.015968430787324905,
-0.016275515779852867,
0.041629940271377563,
0.016238700598478317,
-0.049671463668346405,
0.10361792892217636,
-0.03641274943947792,
-0.026091957464814186,
0.028697233647108078,
-0.039030324667692184,
0.02152554877102375,
-0.02842170000076294,
0.00652774004265666,
-0.021674951538443565,
-0.0018993796547874808,
0.008843629620969296,
0.036138471215963364,
0.04980985075235367,
-0.035063907504081726,
-0.004327123519033194,
-0.00012920550943817943,
0.06722899526357651,
0.029737617820501328,
-0.03355731442570686,
0.032235316932201385,
0.06494948267936707,
0.047132182866334915,
-0.003805664600804448,
0.010059354826807976,
-0.023189295083284378,
-0.031716056168079376,
0.009211388416588306,
0.00003398930130060762,
0.029864996671676636,
0.001814208459109068,
0.011948313564062119,
-0.049467820674180984,
0.01779298670589924,
-0.006730071734637022,
0.03151609003543854,
-0.04368242248892784,
0.08043699711561203,
0.03201034292578697,
-0.0035871672444045544,
0.0287860669195652,
0.07376042008399963,
0.02980685420334339,
0.013745770789682865,
0.0208986084908247,
-0.012608890421688557,
-0.04263106361031532,
-0.0012216895120218396,
0.047853995114564896,
0.04251404479146004,
-0.028673917055130005,
-0.001937491586431861,
0.010704660788178444,
0.09400647133588791,
-0.011179748922586441,
-0.009968827478587627,
-0.0035204633604735136,
-0.06709393113851547,
-0.025038691237568855,
-0.008661240339279175,
0.0424884632229805,
0.024466760456562042,
0.03445890173316002,
0.017010102048516273,
-0.04504680633544922,
-0.020840199664235115,
-0.06300880014896393,
0.030049294233322144,
0.03286844491958618,
0.03675494343042374,
0.027791611850261688,
-0.003419864224269986,
0.04059233143925667,
-0.014952674508094788,
0.010685872286558151,
-0.002393874805420637,
0.0013934007147327065,
-0.0007716860854998231,
-0.00843633059412241,
0.008806115947663784,
-0.0026716089341789484,
0.015235329046845436,
-0.022396357730031013,
-0.01208643987774849,
0.04850291088223457,
-0.023093320429325104,
0.00605012709274888,
-0.06925830245018005,
-0.01985730230808258,
0.03003988042473793,
-0.030408259481191635,
0.04211072996258736,
0.022398682311177254,
0.03012358769774437,
-0.008697009645402431,
-0.00017250516975764185,
0.00998573750257492,
-0.01790260709822178,
-0.03057435154914856,
0.040060095489025116,
-0.04518761485815048,
0.023668188601732254,
-0.03000692091882229,
0.010631218552589417,
0.010522379539906979,
0.008472387678921223,
0.0368783213198185,
-0.009028651751577854,
0.006271625403314829,
-0.03706818446516991,
-0.03258945047855377,
-0.02069646678864956,
-0.009530152194201946,
-0.01668001152575016,
-0.001938908244483173,
0.03251098468899727,
0.004121535923331976,
0.021665723994374275,
0.03818809241056442,
-0.06102437153458595,
-0.025927988812327385,
0.004124089144170284,
0.013417697511613369,
0.012068049982190132,
-0.034846242517232895,
0.02950371988117695,
-0.003647039644420147,
-0.0656508058309555,
-0.026417480781674385,
-0.03674511983990669,
-0.05057530850172043,
0.034643545746803284,
-0.02988680638372898,
0.031536832451820374,
0.001427690265700221,
-0.013626155443489552,
0.046186745166778564,
0.013671275228261948,
-0.02131551131606102,
-0.03884609788656235,
0.000016246927771135233,
0.008987647481262684,
0.014135882258415222,
0.02891208603978157,
0.0070165120996534824,
0.028857439756393433,
0.012400085106492043,
0.014912847429513931,
-0.032172709703445435,
0.024050861597061157,
0.04299333691596985,
-0.012358597479760647,
0.013296724297106266,
-0.017260756343603134,
0.0190863199532032,
-0.012798519805073738,
0.015520570799708366,
0.01948072388768196,
0.0026492334436625242,
-0.005336356814950705,
0.07034536451101303,
-0.0039171501994132996,
-0.05235627293586731,
0.06445645540952682,
-0.019714457914233208,
0.005882772617042065,
-0.020164987072348595,
0.02470233663916588,
0.0036293482407927513,
0.03744404390454292,
0.004152829758822918,
0.009431588463485241,
0.025207458063960075,
0.007370221894234419,
-0.04342446103692055,
0.010999868623912334,
0.01631321758031845,
-0.041580911725759506,
0.011719677597284317,
0.010942541062831879,
0.021716466173529625,
0.042845796793699265,
-0.009997954592108727,
-0.027720468118786812,
0.061054129153490067,
0.031224939972162247,
-0.0027931698132306337,
0.05657332390546799,
-0.041625261306762695,
0.016768503934144974,
-0.06915982067584991,
0.044010452926158905,
-0.02037856914103031,
0.0043786074966192245,
-0.019674288108944893,
0.02773679792881012,
0.025818534195423126,
0.030696701258420944,
-0.01451526302844286,
0.021117040887475014,
-0.028962314128875732,
0.01571034826338291,
-0.07177852839231491,
0.026811910793185234,
-0.006822470109909773,
0.005150585900992155,
0.01719477027654648,
-0.0076436870731413364,
-0.030156506225466728,
-0.046289630234241486,
-0.040515583008527756,
-0.04366752877831459,
0.00969761610031128,
0.021745486184954643,
-0.060884665697813034,
0.00605732062831521,
0.05155864357948303,
0.024274321272969246,
-0.011566787958145142,
0.02414790727198124,
0.056289076805114746,
-0.015272597782313824,
-0.0017232494428753853,
0.0008122351719066501,
0.016613373532891273,
-0.017843889072537422,
-0.0018774830969050527,
0.011757687665522099,
-0.015513598918914795,
-0.019962171092629433,
0.001415845239534974,
-0.005590413231402636,
0.06768646091222763,
0.007605601567775011,
-0.012465668842196465,
-0.028598451986908913,
-0.05419977754354477,
0.009159897454082966,
-0.011664504185318947,
0.03462229669094086,
-0.044701576232910156,
0.000671671936288476,
0.03267665579915047,
0.0019026504596695304,
0.009041858837008476,
0.06412721425294876,
0.03702133521437645,
0.04640667885541916,
-0.04039247706532478,
-0.020106449723243713,
-0.016308141872286797,
-0.011800192296504974,
0.018300535157322884,
0.015515442937612534,
-0.007536742836236954,
-0.04511425271630287,
-0.018790123984217644,
0.015431900508701801,
-0.019206702709197998,
-0.008472448214888573,
0.004440548829734325,
0.034987930208444595,
0.05149845406413078,
0.03562558814883232,
0.014635740779340267,
-0.021037928760051727,
0.00957688968628645,
0.045248597860336304,
0.0231089498847723,
-0.021020179614424706,
-0.06053144857287407,
-0.01654062047600746,
0.016393575817346573,
-0.014816648326814175,
-0.04074574261903763,
0.0026540097314864397,
-0.06958784908056259,
-0.003932959865778685,
0.06434459239244461,
-0.02144135721027851,
0.012665861286222935,
-0.05191008746623993,
0.014134177938103676,
-0.012864891439676285,
0.018712440505623817,
-0.03410473093390465,
-0.005323429126292467,
0.00046718583325855434,
0.039416681975126266,
-0.019564608111977577,
0.013998004607856274,
-0.03181702271103859,
0.008836452849209309,
0.009870698675513268,
0.0264651570469141,
0.04183146357536316,
0.01452905684709549,
-0.024023832753300667,
0.04904693365097046,
-0.029727580025792122,
-0.05985596030950546,
-0.03874759003520012,
0.04622171074151993,
-0.01685519330203533,
-0.007137991022318602,
-0.014783890917897224,
-0.03394295647740364,
0.022018712013959885,
-0.019492127001285553,
-0.005519568454474211,
-0.00035674675018526614,
-0.061797428876161575,
0.0026433488819748163,
0.0024089228827506304,
-0.023275015875697136,
0.026907170191407204,
0.006873717997223139,
-0.07475975155830383,
-0.023569321259856224,
-0.02577194757759571,
0.02966354973614216,
-0.05678441748023033,
-0.024056658148765564,
0.023904860019683838,
-0.01431251596659422,
-0.020990192890167236,
0.02750689536333084,
0.03138484060764313,
0.02541213668882847,
0.0035177883692085743,
-0.030734047293663025,
-0.026433244347572327,
0.015636403113603592,
-0.002578901359811425,
0.008865890093147755,
0.0025533733423799276,
0.02612135373055935,
0.0034055467694997787,
-0.022038450464606285,
0.029950281605124474,
-0.024322839453816414,
-0.016532909125089645,
0.001817910117097199,
0.01947949081659317,
0.005345280282199383,
-0.05442894250154495,
-0.0012515241978690028,
0.012650541961193085,
-0.030747966840863228,
0.0465884730219841,
-0.04202453792095184,
-0.01354501023888588,
0.06969279050827026,
-0.10429075360298157,
-0.027228837832808495,
0.006506182253360748,
-0.007829575799405575,
0.04215848818421364,
-0.024371882900595665,
-0.008818579837679863,
0.009233267977833748,
0.0180100966244936,
-0.09522692859172821,
-0.024516666308045387,
0.018622035160660744,
0.0025353904347866774,
-0.009942279197275639,
-0.023542724549770355,
-0.010329545475542545,
-0.02885502576828003,
-0.012623404152691364,
0.0221061110496521,
0.047007087618112564,
-0.008444453589618206,
-0.01026760321110487,
-0.024795284494757652,
0.006170342676341534,
0.038413625210523605,
-0.039197467267513275,
-0.02191467024385929,
0.025104207918047905,
-0.0369877927005291,
0.019313350319862366,
-0.03481651470065117,
0.06605712324380875,
-0.016855360940098763,
-0.01633584126830101,
0.011677366681396961,
-0.011599427089095116,
-0.03011413849890232,
-0.005471682641655207,
-0.03747478872537613,
0.0397779680788517,
-0.037590764462947845,
-0.035667888820171356,
-0.02308938466012478,
0.04858538508415222,
-0.036836229264736176,
0.022334741428494453,
-0.03348086401820183,
0.018969591706991196,
0.007693791296333075,
-0.03597457334399223,
0.05773722752928734,
-0.003914796747267246,
-0.027311254292726517,
0.030560793355107307,
0.07767343521118164,
-0.01699506677687168,
-0.009169179014861584,
0.026323173195123672,
0.015087280422449112,
0.01405240222811699,
0.024450672790408134,
0.01193479634821415,
0.0014224388869479299,
0.008196990005671978,
-0.014842764474451542,
-0.015541134402155876,
0.01429365947842598,
0.031243329867720604,
0.07054902613162994,
-0.020678065717220306,
0.04998364299535751,
0.026340290904045105,
-0.012079001404345036,
-0.009769955649971962,
-0.06116490438580513,
0.018116984516382217,
0.0004975395859219134,
-0.0012407797621563077,
0.05287250131368637,
-0.06108904629945755,
0.0063102771528065205,
0.04705962538719177,
0.04695598781108856,
-0.018439333885908127,
0.0072916666977107525,
-0.002563078422099352,
0.04539909586310387,
0.006153794936835766,
0.020144829526543617,
-0.046483103185892105,
0.02921423502266407,
-0.026717886328697205,
0.021092625334858894,
-0.021861432120203972,
-0.03329004347324371,
0.027929799631237984,
-0.005626345053315163,
-0.01679312251508236,
-0.024899177253246307,
-0.007295817602425814,
-0.03342072665691376,
0.0005788797279819846,
0.02503811940550804,
0.03239412605762482,
-0.005015148315578699,
-0.0066848257556557655,
0.043138884007930756,
-0.038164373487234116,
-0.013752228580415249,
-0.006334702949970961,
-0.08930888026952744,
-0.021623387932777405,
0.006348638329654932,
-0.07585201412439346,
0.015604055486619473,
0.014846855774521828,
-0.006164421793073416,
0.00012297095963731408,
-0.005530021619051695,
-0.007371078245341778,
0.055246565490961075,
0.029087966307997704,
-0.01940258778631687,
0.07619322836399078,
-0.02550777979195118,
-0.026779379695653915,
0.006552950944751501,
-0.03262333199381828,
0.13065676391124725,
0.03475796803832054,
0.013619794510304928,
-0.07957545667886734,
0.062212370336055756,
-0.011169547215104103,
-0.02127690427005291,
-0.05126062035560608,
0.01596316508948803,
-0.02518862672150135,
0.015767812728881836,
-0.0085421958938241,
0.05847625434398651,
0.034200090914964676,
-0.0394296795129776,
0.05478843301534653,
-0.02070290967822075,
-0.04697886481881142,
-0.03129751607775688,
0.009762212634086609,
-0.024570027366280556,
0.0013795739505439997,
-0.01857193373143673,
0.0061169881373643875,
-0.04079810529947281,
-0.00491307582706213,
-0.01746307499706745,
-0.04503117501735687,
-0.008256370201706886,
0.054796166718006134,
-0.059971123933792114,
0.02251165546476841,
0.05039994418621063,
-0.0293105635792017,
-0.07285867631435394,
-0.004529840312898159,
0.005869345273822546,
0.005692843813449144,
0.033306486904621124,
-0.011472373269498348,
-0.029731348156929016,
0.011357735842466354,
-0.016386674717068672,
0.028661422431468964,
-0.04104238376021385,
0.019187727943062782,
-0.037262748926877975,
-0.02118414267897606,
0.010402101092040539,
-0.0025076798629015684,
0.009150265716016293,
-0.05597878620028496,
-0.04121866822242737,
-0.04380097985267639,
-0.012384100817143917,
-0.028340009972453117,
0.029927881434559822,
0.0004524389805737883,
-0.05201580002903938,
0.015144002623856068,
0.026471983641386032,
-0.008502990007400513,
0.06411849707365036,
-0.013560298830270767,
0.002320891246199608,
0.001273792120628059,
-0.0058437432162463665,
0.00017074721108656377,
0.015651635825634003,
-0.020889785140752792,
0.003744669258594513,
-0.02680116891860962,
-0.058215297758579254,
0.006585759576410055,
0.008203920908272266,
0.030181827023625374,
0.014956850558519363,
0.018379658460617065,
-0.019365916028618813,
-0.040298011153936386,
-0.0032510848250240088,
0.007485082373023033,
-0.03107820264995098,
-0.011733964085578918,
0.010211573913693428,
0.04509593918919563,
0.02980625443160534,
0.023254459723830223,
-0.0017631754744797945,
0.01924515701830387,
-0.047626592218875885,
-0.009424400515854359,
0.005258144810795784,
-0.010630150325596333,
-0.009358126670122147,
0.023298418149352074,
-0.029066534712910652,
-0.04182044789195061,
-0.05272629112005234,
0.02831960842013359,
0.07326134294271469,
0.027798498049378395,
-0.003961082547903061,
0.017960762605071068,
-0.004796053748577833,
0.0025068947579711676,
0.00273158960044384,
-0.06551726162433624,
-0.0018622083589434624,
0.03262219578027725,
-0.016551479697227478,
-0.05458245798945427,
-0.030551327392458916,
-0.009111982770264149,
-0.0021323945838958025,
0.005619952455163002,
0.022701887413859367,
-0.0390203557908535,
0.047773491591215134,
-0.01943046972155571,
0.04983333498239517,
-0.027546487748622894,
-0.02096933126449585,
-0.022999797016382217,
-0.015325580723583698,
-0.01186289731413126,
-0.03395865857601166,
0.022006912156939507,
0.046455878764390945,
-0.02333410643041134,
-0.027521470561623573,
0.03362838551402092,
0.0012065410846844316,
-0.012502278201282024,
0.010108576156198978,
0.04182162508368492,
0.012227191589772701,
0.028132125735282898,
-0.048751410096883774,
-0.005694222170859575,
0.01229964941740036,
-0.005906097125262022,
-0.025782866403460503,
0.034204136580228806,
-0.019352611154317856,
0.003632135223597288,
0.017577113583683968,
-0.015363115817308426,
0.012375340797007084,
0.04309212788939476,
-0.05285191908478737,
-0.0012827692553400993,
0.005344746168702841,
0.004330962896347046,
0.006859752349555492,
0.013706759549677372,
-0.014121741987764835,
-0.01556260697543621,
-0.012704861350357533,
0.05927768722176552,
0.036658283323049545,
-0.04100536182522774,
-0.020477065816521645,
0.013679937459528446,
-0.02615417167544365,
0.01565985567867756,
-0.00616003293544054,
-0.011651053093373775,
-0.0014386891853064299,
-0.014880836941301823,
-0.03497378155589104,
0.006158035714179277,
0.06018323823809624,
0.019487638026475906,
-0.07588138431310654,
0.0014756863238289952,
-0.004871044773608446,
-0.004424695391207933,
0.044644005596637726,
-0.04720897227525711,
-0.010365099646151066,
0.015306944958865643,
-0.08936718851327896,
0.01768139936029911,
-0.0077159209176898,
-0.054362185299396515,
-0.019110826775431633,
-0.02781812660396099,
0.014440429396927357,
0.04544723406434059,
0.03864937275648117,
0.04153477028012276,
0.01629939302802086,
0.01404007151722908,
-0.028737632557749748,
-0.03389182686805725,
0.020391788333654404,
0.02871812880039215,
-0.01076275110244751,
0.01145206205546856,
0.03160327300429344,
-0.03427087143063545,
-0.07056935876607895,
0.04436653479933739,
0.026107126846909523,
0.032952554523944855,
0.01591721549630165,
0.022502252832055092,
-0.0179231446236372,
0.0200691856443882,
-0.01158555131405592,
-0.04841899499297142,
0.004569596610963345,
0.0520026870071888,
0.0033928598277270794,
0.05389440059661865,
-0.01016259752213955,
-0.04065695405006409,
-0.01295152772217989,
-0.02341444604098797,
-0.019112445414066315,
0.021808182820677757,
-0.012174197472631931,
-0.0023623392917215824,
-0.01824815757572651,
0.004945068154484034,
-0.00916319526731968,
-0.03488194942474365,
-0.0025644535198807716,
-0.02639857307076454,
-0.0081245182082057,
0.046473607420921326,
-0.018960170447826385,
0.006727748550474644,
0.015142341144382954,
0.028223197907209396,
-0.005967483855783939,
-0.008594741113483906,
0.0014382476219907403,
-0.020651938393712044,
-0.04365325719118118,
0.0009818306425586343,
0.011630136519670486,
-0.015714488923549652,
-0.024716680869460106,
-0.016664346680045128,
-0.01698010042309761,
0.009402443654835224,
0.027422094717621803,
0.03617243468761444,
0.0195462629199028,
-0.05021194741129875,
0.006846016738563776,
-0.04575951769948006,
0.03687450662255287,
-0.0026530339382588863,
-0.00040791931678541005,
-0.0064541990868747234,
-0.029379427433013916,
-0.019219374284148216,
-0.0013696708483621478,
0.030389688909053802,
0.005766947753727436,
0.01838499680161476,
0.00820152834057808,
0.011501714587211609,
0.002071487018838525,
-0.01614583097398281,
0.026093363761901855,
0.018106382340192795,
-0.04441268742084503,
0.018756520003080368,
-0.030653921887278557,
-0.00454682856798172,
-0.017536330968141556,
-0.01024275366216898,
0.008810863830149174,
0.0587569884955883,
0.016045836731791496,
-0.06044066697359085,
0.040886931121349335,
0.025505490601062775,
-0.01248185709118843,
0.07953355461359024,
-0.033720578998327255,
-0.02549058198928833,
0.035932883620262146,
0.004439028445631266,
-0.038660962134599686,
0.03619297966361046,
-0.014596710912883282,
-0.017498841509222984,
-0.004892216995358467,
-0.02677399478852749,
0.000885383749846369,
-0.008581474423408508,
-0.002966910135000944,
0.05326181650161743,
0.013183066621422768,
0.0047139814123511314,
0.031283143907785416,
-0.007588233333081007,
0.015828875824809074,
0.016245732083916664,
0.003948370926082134,
0.051226306706666946,
-0.019888468086719513,
0.03350246697664261,
0.044297754764556885,
0.031551018357276917,
0.05135094374418259,
-0.011752099730074406,
0.015455166809260845,
0.038820572197437286,
0.04889562726020813,
0.0015996461734175682,
0.05298785865306854,
-0.03472723066806793,
-0.03853313624858856,
0.0189518965780735,
-0.022081537172198296,
-0.000646534375846386,
0.04532511904835701,
-0.008188423700630665,
0.06788744032382965,
-0.043463945388793945,
-0.010724669322371483,
-0.042720165103673935,
-0.019923068583011627,
-0.012296414002776146,
0.016447287052869797,
0.017796507105231285,
0.022982995957136154,
-0.023640558123588562,
0.007378252223134041,
0.013874761760234833,
-0.0013120368821546435,
0.042842693626880646,
-0.010461750440299511,
0.031907714903354645,
-0.017444921657443047,
0.028287243098020554,
0.03883456811308861,
-0.026363380253314972,
-0.020500581711530685,
-0.00557640241459012,
-0.004275474697351456,
0.025087296962738037,
0.06452329456806183,
-0.026884185150265694,
0.008396534249186516,
-0.05527816340327263,
0.03691573068499565,
-0.06536677479743958,
-0.017996149137616158,
-0.0039815581403672695,
0.03369160741567612,
0.01982945390045643,
-0.008624977432191372
] |
<p>I've been considering a career change for a long time and recently discovered the Two-Slit Experiment, which, to put it frankly, blew my mind. I then started some hefty reading and investigation into all things Quantum (Bell, Campbell, entanglement, QIT), which has led me here.</p>
<p>I have 20 years experience in IT working as a programmer, having graduated with a Bachelor in Computer Science back in the early 90s. As mentioned, I have been considering a career change for some time (having become quite burned out in this industry), and have found something that has piqued my interest more than anything else (tho I did consider Astrophysics a couple of years ago). I am not yet sure which area of "Quantum" I will be most drawn to, possibly Quantum Information Theory/Science. </p>
<p>I am aware that there is a significant amount of Maths and Physics pre-requisites involved. It seems likely, given that I have not done any Maths or Physics study probably since I was doing my CS undergrad, that I will need to start over with an undergrad in Science/Physics in order to get the fundamentals.</p>
<p>So my questions are:</p>
<ol>
<li><p>What is the ideal path of education to get to QIT/QIS or QM?</p></li>
<li><p>Is the path to QIT/QIS also via the Physics route? Can I leverage my CS background?</p></li>
<li><p>Resources (books, online courses, etc) that would help with the transition from CS-type thinking to Physics/Maths-type thinking.</p></li>
</ol>
<p>Apologies if this encompasses elements too broad or off-topic, I'm trying to get a better understanding on what is to come following this path. Thanks in advance.</p>
| 10,772 |
[
0.0016290757339447737,
-0.04259749874472618,
-0.021240251138806343,
-0.019050491973757744,
0.02858583629131317,
-0.001588911865837872,
0.0031789098866283894,
-0.04449288547039032,
0.007873707450926304,
-0.02217753231525421,
0.01629010960459709,
0.05350801348686218,
0.03444362431764603,
0.0013350410154089332,
0.019945302978157997,
-0.014684402383863926,
0.03177834674715996,
-0.0602380596101284,
-0.036140844225883484,
0.02650701254606247,
-0.01379619725048542,
0.017626281827688217,
-0.029671378433704376,
0.040567751973867416,
-0.03562983125448227,
0.06529562920331955,
0.02715715393424034,
0.004362157545983791,
-0.0036744456738233566,
0.029362082481384277,
-0.003156923223286867,
-0.01906575635075569,
-0.001131511409766972,
0.013292443007230759,
0.02807924896478653,
-0.018949661403894424,
-0.030947118997573853,
-0.053067807108163834,
0.006701676174998283,
0.029814327135682106,
-0.048772409558296204,
0.009136158972978592,
-0.024166574701666832,
0.04997509717941284,
-0.004493845626711845,
0.0064580244943499565,
-0.009454955346882343,
-0.006996146868914366,
0.023848921060562134,
-0.0627201721072197,
0.05011846497654915,
0.02741246484220028,
0.022078003734350204,
0.009594912640750408,
-0.012362497858703136,
-0.007817848585546017,
0.08210619539022446,
0.055725038051605225,
0.0034159577917307615,
-0.015430773608386517,
0.022659357637166977,
-0.00832971092313528,
-0.0006420151912607253,
-0.007382330019026995,
-0.04761429503560066,
0.01970837265253067,
-0.017995234578847885,
-0.016920853406190872,
0.004789633210748434,
-0.03191957622766495,
0.02754574827849865,
0.04938354715704918,
0.058628149330616,
0.013156497851014137,
0.03543990105390549,
-0.04896596446633339,
0.014333839528262615,
0.009833922609686852,
0.015818120911717415,
0.0235914159566164,
0.022539814934134483,
0.007171940058469772,
0.008007368072867393,
0.05265676602721214,
-0.008013359270989895,
-0.02089947648346424,
0.09886240214109421,
-0.040667250752449036,
-0.014507856220006943,
0.021751390770077705,
0.001031218678690493,
0.039612192660570145,
0.036106809973716736,
0.017734477296471596,
-0.023905813694000244,
-0.0007220447296276689,
-0.01965823955833912,
0.03664615377783775,
0.02554604411125183,
-0.019160941243171692,
-0.018987391144037247,
-0.003838576842099428,
0.028385385870933533,
0.080622598528862,
0.013704726472496986,
-0.005824278574436903,
-0.002529118675738573,
0.021240955218672752,
-0.03231659531593323,
-0.02651493437588215,
-0.023553434759378433,
0.016949612647294998,
-0.011003021150827408,
0.03366044536232948,
-0.019908741116523743,
-0.040941864252090454,
-0.0036455648951232433,
-0.05239638313651085,
0.06914588063955307,
0.07614642381668091,
0.04460624232888222,
-0.05095590278506279,
0.003516266355291009,
-0.009215917438268661,
-0.06328803300857544,
0.0031726565212011337,
0.02354295179247856,
-0.003979923203587532,
-0.04375180974602699,
0.013751509599387646,
-0.005460490472614765,
0.023299967870116234,
0.017584970220923424,
0.013770075514912605,
0.002612049924209714,
-0.016382325440645218,
-0.1486331969499588,
-0.09602183848619461,
0.05047624185681343,
0.009382606483995914,
-0.022042004391551018,
-0.08833252638578415,
0.03147376701235771,
0.046739544719457626,
0.08802637457847595,
-0.013530165888369083,
0.01245320588350296,
-0.03170981630682945,
0.009272081777453423,
0.015944629907608032,
-0.03207378834486008,
0.017053058370947838,
-0.02929740585386753,
0.005983628332614899,
0.0325792133808136,
-0.02541193924844265,
0.02661704085767269,
0.033290207386016846,
-0.003196659032255411,
-0.025498153641819954,
0.040786728262901306,
0.012398690916597843,
-0.03185887634754181,
0.018807124346494675,
0.0017624865286052227,
-0.019953003153204918,
0.09622736275196075,
0.039789363741874695,
0.013343463651835918,
0.03559958189725876,
0.010926835238933563,
-0.004951393231749535,
0.01500189770013094,
0.015097768977284431,
0.0359031967818737,
-0.030566822737455368,
0.009485729038715363,
-0.016804000362753868,
-0.018903134390711784,
-0.03149009868502617,
-0.02470499277114868,
-0.05183298513293266,
-0.01648685522377491,
0.015205352567136288,
0.022681625559926033,
-0.005998690612614155,
-0.0011384760728105903,
-0.011204725131392479,
-0.011058189906179905,
-0.04438379406929016,
-0.015427996404469013,
-0.039981044828891754,
0.0311073400080204,
-0.011839237064123154,
-0.02133568376302719,
0.005472998600453138,
0.011923168785870075,
0.0035966953728348017,
-0.01509035099297762,
-0.04557511582970619,
-0.010887588374316692,
0.01857692562043667,
0.02718149870634079,
-0.01860716938972473,
0.0036232697311788797,
0.09209941327571869,
0.02654896304011345,
-0.02468421682715416,
0.022003555670380592,
-0.062408655881881714,
-0.04874245077371597,
-0.021439481526613235,
0.00562854902818799,
0.037658218294382095,
0.004643603228032589,
0.00584017438814044,
0.0005423985421657562,
0.0003836512623820454,
-0.05394776165485382,
-0.009198246523737907,
-0.04634759947657585,
0.08299918472766876,
0.028228145092725754,
0.013561248779296875,
-0.03438039869070053,
0.03887657821178436,
0.038384247571229935,
0.037041351199150085,
-0.0033725681714713573,
-0.006728233303874731,
-0.028518734499812126,
0.03488437086343765,
0.02561064437031746,
0.008481898345053196,
-0.02718360908329487,
0.035091470927000046,
-0.010163621976971626,
0.03704801946878433,
0.012342276982963085,
-0.01697199046611786,
-0.046786703169345856,
-0.004462912678718567,
0.0011319909244775772,
-0.010253210552036762,
-0.010814252309501171,
0.02298467606306076,
0.020571326836943626,
-0.025073256343603134,
-0.03490065038204193,
0.011307137086987495,
-0.0444672666490078,
0.03188106790184975,
-0.021511225029826164,
0.0038235068786889315,
-0.010154206305742264,
-0.030363844707608223,
0.03637617081403732,
-0.020483721047639847,
-0.004447153769433498,
0.007257033139467239,
-0.002552066231146455,
-0.029704997316002846,
-0.02205696888267994,
-0.015054467134177685,
-0.016353057697415352,
-0.0023876160848885775,
-0.007065789308398962,
0.05004207044839859,
0.03890111297369003,
-0.04819289594888687,
0.012292630039155483,
0.008323648944497108,
-0.005236515309661627,
-0.045649029314517975,
-0.009029801934957504,
0.012869919650256634,
-0.0020386145915836096,
0.013101361691951752,
-0.0642363503575325,
-0.05557020381093025,
-0.0055072554387152195,
-0.00861786212772131,
0.008345166221261024,
0.013406360521912575,
-0.03453220799565315,
0.0244599562138319,
-0.041381753981113434,
-0.02999596856534481,
0.04056773707270622,
-0.042880162596702576,
-0.002547468990087509,
0.002556940307840705,
0.01583523489534855,
-0.04149172827601433,
-0.006168184336274862,
-0.0162887554615736,
0.033565789461135864,
-0.02594705857336521,
-0.013307253830134869,
0.02678634598851204,
-0.0051848748698830605,
-0.03033493645489216,
0.025214143097400665,
-0.022158361971378326,
-0.03112877905368805,
-0.0012477472191676497,
0.009964699856936932,
0.014434503391385078,
-0.012782623991370201,
-0.012136051431298256,
0.03368617594242096,
-0.03254466876387596,
0.031249793246388435,
-0.03952402621507645,
-0.0597306452691555,
0.03255169093608856,
0.024895910173654556,
0.030467865988612175,
0.016075611114501953,
0.008255192078649998,
0.07500752806663513,
0.03615258261561394,
-0.02299790270626545,
-0.01862988993525505,
0.000938168668653816,
0.012637120671570301,
-0.0004096503835171461,
0.019393619149923325,
0.04313138499855995,
-0.004189414903521538,
0.008031363599002361,
-0.006549715995788574,
0.011383404023945332,
0.07078497111797333,
0.008074603043496609,
0.0029486818239092827,
0.02440544217824936,
0.016645826399326324,
0.03910084068775177,
0.03692171722650528,
0.011617502197623253,
-0.06827681511640549,
0.006758464965969324,
-0.000708791718352586,
-0.021065838634967804,
0.0022112091537564993,
-0.012469625100493431,
0.08283782005310059,
-0.015341035090386868,
0.005218925885856152,
-0.022273564711213112,
0.027245599776506424,
-0.01110762357711792,
-0.03993825986981392,
0.010272345505654812,
0.024142317473888397,
0.005874216090887785,
0.0016925152158364654,
-0.011310049332678318,
0.015415316447615623,
0.024269435554742813,
0.007327284198254347,
-0.015178692527115345,
-0.024241819977760315,
-0.02224004454910755,
0.03079175390303135,
-0.05090715363621712,
-0.031617503613233566,
0.06009355187416077,
0.03451826050877571,
0.05003656446933746,
-0.025134317576885223,
-0.03836493939161301,
-0.001629901584237814,
-0.04624311253428459,
-0.0015965404454618692,
-0.011440054513514042,
0.08575093746185303,
-0.004751840606331825,
0.04439782351255417,
0.021972905844449997,
-0.00023048033472150564,
-0.005188926123082638,
0.019728973507881165,
-0.06550653278827667,
0.035815756767988205,
-0.021064210683107376,
-0.00986168347299099,
0.016939105466008186,
-0.012831945903599262,
-0.021061938256025314,
-0.009608183056116104,
-0.04254528507590294,
-0.020357904955744743,
0.02287837490439415,
-0.014545116573572159,
0.052854131907224655,
-0.02635500580072403,
-0.007473415229469538,
-0.008365005254745483,
0.02548171952366829,
0.015145726501941681,
-0.007999294437468052,
0.0012090416857972741,
0.04044485092163086,
-0.05205816403031349,
-0.0319996252655983,
0.014701684936881065,
0.04067288339138031,
0.0013785730116069317,
0.027465522289276123,
0.019724372774362564,
0.014345899224281311,
-0.011242730543017387,
0.021671004593372345,
-0.007369802799075842,
0.046141140162944794,
-0.02194671705365181,
-0.02236306108534336,
0.029423395171761513,
-0.021924041211605072,
-0.012842192314565182,
-0.001677159802056849,
0.07725661247968674,
0.012145732529461384,
0.027427244931459427,
0.015616646967828274,
-0.015400338917970657,
-0.06747369468212128,
0.02303232252597809,
0.08832845091819763,
-0.005652231629937887,
-0.019013598561286926,
-0.002534212777391076,
-0.043625608086586,
-0.02296939492225647,
-0.021581748500466347,
-0.006572338752448559,
0.01184583455324173,
-0.01286255195736885,
0.03805167227983475,
0.021450048312544823,
0.020968366414308548,
-0.036302343010902405,
0.0022901752963662148,
-0.033973876386880875,
0.05892582982778549,
0.0018987488001585007,
0.0031087191309779882,
-0.006452735513448715,
0.025201426818966866,
0.02479703165590763,
-0.008114158175885677,
0.023613663390278816,
-0.06492529809474945,
-0.027140604332089424,
0.030304506421089172,
0.05533377081155777,
0.002115259412676096,
-0.014325423166155815,
-0.06266375631093979,
-0.04312556982040405,
0.0305246040225029,
-0.011873249895870686,
0.060585420578718185,
0.008846370503306389,
-0.030748441815376282,
-0.05035831034183502,
-0.025008995085954666,
0.01769879274070263,
0.007088631857186556,
0.0010345723712816834,
0.03975633904337883,
0.020552802830934525,
-0.0008161284495145082,
-0.041066065430641174,
0.002603459171950817,
0.025555239990353584,
0.04301685467362404,
-0.030911296606063843,
-0.010553028434515,
-0.029286418110132217,
0.027151180431246758,
0.0032656146213412285,
-0.08336755633354187,
-0.001866707461886108,
0.009821237064898014,
-0.018676118925213814,
0.05092822015285492,
-0.026132117956876755,
-0.051533617079257965,
0.0015219340566545725,
0.00019961822545155883,
-0.007420750800520182,
0.023642342537641525,
-0.02413858473300934,
0.06280966848134995,
0.01988578401505947,
0.012221153825521469,
0.028512077406048775,
0.01764669269323349,
-0.054987575858831406,
0.031503092497587204,
-0.01618553325533867,
0.057101450860500336,
-0.0303143709897995,
0.020897626876831055,
0.00701881991699338,
-0.01999017409980297,
-0.04241054505109787,
0.04440903291106224,
-0.016827866435050964,
0.021060051396489143,
-0.013759080320596695,
-0.019622180610895157,
-0.03112945891916752,
0.03780701383948326,
-0.013462992385029793,
-0.02109774388372898,
0.009505318477749825,
0.02554510347545147,
-0.0022902709897607565,
-0.02252230793237686,
0.01441284827888012,
-0.005918996408581734,
0.019056767225265503,
0.02113640122115612,
-0.031166253611445427,
0.02795826457440853,
-0.052667438983917236,
-0.028314724564552307,
0.012308802455663681,
-0.05423242598772049,
0.03640058636665344,
-0.017423860728740692,
0.008049700409173965,
0.03588243946433067,
-0.04035317525267601,
-0.02722896635532379,
0.007769535295665264,
-0.007870761677622795,
-0.008496983908116817,
-0.020702488720417023,
0.027447346597909927,
-0.020764527842402458,
0.02035578526556492,
-0.051508404314517975,
-0.04562947154045105,
-0.011413197964429855,
0.016292480751872063,
-0.02610231749713421,
-0.033233799040317535,
0.02175133116543293,
-0.011626255698502064,
-0.03630765900015831,
0.011707024648785591,
0.031033955514431,
-0.023411951959133148,
-0.006294299382716417,
0.04871123656630516,
0.05462789162993431,
0.032197006046772,
-0.00220451969653368,
0.005179746076464653,
0.019463947042822838,
-0.002097363118082285,
-0.014032900333404541,
0.002634093863889575,
0.04786767438054085,
-0.022002507001161575,
-0.018417304381728172,
-0.06002568453550339,
0.024144334718585014,
0.05340122804045677,
-0.03949107974767685,
-0.012202657759189606,
-0.0021859004627913237,
-0.006500087212771177,
-0.025827396661043167,
-0.022560732439160347,
0.0015708077698946,
0.013473683968186378,
0.010957798920571804,
0.00010518245835555717,
0.002228732453659177,
0.0161165539175272,
-0.029055055230855942,
0.02162468247115612,
0.004729650914669037,
-0.005907796323299408,
0.005677009001374245,
0.030597412958741188,
-0.013383784331381321,
0.02680756151676178,
0.0017812913283705711,
-0.048019472509622574,
-0.04363848268985748,
-0.040375422686338425,
0.01948273740708828,
0.0285018403083086,
-0.020886944606900215,
-0.012773917987942696,
-0.06457322090864182,
-0.02754247933626175,
0.004564116708934307,
0.04637770354747772,
0.01654813252389431,
0.04005332663655281,
0.03582391142845154,
-0.03471584618091583,
-0.02879142016172409,
-0.02309488318860531,
0.004501888062804937,
-0.028197987005114555,
-0.013416034169495106,
0.007865704596042633,
-0.022461337968707085,
-0.009803625755012035,
0.002808733843266964,
0.050070084631443024,
-0.02263301983475685,
-0.0038897257763892412,
0.030190760269761086,
0.03178774192929268,
-0.0020617637783288956,
-0.0387122668325901,
-0.04429851844906807,
0.015061963349580765,
-0.08312392234802246,
0.0406729094684124,
0.015898240730166435,
-0.03041689656674862,
0.035029780119657516,
0.03605083376169205,
-0.014178193174302578,
-0.005612195935100317,
0.00346188573166728,
-0.046797897666692734,
0.000721974647603929,
0.013566209934651852,
-0.0022862672340124846,
-0.016605781391263008,
0.0005395133630372584,
0.047553371638059616,
0.002030903473496437,
-0.0018148730741813779,
-0.005814975593239069,
-0.05640450865030289,
-0.05398361384868622,
-0.0417976938188076,
-0.06387799233198166,
0.031144486740231514,
-0.0171402245759964,
-0.024014631286263466,
0.006060927640646696,
-0.031223395839333534,
0.035141367465257645,
-0.0017516239313408732,
0.0651756227016449,
-0.055777885019779205,
0.04370792955160141,
0.014687198214232922,
-0.0158810093998909,
-0.04095660522580147,
-0.007076086476445198,
0.11705589294433594,
0.08659035712480545,
0.026189232245087624,
-0.06538843363523483,
-0.0055958423763513565,
-0.009022963233292103,
0.024989595636725426,
0.01251306664198637,
0.0221926961094141,
-0.026217300444841385,
0.036235079169273376,
-0.001186997164040804,
0.02502569556236267,
0.04331839084625244,
0.0025555661413818598,
0.06372982263565063,
-0.026980439200997353,
-0.0715065598487854,
-0.018175076693296432,
0.00912176538258791,
-0.006370113231241703,
0.017739642411470413,
-0.024507278576493263,
0.028593195602297783,
-0.06885725259780884,
-0.0019043590873479843,
-0.008356652222573757,
-0.03393629193305969,
0.01987478882074356,
-0.016417978331446648,
-0.03144232556223869,
-0.012528469786047935,
-0.012072817422449589,
-0.014445756562054157,
-0.010018343105912209,
0.03317898139357567,
0.01830258220434189,
-0.019705824553966522,
0.01971486583352089,
0.02718033827841282,
0.02927575632929802,
-0.039765890687704086,
-0.003743850626051426,
0.016936322674155235,
-0.03946695849299431,
0.01792050339281559,
-0.0324585922062397,
0.03006432019174099,
-0.02083154022693634,
-0.016388237476348877,
-0.023951709270477295,
-0.025812506675720215,
0.030062828212976456,
-0.016890890896320343,
0.003762241452932358,
0.01224119309335947,
0.03902244195342064,
-0.0457652322947979,
0.03157011419534683,
-0.022743679583072662,
0.00134015001822263,
-0.0014310136903077364,
0.04315023869276047,
-0.011953678913414478,
-0.02280956320464611,
-0.02372298389673233,
0.012572654522955418,
-0.011615046299993992,
-0.028728974983096123,
0.007463046815246344,
-0.032503943890333176,
0.012647919356822968,
-0.05496818944811821,
-0.03753563016653061,
0.020917266607284546,
0.02174966409802437,
0.07294690608978271,
-0.004476672969758511,
-0.019271904602646828,
-0.010389529168605804,
-0.06018347293138504,
0.009894299320876598,
-0.02808300405740738,
0.024195615202188492,
-0.011675029061734676,
0.012040610425174236,
0.002985393162816763,
0.03469663858413696,
-0.02641337551176548,
0.01088621187955141,
0.023643745109438896,
-0.012245655059814453,
0.034801140427589417,
0.002756308065727353,
-0.011532468721270561,
-0.007741271052509546,
-0.03902987390756607,
0.03699101507663727,
-0.040108781307935715,
0.03742341324687004,
0.010108230635523796,
0.025754719972610474,
0.0021171956323087215,
0.015641862526535988,
-0.006230324041098356,
-0.0017449866281822324,
-0.019407043233513832,
0.0002906238369178027,
-0.04055798426270485,
0.014629803597927094,
0.056478820741176605,
-0.011558196507394314,
-0.03748713806271553,
-0.027049632743000984,
0.006212709937244654,
-0.001003019162453711,
-0.002522242721170187,
-0.008645990863442421,
0.02816140465438366,
-0.004868005868047476,
0.032597918063402176,
-0.04170764982700348,
0.0015845914604142308,
-0.01768370531499386,
0.022253673523664474,
0.0013401784235611558,
-0.032800961285829544,
0.010790984146296978,
0.03359654173254967,
0.024823280051350594,
-0.045273736119270325,
0.007634174544364214,
0.01611374132335186,
-0.007284082937985659,
0.022622445598244667,
-0.014207658357918262,
-0.000316777266561985,
0.015241305343806744,
-0.0025017268490046263,
-0.014927229844033718,
0.03267578408122063,
-0.016397135332226753,
-0.051899105310440063,
0.03319844603538513,
-0.013912314549088478,
0.0029823812656104565,
0.05632408708333969,
-0.014961768873035908,
-0.02769014984369278,
0.02581113949418068,
0.020311951637268066,
-0.03894216939806938,
-0.006170826964080334,
-0.024671131744980812,
-0.020240651443600655,
-0.02373565547168255,
0.00789516419172287,
-0.023768585175275803,
-0.03025790862739086,
0.023520689457654953,
0.03599374368786812,
0.00975865963846445,
0.03015795163810253,
0.01611223816871643,
-0.028733056038618088,
0.005066575948148966,
0.04004942998290062,
-0.010163831524550915,
0.06169021874666214,
0.014732837677001953,
-0.050289086997509,
0.03190438076853752,
0.010012662038207054,
0.01743398979306221,
-0.08993259072303772,
0.0032324164640158415,
0.030041737481951714,
0.0052057672291994095,
0.04737606272101402,
-0.043650973588228226,
0.03271675854921341,
0.03384220227599144,
-0.05727383494377136,
0.042992834001779556,
-0.0076173897832632065,
-0.023826628923416138,
0.009347894228994846,
0.011856474913656712,
-0.028680309653282166,
0.022978035733103752,
-0.014042625203728676,
0.023922383785247803,
0.03508208692073822,
0.03978380560874939,
0.008782237768173218,
-0.006556242238730192,
-0.017339307814836502,
-0.018884731456637383,
-0.022963881492614746,
0.004606750328093767,
0.03847930207848549,
-0.03942982852458954,
-0.01467710267752409,
0.024158773943781853,
-0.02799246273934841,
0.03219688683748245,
0.0036155644338577986,
0.00252496893517673,
0.03849990665912628,
0.03580087423324585,
0.032778121531009674,
-0.025078900158405304,
0.029825996607542038,
0.009484809823334217,
0.04595956578850746,
0.04030000418424606,
-0.0007752323290333152,
-0.012860686518251896,
0.025810126215219498,
-0.03528919443488121,
-0.022359434515237808,
0.020645257085561752,
-0.0031895823776721954,
0.029405424371361732,
0.01770804263651371,
-0.027376072481274605,
0.0034349567722529173,
0.01964428462088108,
0.008856946602463722,
-0.07395058125257492,
-0.025090711191296577,
0.025749608874320984,
0.025023505091667175,
0.015944765880703926,
0.02755039371550083,
-0.01177231129258871,
-0.04989251121878624,
0.03557872027158737,
0.028224948793649673,
0.006555488798767328,
-0.047979265451431274,
-0.030687576159834862,
0.026644391939044,
0.029788218438625336,
0.0414278618991375,
-0.01836537756025791,
-0.011336177587509155,
0.060789674520492554,
-0.020006326958537102,
0.06109238415956497,
0.023706747218966484,
-0.009741478599607944,
-0.019697559997439384,
-0.06211721524596214,
0.0569668784737587,
0.0107264444231987,
0.013892926275730133,
-0.015793226659297943,
-0.03921276703476906,
0.009360714815557003,
-0.00921376422047615,
0.0888877883553505,
-0.0070231640711426735,
0.007784042041748762,
-0.022747637704014778,
-0.013522276654839516,
0.048125430941581726,
-0.035785090178251266,
-0.018765803426504135,
-0.028390103951096535,
-0.007910903543233871,
-0.010191993787884712,
-0.015452108345925808,
-0.00562647171318531,
0.01526026614010334,
0.05648455768823624,
-0.012607044540345669,
0.04083341360092163,
-0.011472293175756931,
-0.020166298374533653,
0.03553202003240585,
0.0024399899411946535,
0.017918549478054047,
0.049953557550907135,
-0.011801764369010925,
0.018679635599255562,
0.03604031354188919,
-0.04051601514220238,
-0.009309363551437855,
0.06815306842327118,
-0.04730378836393356,
-0.011625878512859344,
-0.01929374597966671,
-0.045675843954086304,
-0.004484214819967747,
-0.08561477810144424,
-0.040117427706718445,
-0.001252354821190238,
-0.0475362092256546,
0.001670796307735145,
0.05984780192375183,
-0.013106029480695724,
0.015420653857290745,
0.00863877683877945,
0.018488207831978798,
0.011609334498643875,
-0.02053346484899521,
-0.003186755580827594,
0.025790903717279434,
0.051772117614746094,
0.01740296557545662,
0.04405435174703598,
0.05588835850358009,
0.01419595256447792,
0.01962967962026596,
-0.012049826793372631,
0.010453312657773495,
-0.05098079890012741,
0.004743489902466536,
0.05322008207440376,
-0.0063151526264846325,
-0.020191853865981102,
0.03453706577420235,
-0.05116619914770126,
0.06685663014650345,
-0.04016409069299698,
0.008505817502737045,
0.004461099859327078,
0.010808825492858887,
-0.020898114889860153,
0.016489166766405106,
-0.005859458819031715,
0.051846232265233994,
-0.02519938163459301,
0.005496643017977476,
-0.025685079395771027,
0.0306046474725008,
0.022449757903814316,
-0.032186564058065414,
0.05101148784160614,
0.03659083694219589,
-0.02303730510175228,
0.0017218200955539942,
-0.038841478526592255,
-0.018629971891641617,
-0.045033928006887436,
-0.0012907297350466251,
0.03045874834060669,
-0.02950054407119751,
-0.012779159471392632,
-0.0018201752100139856,
0.018878720700740814,
0.05067283660173416,
-0.023419223725795746,
0.023336920887231827,
-0.02246675454080105,
-0.0008492794586345553,
-0.020762307569384575,
-0.0033852397464215755
] |
<p>The paramount object in generalized gomplex geometry is the Courant algebroid $TM\oplus T^\star M$, where the manifold $M$ is called <em>background geometry</em> I think (I am not sure). More generally this Courant algebroid can be twisted by a closed 3-form $H$ on $M$, which I suspect is called a <em>flux</em> (I am not sure too). In fact P. Severa shown that every exact Courant algebroid arise as such a twist of the standard Courant algebroid $TM\oplus T^\star M$. I think these objects arise in Physics when one tries to make compactifications with fluxes in String Theory, which are more realistic ones. They also appear in the AdS-/CFT correspondence (see <a href="http://physics.stackexchange.com/questions/27615/generalized-complex-geometry-and-theoretical-physics">Generalized Complex Geometry and Theoretical Physics</a>). Please correct me if I am saying something wrong.</p>
<p>Could somebody sum up the way these forms $H$ appear in Physics in mathematical terms? However my true question is the following: could somebody provide concrete examples of both manifolds $M$ and forms $H$ such that, when combined together into the twisted Courant algebroid $(TM\oplus T^\star M,H)$ they are relevant to String Theory?</p>
<p>Thank you!</p>
| 10,773 |
[
0.0073027838952839375,
0.0015769783640280366,
0.02067827433347702,
-0.04819358140230179,
0.020792461931705475,
0.01692705787718296,
-0.032775722444057465,
-0.04824597015976906,
-0.00846064928919077,
-0.06010005623102188,
0.020763151347637177,
0.030379438772797585,
0.0440603643655777,
0.02822573110461235,
0.012267034500837326,
-0.01557676587253809,
-0.041703514754772186,
-0.023351319134235382,
-0.012935105711221695,
-0.01374725066125393,
0.04711241275072098,
0.008804434910416603,
-0.0032610874623060226,
0.010076106525957584,
0.02354574203491211,
0.022738369181752205,
-0.004852986428886652,
0.02073923498392105,
0.033012788742780685,
0.05729294940829277,
0.017281880602240562,
-0.02409040741622448,
-0.012167618609964848,
0.007773315533995628,
-0.020050030201673508,
-0.0072071910835802555,
0.0006090477108955383,
-0.000692726403940469,
0.012516967952251434,
0.00992180872708559,
-0.02712557651102543,
-0.04093825817108154,
-0.05295303836464882,
0.04341759905219078,
-0.024399133399128914,
-0.00039808140718378127,
-0.0356728658080101,
-0.02955523692071438,
0.0657099187374115,
-0.06139923259615898,
0.07832600921392441,
-0.00037519403849728405,
-0.013735020533204079,
-0.010214907117187977,
0.01481518242508173,
0.015353561379015446,
0.057945623993873596,
0.07214409112930298,
0.013876204378902912,
-0.04204470291733742,
-0.04745836928486824,
-0.04372366517782211,
-0.002386783016845584,
-0.05069852992892265,
-0.06071319058537483,
0.026497986167669296,
0.012756978161633015,
0.004471096210181713,
-0.005850226618349552,
-0.028788898140192032,
-0.011041977442800999,
-0.0018220776692032814,
-0.02063225395977497,
0.00003984256545663811,
-0.004618930630385876,
0.0055662477388978004,
-0.009518840350210667,
-0.025141224265098572,
0.06319762021303177,
0.015499177388846874,
0.02712434157729149,
0.009342174977064133,
-0.019881071522831917,
-0.0039955913089215755,
0.012258453294634819,
-0.000890335941221565,
0.08637535572052002,
-0.002279836917296052,
-0.03471636772155762,
0.06421059370040894,
-0.018987691029906273,
-0.018658870831131935,
0.060451872646808624,
0.004640583414584398,
-0.02628680132329464,
0.021519381552934647,
0.01063639484345913,
0.053204771131277084,
-0.026348933577537537,
0.023716701194643974,
-0.019469117745757103,
-0.04960988461971283,
-0.007169264834374189,
0.07053777575492859,
0.016971834003925323,
-0.008133070543408394,
-0.013083369471132755,
-0.005252772942185402,
-0.04647771641612053,
0.003853135509416461,
-0.03128580003976822,
0.019008925184607506,
0.024343781173229218,
-0.011705332435667515,
-0.009819062426686287,
-0.03519788756966591,
-0.00640870351344347,
-0.03679047152400017,
0.057997334748506546,
0.08685498684644699,
0.07705662399530411,
-0.021729493513703346,
0.03396933525800705,
-0.028793364763259888,
-0.08000649511814117,
-0.020518900826573372,
0.04868268966674805,
-0.007093607913702726,
-0.042132243514060974,
0.010750485584139824,
-0.0019274980295449495,
-0.05367112159729004,
0.04908100143074989,
-0.0030980256851762533,
0.035687610507011414,
-0.004264190327376127,
-0.07107844948768616,
-0.034772031009197235,
0.022365350276231766,
0.02356717549264431,
-0.03461223468184471,
-0.04448713734745979,
-0.004285548813641071,
0.009172280319035053,
0.07750236243009567,
0.009149745106697083,
0.005443823058158159,
0.016076091676950455,
0.04155471548438072,
0.016439665108919144,
-0.035578299313783646,
-0.03096252866089344,
0.01203165389597416,
-0.050887465476989746,
-0.04210010543465614,
-0.05431046709418297,
0.002448432147502899,
0.010893723927438259,
0.001954942010343075,
0.010249241255223751,
0.08534537255764008,
-0.00512335728853941,
0.012830588035285473,
0.021343059837818146,
-0.0124641302973032,
-0.04902580752968788,
0.055259354412555695,
-0.02798413671553135,
0.0033515733666718006,
0.0025527530815452337,
0.024304304271936417,
0.013042139820754528,
0.034670379012823105,
0.022582026198506355,
-0.026257885619997978,
-0.04521007090806961,
-0.0013859980972483754,
0.05151388794183731,
-0.025409653782844543,
0.03482336550951004,
-0.01384800672531128,
-0.006351139862090349,
0.01620655506849289,
0.011159919202327728,
-0.006035458762198687,
0.040353935211896896,
-0.02304217591881752,
-0.019367272034287453,
0.04065684601664543,
-0.06611450761556625,
0.04088762030005455,
-0.02086997590959072,
-0.026698948815464973,
-0.005611309316009283,
-0.032573677599430084,
0.0005239446181803942,
0.011568192392587662,
0.054818134754896164,
-0.007039971649646759,
-0.033657584339380264,
0.025606421753764153,
0.030338143929839134,
0.0007196076330728829,
0.012962598353624344,
0.002861136570572853,
0.002333504380658269,
0.01250741258263588,
-0.028607014566659927,
0.040128469467163086,
0.0227133147418499,
0.0014857723144814372,
-0.0260285884141922,
-0.018048765137791634,
0.0355965830385685,
-0.024709321558475494,
-0.011131037026643753,
0.01909463480114937,
0.018660804256796837,
-0.0011477753287181258,
0.04804980754852295,
-0.029742809012532234,
0.012954025529325008,
0.041038766503334045,
0.029689045622944832,
-0.002444018144160509,
0.05386793613433838,
-0.0050817071460187435,
-0.003973293583840132,
-0.020368777215480804,
-0.014751745387911797,
-0.01693033240735531,
-0.004898620303720236,
0.04922641068696976,
0.07048028707504272,
-0.034330740571022034,
-0.001352230436168611,
0.013931808061897755,
0.05073073133826256,
0.030200371518731117,
0.011176995001733303,
0.003350808285176754,
-0.038943782448768616,
0.008469278924167156,
0.014586292207241058,
0.007221913430839777,
0.006096789613366127,
0.01438802108168602,
0.01153089851140976,
-0.004278142005205154,
0.01966293528676033,
-0.07086282223463058,
0.0691191554069519,
-0.03920898959040642,
0.01605377532541752,
-0.006017251871526241,
0.0072765345685184,
0.05333356186747551,
-0.028658391907811165,
0.02596084214746952,
0.037414319813251495,
0.01081998273730278,
0.0013887464301660657,
-0.014014198444783688,
-0.01698826253414154,
0.017413107678294182,
-0.018359221518039703,
0.0031329472549259663,
-0.035350680351257324,
-0.004672993440181017,
-0.052935123443603516,
-0.018000707030296326,
-0.015704838559031487,
0.03738878667354584,
-0.021480649709701538,
0.025129949674010277,
0.020049596205353737,
-0.005416048225015402,
0.07019353657960892,
-0.011403416283428669,
-0.03143598139286041,
0.05358511209487915,
-0.035546910017728806,
0.01587294042110443,
0.027011552825570107,
-0.06501688063144684,
0.03643031418323517,
-0.08592883497476578,
-0.022048482671380043,
0.07442706823348999,
0.007204276509582996,
0.0025438189040869474,
0.001754268421791494,
-0.03686240687966347,
-0.012392943724989891,
-0.03624136745929718,
-0.0010579315712675452,
0.048490192741155624,
-0.03579218313097954,
0.022949349135160446,
0.04973851889371872,
0.016366859897971153,
-0.02589854970574379,
-0.017334356904029846,
-0.009375597350299358,
-0.04210812970995903,
-0.011411034502089024,
-0.01735345460474491,
-0.012594564817845821,
-0.0609954334795475,
0.05028373375535011,
0.004771110601723194,
-0.03819616883993149,
0.013898950070142746,
-0.04805373027920723,
-0.01159871369600296,
0.01907528191804886,
-0.0023898279760032892,
0.03262598067522049,
0.033661723136901855,
-0.03425827994942665,
0.0956563651561737,
0.021110987290740013,
-0.049008868634700775,
-0.04542095214128494,
0.018030604347586632,
-0.008024245500564575,
-0.031834278255701065,
0.018321773037314415,
0.03933726251125336,
-0.01988578774034977,
-0.0012078173458576202,
0.04419941455125809,
0.010293401777744293,
0.021487444639205933,
-0.006695528049021959,
-0.034165699034929276,
0.0030172248370945454,
0.004026895854622126,
0.03208072483539581,
0.04531275853514671,
-0.004451165907084942,
-0.025258611887693405,
0.004733778070658445,
0.00021821679547429085,
0.03165766969323158,
0.024715328589081764,
-0.02313164807856083,
0.03254669904708862,
-0.005978645756840706,
0.011487607844173908,
0.004962655249983072,
0.0528477281332016,
0.01633584126830101,
-0.030998095870018005,
-0.027227334678173065,
0.036421164870262146,
0.048938311636447906,
-0.033578719943761826,
0.005460066720843315,
0.040918756276369095,
0.04222775995731354,
-0.0005767479888163507,
-0.02249404974281788,
-0.011175217106938362,
0.014474269933998585,
0.018810436129570007,
-0.04075963422656059,
-0.054440952837467194,
0.015382240526378155,
0.051179803907871246,
0.004561504814773798,
0.005927430000156164,
-0.018672460690140724,
0.03440956771373749,
-0.06381093710660934,
0.004038464277982712,
0.023272471502423286,
0.043474216014146805,
-0.021541545167565346,
0.043656449764966965,
-0.00808731373399496,
-0.004274243023246527,
0.003801516490057111,
0.006924362853169441,
-0.02876666560769081,
-0.00001379941386403516,
-0.05585157126188278,
0.0313427597284317,
-0.0009879599092528224,
0.008292942307889462,
-0.0018426284659653902,
0.02641010284423828,
-0.039969559758901596,
-0.027501165866851807,
0.0008038266096264124,
-0.07813446968793869,
-0.004907387308776379,
-0.03797613084316254,
-0.06185215711593628,
-0.008202651515603065,
0.04783495515584946,
0.017736339941620827,
0.0035427946131676435,
0.011771094053983688,
0.014444796368479729,
-0.02457290329039097,
-0.015360746532678604,
-0.004133995156735182,
0.051995668560266495,
-0.019916918128728867,
0.04527627304196358,
0.05526111274957657,
0.0359397791326046,
-0.003956266678869724,
0.03771151974797249,
-0.0020878175273537636,
0.046843189746141434,
-0.01415376365184784,
-0.020390743389725685,
0.04544868692755699,
-0.048976827412843704,
-0.028256837278604507,
0.005829910282045603,
0.06455498933792114,
0.011217305436730385,
-0.0267897117882967,
0.021020932123064995,
0.01449402142316103,
0.00627821683883667,
0.011379105970263481,
0.05510614439845085,
0.011401420459151268,
-0.04238351061940193,
-0.06585879623889923,
-0.027387067675590515,
-0.026137473061680794,
0.004206222016364336,
-0.000173559135873802,
-0.029882073402404785,
-0.017989030107855797,
0.006479175295680761,
-0.0006574284052476287,
-0.017786424607038498,
-0.0154657494276762,
-0.014933641068637371,
0.029227323830127716,
0.0033010768238455057,
0.015133013017475605,
0.029163289815187454,
0.011958892457187176,
0.06548211723566055,
0.0470132976770401,
-0.016595743596553802,
-0.009151468053460121,
-0.08699679374694824,
-0.009393855929374695,
0.04549644887447357,
-0.008333704434335232,
0.015408198349177837,
-0.0041235219687223434,
-0.0218372642993927,
-0.013255635276436806,
0.05114193260669708,
0.006118881981819868,
0.05057414621114731,
0.008697602897882462,
-0.03441784903407097,
0.004303291440010071,
0.005298679694533348,
0.023079194128513336,
0.03171541914343834,
-0.03080628626048565,
0.007853695191442966,
-0.01701497659087181,
0.016138872131705284,
-0.005134627688676119,
0.027891011908650398,
-0.0003356636152602732,
0.004201880190521479,
0.05646032840013504,
-0.02227911166846752,
-0.0002803909301292151,
0.039242371916770935,
-0.006270781625062227,
-0.04966532811522484,
0.000991367967799306,
0.029202427715063095,
-0.05707443132996559,
0.05263169854879379,
-0.0371042937040329,
0.012959178537130356,
-0.023009242489933968,
0.026002148166298866,
0.025669554248452187,
0.03814949095249176,
-0.005491186864674091,
0.022631192579865456,
0.033824604004621506,
0.00041899856296367943,
0.01959456317126751,
0.007464678958058357,
0.026026984676718712,
-0.02589011751115322,
-0.005927675869315863,
0.02742551639676094,
-0.006638666149228811,
-0.009259295649826527,
-0.023958345875144005,
-0.0007101506926119328,
-0.06314513832330704,
0.057526927441358566,
-0.045100484043359756,
-0.010140418075025082,
0.00023892252647783607,
-0.0526985302567482,
0.008787933737039566,
0.027758002281188965,
0.012199044227600098,
-0.042835745960474014,
0.013286820612847805,
0.018663277849555016,
0.018277041614055634,
-0.02470654435455799,
0.001957701286301017,
-0.03491780161857605,
-0.021745609119534492,
0.019089581444859505,
0.014932951889932156,
0.025972533971071243,
-0.029666947200894356,
0.005356846377253532,
0.02261577546596527,
-0.039790116250514984,
0.016980119049549103,
-0.03374330326914787,
-0.014807473868131638,
0.015315967611968517,
-0.029865773394703865,
-0.03657812625169754,
-0.0195954367518425,
-0.04970787093043327,
0.011724716052412987,
-0.017214182764291763,
0.009985139593482018,
0.037227604538202286,
-0.027822168543934822,
-0.060505881905555725,
-0.015408201143145561,
0.04977569729089737,
0.04356179013848305,
-0.029600292444229126,
-0.0021102637983858585,
0.025874055922031403,
-0.05890892818570137,
-0.02884974144399166,
-0.0262803565710783,
0.05169106274843216,
-0.08799227327108383,
0.027781091630458832,
0.014410950243473053,
0.06167349964380264,
0.0023885599803179502,
-0.020929645746946335,
0.012318352237343788,
0.02428712323307991,
0.015332888811826706,
0.012684001587331295,
0.012693218886852264,
0.0010478742187842727,
-0.005725393537431955,
-0.0065270341001451015,
-0.022643882781267166,
-0.027518706396222115,
0.028845282271504402,
-0.021742066368460655,
-0.01696462742984295,
0.03652144968509674,
0.024169187992811203,
0.03731409087777138,
-0.008863784372806549,
0.011625982820987701,
0.016551636159420013,
0.018790747970342636,
-0.048824477940797806,
0.030818594619631767,
0.03690951690077782,
-0.07085921615362167,
0.03129551559686661,
0.012191164307296276,
-0.021869637072086334,
-0.01849653571844101,
0.027485350146889687,
0.02074442058801651,
-0.042666513472795486,
-0.004917843732982874,
-0.024535875767469406,
-0.011352854780852795,
0.0024878913536667824,
-0.0002047466696240008,
0.03912898525595665,
0.006085207220166922,
-0.01502162218093872,
-0.033075422048568726,
-0.005230226553976536,
-0.011165601201355457,
0.054941046983003616,
-0.03069881536066532,
0.030959324911236763,
0.009520617313683033,
0.0024561916943639517,
0.010742723010480404,
-0.005067802499979734,
-0.0416661873459816,
0.01648622937500477,
-0.015689697116613388,
0.008314249105751514,
-0.09761212021112442,
-0.012730032205581665,
0.06371688842773438,
0.04804206266999245,
-0.07068975269794464,
0.044057995080947876,
-0.004934648983180523,
0.019717350602149963,
-0.00940769910812378,
0.006466759368777275,
-0.039206329733133316,
0.026097649708390236,
-0.04118482768535614,
0.014455304481089115,
0.028429005295038223,
-0.02715301513671875,
0.009344656951725483,
0.030607815831899643,
0.002236768836155534,
-0.041851915419101715,
-0.03742636740207672,
-0.05134986713528633,
0.04919366165995598,
0.011684964410960674,
0.044086914509534836,
-0.01103273406624794,
-0.014188547618687153,
0.05723945051431656,
0.018440429121255875,
-0.0027748055290430784,
-0.0010209295433014631,
-0.07307861000299454,
-0.017919303849339485,
-0.013131208717823029,
-0.05732253938913345,
0.036858223378658295,
0.0058393026702106,
-0.004486420191824436,
-0.006194037385284901,
-0.03611862659454346,
0.00032303319312632084,
0.012418560683727264,
0.032633014023303986,
0.01012185588479042,
0.044012315571308136,
-0.009938118048012257,
0.026422342285513878,
-0.021278638392686844,
0.00272379326634109,
0.1597132831811905,
0.042948830872774124,
0.0039997398853302,
-0.10690557211637497,
0.004776812624186277,
0.009128941223025322,
0.02725290320813656,
-0.03997058421373367,
0.025590334087610245,
0.02212829515337944,
-0.008030742406845093,
-0.025345399975776672,
0.06872323900461197,
-0.013279573991894722,
-0.02138320915400982,
0.0672873705625534,
-0.021749580278992653,
-0.025475051254034042,
-0.007056812755763531,
-0.0277711171656847,
0.0009213033481501043,
-0.008735484443604946,
-0.07264202833175659,
0.007326912600547075,
-0.00973853375762701,
0.046479444950819016,
-0.019990205764770508,
-0.02548913098871708,
0.017173299565911293,
0.037007708102464676,
-0.038459327071905136,
-0.007906176149845123,
-0.019174564629793167,
-0.0348285436630249,
-0.02126779779791832,
0.01669519953429699,
0.018866434693336487,
0.016968633979558945,
0.036103200167417526,
0.02851109579205513,
0.0018227642867714167,
0.019337421283125877,
0.010468308813869953,
0.02455965429544449,
-0.03324379771947861,
-0.0267614908516407,
-0.018274076282978058,
0.027196066454052925,
-0.008574745617806911,
0.059883974492549896,
0.016862157732248306,
-0.03660188615322113,
0.0012802263954654336,
-0.012444152496755123,
-0.006809675134718418,
-0.04506013169884682,
0.010535932146012783,
-0.023958949372172356,
-0.021386921405792236,
-0.013398109935224056,
0.030420741066336632,
0.014352737925946712,
0.020783785730600357,
-0.01105791050940752,
-0.006357137579470873,
0.021648813039064407,
-0.020751504227519035,
0.04199900105595589,
0.041917599737644196,
-0.00872205663472414,
-0.03227989375591278,
0.014644179493188858,
-0.022111136466264725,
0.005526551511138678,
0.02887367084622383,
0.008737431839108467,
0.03051174059510231,
0.033377595245838165,
-0.006422916892915964,
-0.013240818865597248,
-0.009384877048432827,
0.012871908023953438,
0.0020204365719109774,
-0.016622744500637054,
-0.043782178312540054,
-0.020919064059853554,
0.04709397628903389,
0.01585986837744713,
-0.011732504703104496,
-0.025067422538995743,
-0.029875705018639565,
0.025163017213344574,
0.006722724996507168,
-0.005001027602702379,
-0.04351454973220825,
-0.004964196123182774,
-0.03454352915287018,
-0.028808128088712692,
-0.006927073001861572,
-0.0237779151648283,
0.01223826501518488,
-0.0047239456325769424,
-0.03543415665626526,
0.04796377196907997,
0.017629504203796387,
-0.007419236470013857,
0.011156047694385052,
-0.03984386473894119,
0.016285037621855736,
-0.018920935690402985,
0.0343363918364048,
-0.05595894902944565,
-0.04409481957554817,
-0.006346174981445074,
-0.022690424695611,
0.017710398882627487,
0.03873741254210472,
-0.017492232844233513,
0.01132270973175764,
-0.004706942476332188,
0.029733678326010704,
0.0019175371853634715,
0.019281156361103058,
-0.028916405513882637,
-0.0012369853211566806,
0.04314323514699936,
-0.009507337585091591,
0.004175584763288498,
0.01291472464799881,
-0.038699254393577576,
-0.048255354166030884,
0.04318470135331154,
0.03862756863236427,
-0.022128421813249588,
0.009936227463185787,
0.026428747922182083,
0.00589786795899272,
0.024635236710309982,
0.004699557088315487,
-0.035559333860874176,
0.0023154912050813437,
-0.04381019249558449,
-0.024874158203601837,
0.031876929104328156,
0.013504822738468647,
-0.00600760942324996,
-0.0018552161054685712,
-0.02645484358072281,
-0.016583366319537163,
0.04330538585782051,
0.011785672977566719,
-0.004809355828911066,
0.012773239985108376,
-0.015039141289889812,
-0.0061988839879632,
-0.03938036784529686,
0.02828635461628437,
-0.000758425216190517,
0.015240530483424664,
0.001866592327132821,
0.03253495320677757,
0.008007590658962727,
-0.009905395098030567,
-0.04795313999056816,
-0.03438163921236992,
-0.00492039555683732,
-0.00953286699950695,
0.04229739308357239,
0.013258278369903564,
0.007646630518138409,
-0.07342018932104111,
0.03622816503047943,
0.03267664089798927,
0.028511203825473785,
-0.07231844961643219,
-0.010103952139616013,
0.048702795058488846,
0.02440936490893364,
0.057441480457782745,
-0.03662910312414169,
0.0063185179606080055,
0.005550617352128029,
-0.043562497943639755,
0.020448332652449608,
-0.0336761437356472,
-0.02442098967730999,
-0.015474652871489525,
-0.011750598438084126,
-0.03999694436788559,
0.029313871636986732,
0.030485350638628006,
0.03146173059940338,
0.0180234145373106,
0.027948930859565735,
-0.020265400409698486,
-0.019640641286969185,
-0.036255981773138046,
-0.004854199010878801,
-0.017129089683294296,
-0.0217601228505373,
0.0760788768529892,
-0.0009085981291718781,
-0.045565415173769,
0.027202025055885315,
0.017085159197449684,
-0.004417902324348688,
-0.04407139867544174,
0.012107607908546925,
0.004546778742223978,
-0.0006319672684185207,
0.010828264057636261,
0.006270133890211582,
-0.020550401881337166,
0.01227798406034708,
0.009922508150339127,
-0.007227256894111633,
-0.006928539369255304,
0.013483957387506962,
0.007369395811110735,
-0.0317356176674366,
0.0002911317569669336,
0.021588969975709915,
-0.017976107075810432,
-0.04740156605839729,
-0.020335009321570396,
-0.0032248254865407944,
0.006206062622368336,
-0.007605547085404396,
0.0068104942329227924,
-0.03217855468392372,
0.010591826401650906,
0.03519405424594879,
0.0018229521811008453,
0.0009477409184910357,
0.05112304165959358,
-0.0037756559904664755,
-0.05014398694038391,
0.012223555706441402,
0.024809489026665688,
0.001261802390217781,
-0.05663155019283295,
-0.004056677222251892,
-0.009042724035680294,
0.005656360648572445,
0.019689204171299934,
-0.03161710128188133,
0.009438354521989822,
0.055754758417606354,
-0.03163949027657509,
0.04711604863405228,
-0.021143751218914986,
-0.05108598992228508,
-0.024219278246164322,
-0.03814899921417236,
0.009134048596024513,
0.007740004453808069,
0.014389694668352604,
0.00856363121420145,
0.00453268364071846,
0.017268775030970573,
0.03733551874756813,
0.029227934777736664,
-0.04775375500321388,
-0.008761934004724026,
0.04328810051083565,
0.0011223985347896814,
0.007786359637975693,
-0.031367793679237366,
0.016128500923514366,
0.03855296969413757,
-0.01942446455359459,
0.04005509987473488,
0.01459380704909563,
0.004791345447301865,
0.007056862115859985,
0.025230756029486656,
0.006787690334022045,
0.016501253470778465,
-0.01502982061356306,
-0.025982577353715897,
0.022362839430570602,
0.05121177062392235,
-0.01318388245999813,
0.0782751739025116,
-0.00010924573871307075,
-0.00501286331564188,
0.007042305078357458,
-0.01575009897351265,
0.008606921881437302,
0.00892667006701231,
-0.021839093416929245,
-0.013981081545352936,
-0.03896414488554001,
0.006475210189819336,
0.010829164646565914,
-0.05436112731695175,
-0.016280539333820343,
0.03383307158946991,
-0.021522287279367447,
-0.007849168963730335,
0.07863013446331024,
0.010124576278030872,
0.02681857906281948,
-0.011851408518850803,
0.006407834589481354,
0.00853712484240532,
0.002369762398302555,
0.04352066293358803,
0.02037101984024048,
0.0509491041302681,
0.005978672299534082,
-0.017655543982982635,
-0.009892882779240608,
-0.027069881558418274,
0.015001436695456505,
-0.030692359432578087,
0.03576673939824104,
-0.021152596920728683,
-0.013752108439803123,
0.0139019675552845,
-0.030131731182336807,
0.033660244196653366,
0.011764702387154102,
-0.02929133176803589,
0.06981582939624786,
-0.049612656235694885,
-0.024102216586470604,
-0.01771591417491436,
0.017265163362026215,
0.008304920978844166,
0.03743959590792656,
0.0063710641115903854,
0.031989797949790955,
-0.027829179540276527,
-0.00428107799962163,
0.002532210201025009,
-0.010714023374021053,
0.012806398794054985,
-0.039168909192085266,
-0.0032999629620462656,
-0.013930226676166058,
-0.02761102467775345,
0.02299666404724121,
-0.05032502859830856,
-0.02905968576669693,
-0.0375058613717556,
-0.028117187321186066,
0.026400839909911156,
0.04223719611763954,
-0.02477196604013443,
-0.024762379005551338,
-0.041806403547525406,
0.0560380294919014,
-0.09434182196855545,
-0.013288857415318489,
-0.009681511670351028,
0.021360384300351143,
-0.012933148071169853,
-0.00713242357596755
] |
<p>Just what the title states.</p>
<p>Pretty much all movement on Earth is by pushing against the much greater mass of Earth. Given there are easily thousands of aircraft taking flight/landing, and a lesser number of rockets (Satellite launch etc). Understandably the effect of aircraft would be reduced because an aircraft (usually) comes to ground eventually but with a reduced mass by virtue of the reduced fuel mass ... </p>
<p>How much is Earth's orbit affected by such reaction if observed/calculated over an extended period - say, of the order of millenia or longer? </p>
| 10,774 |
[
-0.013877290301024914,
-0.027820896357297897,
0.006432563532143831,
0.00472886161878705,
0.03126153349876404,
0.02403099834918976,
-0.0004934789030812681,
-0.050935085862874985,
0.007538829930126667,
-0.06856375932693481,
-0.030403966084122658,
0.023826757445931435,
0.05855703353881836,
-0.019198931753635406,
-0.014014646410942078,
0.007734186481684446,
-0.05031273514032364,
0.013547451235353947,
0.02598745934665203,
-0.055182453244924545,
-0.002695033559575677,
-0.0015431658830493689,
0.014370622113347054,
-0.00770097179338336,
-0.02745402418076992,
0.024674292653799057,
0.021445777267217636,
-0.0272440854460001,
0.030173910781741142,
0.03806575387716293,
0.016339929774403572,
0.018337978050112724,
-0.012103303335607052,
0.049533482640981674,
0.03416047990322113,
0.048430487513542175,
-0.04256992042064667,
-0.039370592683553696,
-0.006388821639120579,
0.05562935397028923,
-0.035044312477111816,
-0.01762348972260952,
-0.00612291507422924,
0.043874673545360565,
-0.01662498340010643,
0.03745594620704651,
0.00016365983174182475,
0.009224318899214268,
0.09140273183584213,
-0.05916201323270798,
0.0731973722577095,
-0.019486816599965096,
0.006023687776178122,
0.03345239907503128,
-0.00036927624023519456,
-0.03236493468284607,
0.06259981542825699,
0.06520707160234451,
-0.002278157277032733,
-0.003988057840615511,
0.008928039111196995,
-0.01631811261177063,
-0.008914156816899776,
-0.028937064111232758,
0.004295049700886011,
0.046970900148153305,
-0.027843117713928223,
-0.01896347850561142,
0.03249231353402138,
0.044577717781066895,
0.0008231949177570641,
0.000876398931723088,
0.023881619796156883,
-0.009926528669893742,
0.01812218688428402,
-0.040437959134578705,
0.05670786648988724,
-0.002916627796366811,
0.04391457140445709,
0.06728265434503555,
-0.0753396525979042,
-0.005486241076141596,
0.0390344113111496,
0.07352828234434128,
0.01766980066895485,
0.03409179672598839,
0.048801079392433167,
-0.03848244249820709,
-0.0075143869034945965,
0.01576508954167366,
-0.010132256895303726,
-0.0022045958321541548,
0.020768413320183754,
-0.01917435973882675,
-0.028757190331816673,
0.03069494664669037,
0.00470831198617816,
0.0639881119132042,
0.027932293713092804,
-0.004849717952311039,
0.00737950811162591,
-0.009498326107859612,
-0.011036431416869164,
0.05348099023103714,
0.013434430584311485,
0.026516294106841087,
-0.05959785729646683,
-0.024978386238217354,
-0.03297547996044159,
-0.023086825385689735,
-0.013124960474669933,
-0.012119615450501442,
-0.0032069962471723557,
-0.04064696654677391,
0.01720493845641613,
0.004986103158444166,
-0.006029818207025528,
-0.016651427373290062,
0.030757363885641098,
0.019503049552440643,
0.06838668137788773,
0.005672281142324209,
0.024600068107247353,
-0.007496956270188093,
-0.05047659948468208,
-0.0036454249639064074,
0.034984294325113297,
-0.02749830298125744,
-0.031321994960308075,
0.02342560514807701,
-0.012086731381714344,
-0.031444717198610306,
0.014235385693609715,
-0.030103780329227448,
0.0667593777179718,
-0.00029537631780840456,
-0.06707386672496796,
-0.0410647988319397,
0.04645548015832901,
0.016878603026270866,
0.029605956748127937,
-0.062440887093544006,
0.01197668258100748,
-0.007349630352109671,
0.07777321338653564,
0.0116873262450099,
0.004595243372023106,
0.018856599926948547,
0.057812005281448364,
0.00797759834676981,
-0.0372529998421669,
-0.0007688166806474328,
-0.002403511432930827,
-0.06057671830058098,
-0.020305335521697998,
-0.0994250550866127,
0.0029496457427740097,
0.02972424402832985,
-0.004446611274033785,
0.0060113053768873215,
0.0476105660200119,
-0.0011070405598729849,
-0.002383638871833682,
-0.023400023579597473,
0.01603802479803562,
-0.012390697374939919,
0.08115018904209137,
0.03624854236841202,
-0.048470452427864075,
0.019820528104901314,
0.06726039201021194,
0.05842320993542671,
0.014021211303770542,
0.007702317088842392,
0.056616101413965225,
-0.06274934858083725,
0.015469596721231937,
-0.03465869650244713,
-0.040697675198316574,
-0.01268694642931223,
-0.003171488642692566,
-0.05779057368636131,
-0.03568919748067856,
-0.00032749876845628023,
0.024722594767808914,
0.030182955786585808,
-0.021866383031010628,
0.01378297433257103,
0.030872970819473267,
-0.05726371705532074,
-0.049901675432920456,
-0.07729079574346542,
0.04225010424852371,
-0.011026276275515556,
0.01687619276344776,
-0.006737080868333578,
-0.013982852920889854,
-0.0024768749717622995,
-0.04718182981014252,
-0.03927301615476608,
0.005318415816873312,
0.0014789705164730549,
-0.015960654243826866,
-0.010364385321736336,
0.003467126050963998,
0.04684286564588547,
0.007861164398491383,
0.004608731716871262,
-0.021606843918561935,
-0.0073022968135774136,
-0.04972445219755173,
0.0011366723338142037,
-0.04250200465321541,
0.025116784498095512,
0.032681889832019806,
0.020864780992269516,
-0.004505952820181847,
0.0005784748937003314,
0.020782815292477608,
0.027061928063631058,
-0.033842783421278,
0.11361460387706757,
0.053724028170108795,
0.03041968122124672,
0.016259707510471344,
0.06579142063856125,
0.029823165386915207,
-0.029087301343679428,
-0.007877298630774021,
-0.033256445080041885,
-0.056519411504268646,
-0.06395193189382553,
0.019912024959921837,
-0.01372622326016426,
-0.021024323999881744,
0.035826750099658966,
0.03613302484154701,
0.03845014050602913,
0.031142257153987885,
0.029464054852724075,
0.0012981928884983063,
-0.006838924717158079,
0.020476367324590683,
0.034759365022182465,
-0.00953778624534607,
0.00027799431700259447,
0.007757608778774738,
0.009384666569530964,
-0.019051415845751762,
0.0044584721326828,
-0.03160978481173515,
0.013172190636396408,
0.026687059551477432,
0.004909689072519541,
-0.0384707972407341,
-0.0002882643020711839,
0.02526501938700676,
-0.02223784290254116,
0.031134281307458878,
0.009606866165995598,
-0.014370030723512173,
0.0038083475083112717,
-0.01722221076488495,
-0.0008548230398446321,
-0.006438817363232374,
-0.0003031036467291415,
-0.03458419442176819,
-0.009501684457063675,
0.049049217253923416,
-0.05382712185382843,
0.03200753405690193,
-0.023597199469804764,
-0.002294632140547037,
-0.03230765461921692,
0.00007733036909485236,
-0.00010762491001514718,
0.014169967733323574,
0.031408753246068954,
-0.005134387407451868,
-0.031700268387794495,
-0.033504191786050797,
-0.05093403160572052,
-0.0251598097383976,
0.018429813906550407,
-0.018746400251984596,
0.01721886731684208,
-0.018893929198384285,
-0.01942307874560356,
0.05417310446500778,
0.019889725372195244,
0.02627567946910858,
0.05200649052858353,
-0.032132700085639954,
-0.07025768607854843,
-0.0355951301753521,
-0.04444855824112892,
-0.038675274699926376,
-0.006469078827649355,
0.009218355640769005,
0.06216541677713394,
0.0295573677867651,
0.0032676069531589746,
0.005833706818521023,
-0.06561742722988129,
-0.01111296471208334,
-0.0008862856193445623,
0.015966450795531273,
-0.026651179417967796,
-0.06362209469079971,
0.01917068287730217,
-0.029715556651353836,
-0.03259759023785591,
-0.029480665922164917,
-0.024573391303420067,
-0.017824329435825348,
0.015893546864390373,
-0.023467879742383957,
0.04305167496204376,
-0.005726542789489031,
-0.07107950001955032,
0.056126125156879425,
0.008641944266855717,
0.025760451331734657,
-0.03008357807993889,
0.007366223260760307,
0.021481327712535858,
0.03641188517212868,
-0.005483160726726055,
0.020035361871123314,
0.030583806335926056,
0.003635094966739416,
0.0369059294462204,
-0.01293623261153698,
-0.02616332471370697,
0.013043313287198544,
-0.036831196397542953,
0.0025061334017664194,
-0.010663782246410847,
0.02680862508714199,
0.02958783321082592,
0.017363885417580605,
-0.0038621071726083755,
0.02397138625383377,
-0.022661631926894188,
0.03503233566880226,
0.00042810107697732747,
-0.034800659865140915,
0.028619160875678062,
0.00898844562470913,
-0.020227668806910515,
0.01181205827742815,
0.04835982620716095,
0.008701526559889317,
-0.0028940499760210514,
-0.021347735077142715,
0.009388008154928684,
0.032134782522916794,
0.03664108365774155,
-0.025119567289948463,
0.009452162310481071,
0.07928073406219482,
0.007905163802206516,
-0.05415967479348183,
0.004357777535915375,
0.01571633480489254,
-0.016364090144634247,
-0.021461177617311478,
-0.03894946724176407,
0.033357419073581696,
-0.002218512585386634,
-0.0011653737165033817,
0.01686302199959755,
-0.018188608810305595,
0.011901452206075191,
-0.07350750267505646,
-0.021113691851496696,
-0.036417484283447266,
0.042471833527088165,
-0.030688636004924774,
-0.0012425279710441828,
-0.01097832154482603,
-0.004434116650372744,
0.004744910169392824,
0.012094149366021156,
-0.08446945250034332,
0.006635222118347883,
-0.05316748470067978,
-0.04384882003068924,
0.04460194706916809,
0.041796326637268066,
-0.034255627542734146,
-0.02022910863161087,
-0.01908734254539013,
-0.03863081336021423,
0.00563102075830102,
-0.047838129103183746,
-0.01041259802877903,
-0.02495526894927025,
-0.04058179631829262,
-0.01310889981687069,
-0.00032049071160145104,
0.04740556702017784,
-0.033466633409261703,
0.040398601442575455,
0.04097173735499382,
-0.038474828004837036,
-0.048077575862407684,
-0.05480068176984787,
0.034656818956136703,
-0.02370319701731205,
0.004164935555309057,
-0.013376905582845211,
0.029000135138630867,
-0.05588687211275101,
0.038377873599529266,
0.006756553426384926,
-0.009267313405871391,
-0.015310681425035,
0.038958847522735596,
-0.04532398283481598,
-0.03456230089068413,
-0.01944320648908615,
0.042189083993434906,
-0.009807359427213669,
-0.012571536004543304,
0.022957438603043556,
0.016835518181324005,
0.022106843069195747,
0.026552222669124603,
0.021983396261930466,
0.04339684173464775,
0.028863735496997833,
0.024301020428538322,
-0.02096240408718586,
-0.01238618977367878,
-0.02990759164094925,
-0.0030453428626060486,
0.01900978945195675,
-0.01719686947762966,
0.0031021623872220516,
-0.001378824352286756,
0.035216622054576874,
0.04427962005138397,
-0.022246213629841805,
0.015556839294731617,
0.0016970218857750297,
0.002994765527546406,
-0.00878412276506424,
0.030257128179073334,
0.01040206104516983,
0.006811995059251785,
0.033887628465890884,
0.006702607963234186,
0.003946889657527208,
-0.09747722744941711,
-0.0006345788133330643,
0.048952776938676834,
0.025103027001023293,
-0.0002546612231526524,
0.0055886502377688885,
-0.028696687892079353,
-0.015955941751599312,
0.02064032293856144,
-0.024309081956744194,
0.025584092363715172,
-0.018091591075062752,
0.018851207569241524,
0.017614440992474556,
-0.0236884243786335,
-0.010785020887851715,
-0.007847554981708527,
-0.003450306598097086,
-0.028242439031600952,
0.006019419990479946,
0.01234054658561945,
0.02681555785238743,
0.03327358514070511,
0.03377570956945419,
0.01140699815005064,
0.05587431415915489,
0.015492207370698452,
-0.020205792039632797,
-0.02949131652712822,
-0.05446092039346695,
-0.04260723292827606,
-0.0040710680186748505,
0.005871481262147427,
-0.03429412841796875,
0.031092064455151558,
-0.026388879865407944,
-0.032065071165561676,
0.02635350078344345,
-0.0021518401335924864,
-0.0022865531500428915,
-0.08127924799919128,
-0.040782131254673004,
0.015509459190070629,
0.04616717994213104,
-0.01758050173521042,
0.015235023573040962,
0.03272661194205284,
-0.019530128687620163,
0.018700122833251953,
0.05225364863872528,
-0.004009181167930365,
-0.010216500610113144,
0.0238457340747118,
0.03965819254517555,
0.014837927184998989,
-0.015908103436231613,
0.032671526074409485,
-0.0022454841528087854,
0.0006352069322019815,
-0.0034653604961931705,
-0.010008879005908966,
-0.024578630924224854,
0.024723917245864868,
-0.013475779443979263,
0.030080704018473625,
-0.006198923569172621,
0.0778462141752243,
-0.012338688597083092,
-0.035495176911354065,
0.01304703950881958,
0.01554489228874445,
0.021150918677449226,
0.004772804211825132,
-0.017909632995724678,
-0.005807502195239067,
-0.0028446984943002462,
0.003520096419379115,
0.018701165914535522,
-0.04836444556713104,
0.06429921835660934,
-0.02210879512131214,
-0.014063443057239056,
0.03979776054620743,
-0.08286374062299728,
-0.03141257166862488,
0.03003322333097458,
-0.028129108250141144,
0.0385088175535202,
0.008259018883109093,
-0.012740911915898323,
0.03217993304133415,
0.02728389948606491,
-0.0446445494890213,
-0.05509096011519432,
0.03923957794904709,
0.021326320245862007,
0.028281519189476967,
-0.03970944508910179,
-0.02278408594429493,
-0.04142861068248749,
-0.029692990705370903,
0.029966235160827637,
0.04080301895737648,
-0.06058391556143761,
-0.0028646918945014477,
0.02143692597746849,
-0.014138957485556602,
0.05174432694911957,
-0.029694989323616028,
-0.05389971286058426,
0.013919300399720669,
0.012295756489038467,
-0.002097493503242731,
-0.04579201340675354,
0.07416824251413345,
-0.036857325583696365,
-0.020835937932133675,
-0.013653130270540714,
-0.03042353130877018,
0.013636820949614048,
-0.03693253546953201,
0.022160714492201805,
0.04936271160840988,
-0.01100069284439087,
0.04650731384754181,
-0.008311320096254349,
0.016707686707377434,
-0.0005697185406461358,
0.014098423533141613,
0.017962316051125526,
0.016552861779928207,
-0.010438122786581516,
-0.03759809955954552,
0.031136108562350273,
0.005372004117816687,
-0.04604639858007431,
-0.01820741780102253,
0.05820388346910477,
0.016533855348825455,
-0.012354632839560509,
0.016484703868627548,
-0.008053858764469624,
0.02962048165500164,
-0.034534674137830734,
-0.021697085350751877,
0.04575823247432709,
-0.015188448131084442,
-0.011315771378576756,
-0.025406885892152786,
-0.030942648649215698,
0.0023655283730477095,
0.053772296756505966,
-0.041885118931531906,
0.037533462047576904,
0.015146066434681416,
0.038525063544511795,
0.0247868113219738,
0.010834985412657261,
0.008702709339559078,
0.0009014848619699478,
-0.022473640739917755,
0.005731621757149696,
-0.021612893790006638,
0.009029286913573742,
0.044633109122514725,
0.010042323730885983,
-0.017576495185494423,
-0.01433830987662077,
0.016367323696613312,
0.0069386656396090984,
0.07163748145103455,
-0.014211775735020638,
-0.01082818303257227,
0.018112996593117714,
-0.019988369196653366,
0.025766346603631973,
0.019260315224528313,
-0.011687442660331726,
0.05486651510000229,
0.040033575147390366,
0.025290191173553467,
-0.013427890837192535,
-0.026987740769982338,
-0.0472341813147068,
0.011928542517125607,
-0.025890398770570755,
0.0012749003944918513,
0.010116318240761757,
0.005563194863498211,
0.03001529537141323,
0.016993185505270958,
-0.018924610689282417,
0.002827538875862956,
-0.0655050054192543,
-0.05436336249113083,
-0.018832560628652573,
-0.04698673263192177,
0.024019701406359673,
0.009477843530476093,
-0.023012898862361908,
0.008302535861730576,
-0.00356451328843832,
0.00165422516874969,
0.023726575076580048,
0.04254180192947388,
-0.02111366204917431,
0.0972101092338562,
-0.03147083893418312,
0.023036299273371696,
-0.02266121469438076,
0.024328216910362244,
0.11156804859638214,
0.00956413708627224,
0.01261298917233944,
-0.03994007408618927,
-0.002438002498820424,
-0.005537333432585001,
-0.0075537231750786304,
-0.05063227191567421,
-0.03634573891758919,
0.0184500589966774,
-0.02868041582405567,
0.03119058534502983,
0.028349541127681732,
-0.017105508595705032,
-0.06468391418457031,
0.04677140712738037,
-0.03186745196580887,
-0.029152754694223404,
-0.004027341026812792,
-0.015929218381643295,
0.00023175455862656236,
-0.008101731538772583,
-0.028880609199404716,
0.009790853597223759,
-0.035964690148830414,
-0.016403470188379288,
-0.03639179840683937,
-0.032313477247953415,
0.0032825113739818335,
0.020384853705763817,
-0.08082785457372665,
0.007368575315922499,
0.013999604620039463,
-0.028459597378969193,
-0.05173342674970627,
0.039214275777339935,
0.003402098547667265,
0.023547060787677765,
-0.0005371161969378591,
0.05329553782939911,
0.02667711116373539,
0.022233620285987854,
-0.010805263184010983,
-0.014111415483057499,
-0.026713479310274124,
0.024286581203341484,
-0.04223306477069855,
0.04933876171708107,
0.014790771529078484,
-0.0023841354995965958,
0.005770046729594469,
-0.027139270678162575,
0.004295264836400747,
-0.03564523532986641,
-0.009798032231628895,
0.01232870016247034,
0.0062829433009028435,
0.0042465985752642155,
-0.056552328169345856,
0.023166712373495102,
0.01908125728368759,
-0.001448691706173122,
0.022256791591644287,
0.009883629158139229,
0.011139536276459694,
0.008124877698719501,
-0.03175276517868042,
0.04415854066610336,
-0.015412110835313797,
-0.013413318432867527,
-0.03797571361064911,
0.006212275475263596,
-0.05700446292757988,
0.0006094161653891206,
0.010197176598012447,
0.023964475840330124,
0.030058909207582474,
-0.0029697916470468044,
-0.019826656207442284,
-0.050897207111120224,
-0.023790013045072556,
0.050377268344163895,
-0.019976267591118813,
-0.005820749793201685,
-0.013063578866422176,
-0.025503909215331078,
0.0279811043292284,
0.007033074274659157,
-0.010143759660422802,
0.007645650766789913,
-0.02245323918759823,
0.05927983671426773,
0.005788885988295078,
-0.038525115698575974,
-0.03748292848467827,
0.04867955297231674,
-0.0036119960714131594,
0.009540419094264507,
0.00701505783945322,
0.05386456102132797,
0.016288219019770622,
-0.03859884664416313,
0.018745053559541702,
0.03228996321558952,
-0.001581688062287867,
0.035296812653541565,
0.023128829896450043,
-0.030384277924895287,
-0.0018963321344926953,
-0.0032165248412638903,
-0.02614966593682766,
0.0007128533907234669,
0.033175405114889145,
-0.023392530158162117,
-0.020793095231056213,
-0.031217999756336212,
0.003268278669565916,
-0.01739407517015934,
0.08685076236724854,
-0.03319377079606056,
0.02026817388832569,
-0.012360204011201859,
0.03753044083714485,
-0.042849164456129074,
0.008616864681243896,
0.02498510479927063,
-0.012201457284390926,
-0.010630005970597267,
0.03196331858634949,
-0.017832409590482712,
0.01204118225723505,
0.0046952939592301846,
0.008618694730103016,
0.005506415385752916,
0.027639344334602356,
0.002128991996869445,
-0.01438275258988142,
0.04823065921664238,
-0.05670710280537605,
-0.010003676638007164,
0.027054641395807266,
-0.024292470887303352,
-0.05407044664025307,
0.05153369903564453,
-0.057644084095954895,
0.043376706540584564,
0.01704583875834942,
-0.018052540719509125,
-0.039727162569761276,
0.07569622993469238,
-0.010112513788044453,
-0.008177955634891987,
0.016385167837142944,
0.034015022218227386,
-0.02824478968977928,
-0.0025173467583954334,
-0.012006440199911594,
-0.02147817052900791,
-0.028836321085691452,
0.007111717015504837,
0.03369881585240364,
-0.023515233770012856,
0.000935504911467433,
-0.019754908978939056,
-0.05129684507846832,
-0.02369658276438713,
0.010782210156321526,
0.005269286222755909,
0.03169146552681923,
0.03754856809973717,
-0.026787186041474342,
-0.008997679688036442,
0.006846243515610695,
-0.009990830905735493,
-0.06800089031457901,
-0.0022825251799076796,
-0.008983248844742775,
-0.011041853576898575,
0.042132697999477386,
-0.03151196986436844,
0.021300513297319412,
0.01992449164390564,
-0.07478854805231094,
0.02408633753657341,
-0.054530154913663864,
-0.0031685635913163424,
-0.01771668717265129,
-0.026125114411115646,
0.048775628209114075,
0.06780342757701874,
0.04018016532063484,
0.027997009456157684,
0.004201771225780249,
-0.005834680050611496,
-0.015896793454885483,
-0.008706607855856419,
0.056841764599084854,
-0.010877189226448536,
-0.021001912653446198,
0.01038464903831482,
0.04674709960818291,
-0.021550437435507774,
-0.045645564794540405,
0.04690752550959587,
0.02958356775343418,
0.02588145062327385,
-0.03174446523189545,
0.024747587740421295,
0.0009120190516114235,
0.027387166395783424,
-0.001014932757243514,
0.0034446038771420717,
0.01432290393859148,
0.03616324067115784,
-0.015946000814437866,
-0.0048690857365727425,
-0.041533421725034714,
0.013982460834085941,
0.0122035201638937,
-0.024803435429930687,
0.023606911301612854,
0.008095856755971909,
0.010732459835708141,
0.03484772518277168,
-0.02156110107898712,
0.030587418004870415,
0.010807274840772152,
0.01642095483839512,
-0.012097821570932865,
-0.0421307347714901,
0.008875944651663303,
0.013718772679567337,
-0.019431959837675095,
-0.035941142588853836,
0.030637361109256744,
0.0028194431215524673,
0.016298143193125725,
-0.04157028719782829,
-0.045313406735658646,
-0.00508709205314517,
-0.03860859572887421,
0.0020891092717647552,
-0.020992690697312355,
-0.03617365285754204,
-0.05288340896368027,
-0.02703195996582508,
-0.044572144746780396,
0.022788511589169502,
0.005294129718095064,
0.0006264907424338162,
0.007630874868482351,
-0.061263129115104675,
0.01853632554411888,
-0.05850039795041084,
0.035259753465652466,
0.011307971552014351,
0.022633813321590424,
-0.023920532315969467,
-0.040612220764160156,
0.019805025309324265,
-0.02214844338595867,
0.0235291700810194,
0.005661746021360159,
-0.0034429500810801983,
0.013117634691298008,
-0.03023538738489151,
-0.004873631987720728,
-0.038956351578235626,
-0.000491574639454484,
-0.0075065153650939465,
-0.04410190135240555,
0.01755731739103794,
-0.03458111360669136,
-0.021455412730574608,
-0.006359027232974768,
0.0008071950869634748,
-0.01831015571951866,
0.0023250377271324396,
0.016170542687177658,
-0.026016559451818466,
0.04596063867211342,
0.04002947360277176,
0.038995180279016495,
0.05676562711596489,
0.04648797586560249,
0.014210264198482037,
0.009779081679880619,
0.01158659253269434,
-0.037102993577718735,
0.06166500598192215,
-0.01766173541545868,
0.00012602309288922697,
-0.03706084564328194,
0.011986348778009415,
0.006245430093258619,
-0.03721874952316284,
0.027896713465452194,
0.04946408048272133,
-0.004148604813963175,
-0.0028254238422960043,
0.02022639289498329,
0.019890839233994484,
0.030498338863253593,
-0.007690161466598511,
0.02117028459906578,
0.016103621572256088,
0.020867524668574333,
-0.004480281379073858,
0.017446473240852356,
-0.007877613417804241,
0.005587665364146233,
0.020229030400514603,
0.005764769855886698,
0.014097708277404308,
0.025067036971449852,
0.04279462620615959,
0.007947875186800957,
-0.03039994277060032,
0.005813152063637972,
0.002878102008253336,
-0.017572149634361267,
0.017038937658071518,
0.04265013337135315,
0.007377001456916332,
0.06544668972492218,
0.013863326981663704,
0.02974323369562626,
0.02589057944715023,
-0.00891697034239769,
0.029927387833595276,
0.018164267763495445,
-0.005830148700624704,
0.0003062238683924079,
-0.004864356480538845,
-0.002266321098431945,
0.008292465470731258,
0.01568380743265152,
0.022224674001336098,
-0.014483916573226452,
0.026040246710181236,
-0.012831875123083591,
-0.01407469529658556,
0.009680493734776974,
-0.031594257801771164,
-0.04000772535800934,
-0.0014432684984058142,
0.04433535411953926,
0.06827159225940704,
0.013185926713049412,
-0.0023343616630882025,
0.011670614592730999,
-0.04670661687850952,
0.020571425557136536,
-0.03786671161651611,
-0.03320027142763138,
-0.03811555728316307,
0.02551306039094925,
0.0065823690965771675,
-0.025543250143527985
] |
<p>I am trying to understand why radio waves pass though the human body, light does not, but X-rays still pass. </p>
<p>In my mind I imagine that radio waves don't supply enough energy and don't excite any interesting modes of the material that they hit. This is in contrast to the photon excitation and associated scattering I imagine when a light beam hits a material. </p>
<p>I am confused as to why this doesn't happen for X-rays? I mean they come out the other end, so I assume that they have a pretty good transmission though soft tissue. </p>
<p>Certainly, the 1MeV is a enough to excite the band-gaps in the human body which, in turn, should cause all the X-rays to be absorbed?</p>
| 10,775 |
[
-0.027604198083281517,
-0.04101620614528656,
0.0039052139036357403,
-0.06378045678138733,
-0.024047190323472023,
0.049589384347200394,
-0.03767324611544609,
-0.012659714557230473,
-0.000972698035184294,
-0.02767897956073284,
0.018299946561455727,
0.044943828135728836,
0.059821344912052155,
0.014192198403179646,
0.025228578597307205,
-0.028441814705729485,
-0.006021097302436829,
-0.03482326492667198,
-0.020863575860857964,
-0.054372478276491165,
-0.006373667158186436,
0.010212759487330914,
0.00019666747539304197,
0.026244137436151505,
-0.03789522871375084,
0.03775681182742119,
0.026406334713101387,
0.005445668939501047,
0.029431629925966263,
0.023228943347930908,
0.026965050026774406,
-0.002721007214859128,
-0.027733221650123596,
0.0146699333563447,
0.004584681708365679,
-0.013049371540546417,
-0.06677926331758499,
-0.03818492591381073,
-0.0227988101541996,
0.02031223103404045,
0.004058597143739462,
-0.042409561574459076,
0.00893128290772438,
0.018204065039753914,
-0.02591588720679283,
-0.0021443446166813374,
0.01995030976831913,
-0.0074072107672691345,
0.007542978972196579,
-0.04120120406150818,
0.06997722387313843,
-0.019884422421455383,
0.05908740684390068,
0.0027689700946211815,
-0.00665850518271327,
-0.011855671182274818,
0.09901822358369827,
0.09825755655765533,
0.029795927926898003,
-0.04835022985935211,
0.00016618834342807531,
-0.007136845495551825,
-0.060704972594976425,
0.004707412328571081,
-0.008311832323670387,
0.011989977210760117,
-0.028303390368819237,
-0.030282188206911087,
0.05292055383324623,
0.00926903448998928,
0.049086108803749084,
0.016311807557940483,
0.011616125702857971,
-0.017192067578434944,
0.0006948651280254126,
-0.005643554497510195,
0.03397834300994873,
0.03325330466032028,
0.041530199348926544,
0.028212307021021843,
-0.016228804364800453,
-0.018962884321808815,
0.033365339040756226,
0.02595902793109417,
-0.034506458789110184,
0.007894819602370262,
0.07026900351047516,
-0.01402824092656374,
-0.00956061203032732,
0.038556940853595734,
0.0018681257497519255,
0.010763365775346756,
0.057071831077337265,
0.03386566415429115,
0.010518956929445267,
0.029927942901849747,
-0.025281168520450592,
0.06329429894685745,
0.012373846024274826,
-0.04311559721827507,
0.011317566968500614,
0.012304379604756832,
0.0575425922870636,
0.055527057498693466,
0.0069892252795398235,
-0.03055541217327118,
-0.013608961366117,
0.022164080291986465,
-0.023344727233052254,
0.01303840707987547,
-0.01624906063079834,
0.014325618743896484,
0.015035574324429035,
-0.003204979235306382,
0.011236980557441711,
-0.02803538180887699,
0.003920676186680794,
-0.054875776171684265,
0.06336893141269684,
0.10262864083051682,
0.04437712952494621,
-0.0021693946328014135,
0.006960137281566858,
-0.025529038161039352,
-0.06864433735609055,
-0.012917561456561089,
0.011057695373892784,
0.00028092958382330835,
-0.032194238156080246,
0.010627244599163532,
-0.03816794976592064,
-0.019451865926384926,
0.04330459237098694,
-0.02445918135344982,
0.035138219594955444,
-0.057274024933576584,
-0.11303435266017914,
-0.0340210385620594,
0.040662139654159546,
0.008292490616440773,
-0.02034160867333412,
-0.06684485822916031,
0.014629567973315716,
0.03861472010612488,
0.0796990692615509,
0.009939543902873993,
-0.0018582803895696998,
-0.006787989754229784,
0.03145362436771393,
-0.005659190472215414,
0.015181365422904491,
-0.003163056680932641,
-0.004929062444716692,
-0.003681286470964551,
0.006070486269891262,
-0.044647857546806335,
0.025369009003043175,
0.033190615475177765,
0.006533380597829819,
-0.036747194826602936,
0.033241502940654755,
-0.031054852530360222,
-0.004734070971608162,
-0.010125435888767242,
-0.023316197097301483,
-0.034263502806425095,
0.06286696344614029,
0.018118154257535934,
0.02045581117272377,
0.034910619258880615,
0.015730302780866623,
0.025360053405165672,
-0.009224695153534412,
0.017642585560679436,
-0.008679050952196121,
-0.044077418744564056,
-0.004307499621063471,
-0.009503409266471863,
-0.023325547575950623,
-0.0034493068233132362,
-0.0511009655892849,
-0.035635415464639664,
0.002484839642420411,
0.0024240687489509583,
0.013765646144747734,
0.05318634584546089,
0.020000210031867027,
-0.016716161742806435,
0.007091019302606583,
-0.019406599923968315,
-0.01303029339760542,
-0.01509444322437048,
0.016952693462371826,
0.005356346722692251,
-0.02279069647192955,
-0.011665859259665012,
0.014000346884131432,
-0.02186395227909088,
-0.012486131861805916,
-0.034484829753637314,
-0.014040703885257244,
0.019077152013778687,
0.0092924190685153,
-0.001891349209472537,
0.003094833344221115,
0.07151231169700623,
0.027431147173047066,
0.0005878425436094403,
0.0175866037607193,
0.0027343507390469313,
-0.043322741985321045,
0.01781393215060234,
-0.0513494610786438,
0.04957651346921921,
-0.007510574534535408,
0.00783494208008051,
-0.006551498547196388,
-0.015925584360957146,
-0.03841352090239525,
0.0470980629324913,
-0.0104746762663126,
0.07792016118764877,
0.0200311578810215,
0.0040835062973201275,
-0.03351350128650665,
0.05839946120977402,
0.004180959425866604,
0.008329092524945736,
-0.01048258412629366,
-0.06154778227210045,
-0.06624581664800644,
-0.0146107729524374,
0.03113728016614914,
-0.013584568165242672,
-0.060353972017765045,
0.024812253192067146,
0.012156922370195389,
0.060967084020376205,
0.05659984052181244,
0.053261648863554,
-0.02524605020880699,
-0.04065430164337158,
0.0003186760877724737,
0.0031939330510795116,
0.0038862647488713264,
-0.012862847186625004,
0.010758628137409687,
0.003999471664428711,
0.0024868559557944536,
-0.015946412459015846,
0.0162549689412117,
0.023149143904447556,
-0.0077561866492033005,
0.03254645690321922,
-0.007804568391293287,
-0.04546188935637474,
0.00985803548246622,
0.0017699073068797588,
-0.00693236431106925,
0.008788671344518661,
-0.025594497099518776,
-0.0024097352288663387,
-0.039309028536081314,
0.01100828591734171,
0.02214214950799942,
0.015007173642516136,
-0.010100099258124828,
-0.005052901338785887,
0.00197661854326725,
-0.07793398201465607,
-0.005605513229966164,
-0.043872542679309845,
-0.01215010229498148,
-0.020049067214131355,
-0.02966603823006153,
0.019504038617014885,
0.02910492941737175,
0.02585269697010517,
-0.020163733512163162,
-0.019813936203718185,
0.023500600829720497,
-0.025857212021946907,
-0.006827102974057198,
0.011843792162835598,
0.0058458177372813225,
-0.012709318660199642,
-0.04679612070322037,
-0.002837971318513155,
0.05398116260766983,
-0.007430708967149258,
0.0016341176815330982,
0.008993355557322502,
-0.030800215899944305,
-0.07563689351081848,
-0.011577409692108631,
-0.005761545617133379,
0.0014979761326685548,
0.011881763115525246,
0.021191293373703957,
0.08752968907356262,
0.03513986989855766,
-0.041795261204242706,
0.01634548045694828,
-0.020480236038565636,
-0.000698120566084981,
-0.013296157121658325,
-0.011843823827803135,
0.011560440063476562,
-0.03529255464673042,
-0.003449832322075963,
0.016362598165869713,
-0.05762147530913353,
0.02798289619386196,
-0.03304849565029144,
-0.022843368351459503,
0.03870509937405586,
0.005631117150187492,
0.034307416528463364,
-0.003172634169459343,
0.010094054043293,
0.03841104358434677,
0.035778746008872986,
-0.030093759298324585,
-0.021101217716932297,
0.005046874284744263,
-0.008702903985977173,
-0.030255746096372604,
0.06399023532867432,
0.05888992175459862,
-0.0028027407824993134,
0.030705122277140617,
0.01879896968603134,
0.02736089564859867,
0.05516820400953293,
0.022828735411167145,
0.0039078546687960625,
-0.00435400428250432,
0.0171650480479002,
-0.014944900758564472,
0.0239272303879261,
0.016553375869989395,
-0.04839552566409111,
-0.006681359373033047,
0.0037221366073936224,
0.011591303162276745,
0.03593110293149948,
-0.039413295686244965,
0.039848748594522476,
0.0036120512522757053,
0.0359107069671154,
-0.0403452031314373,
-0.00921097956597805,
0.0006024150643497705,
0.008184337057173252,
-0.002622556174173951,
0.04453500732779503,
0.06866089254617691,
-0.009597256779670715,
0.008194920606911182,
0.01617051102221012,
0.06208143010735512,
-0.017084253951907158,
-0.009315193630754948,
0.00877574272453785,
0.02055099979043007,
0.003922793548554182,
-0.008527872152626514,
-0.009694399312138557,
0.054534297436475754,
0.033714085817337036,
0.046726156026124954,
-0.02185092121362686,
-0.019371656700968742,
-0.039820753037929535,
-0.013441379182040691,
-0.015314077958464622,
0.008879968896508217,
0.06678749620914459,
0.007383233867585659,
0.06721238791942596,
0.041732944548130035,
0.0005942446296103299,
0.004363301210105419,
-0.012093765661120415,
-0.07949653267860413,
0.005738601554185152,
-0.01681060716509819,
-0.00045481929555535316,
-0.0006901493761688471,
-0.021240297704935074,
-0.04816986992955208,
-0.0040668584406375885,
-0.050983726978302,
-0.0014305880758911371,
-0.022518673911690712,
-0.057792726904153824,
0.017621465027332306,
0.0008295830339193344,
-0.052156977355480194,
-0.030667772516608238,
0.031232835724949837,
0.019559480249881744,
-0.010884726420044899,
-0.030166566371917725,
0.02424156293272972,
0.0053419871255755424,
0.0320063978433609,
-0.027265410870313644,
0.027708755806088448,
0.010961477644741535,
0.041343703866004944,
0.02665676549077034,
-0.03711824119091034,
-0.020166592672467232,
-0.002964910352602601,
0.01679176837205887,
0.023280752822756767,
0.009991330094635487,
-0.029884569346904755,
-0.039498671889305115,
-0.03596116974949837,
-0.010151438415050507,
-0.0207290630787611,
0.03199185058474541,
0.0022915040608495474,
0.003817320801317692,
0.02442958392202854,
0.004496435169130564,
-0.007853030227124691,
0.03528629615902901,
0.015642132610082626,
-0.009714758954942226,
-0.025237245485186577,
-0.03671235963702202,
-0.030258553102612495,
-0.053656045347452164,
-0.016205869615077972,
0.02649117261171341,
0.001436354243196547,
0.014202619902789593,
-0.000671637593768537,
0.03356239199638367,
0.008210224099457264,
-0.002603985136374831,
-0.028219357132911682,
0.0022276665549725294,
-0.024839021265506744,
-0.013403438962996006,
-0.020309459418058395,
0.00828559324145317,
0.03140943869948387,
0.07052640616893768,
-0.008334483951330185,
-0.0013148761354386806,
-0.06808499246835709,
-0.015181876718997955,
0.027953626587986946,
0.05583576858043671,
-0.01216826867312193,
-0.043771740049123764,
-0.040673770010471344,
0.006853910628706217,
0.013825071975588799,
-0.02072676457464695,
0.02786431461572647,
-0.04761281982064247,
-0.024482719600200653,
-0.03256090730428696,
-0.04373990744352341,
-0.029582392424345016,
-0.017817284911870956,
0.0049698553048074245,
-0.0141246123239398,
-0.011747702956199646,
-0.02109540067613125,
-0.013148966245353222,
0.0009604683145880699,
0.021500900387763977,
0.0408141054213047,
0.0020516621880233288,
0.009540805593132973,
0.0120040038600564,
0.054569512605667114,
-0.015388935804367065,
-0.07645457237958908,
0.0007623047567903996,
-0.0016009300015866756,
-0.022359199821949005,
0.04912082105875015,
0.00000805435047368519,
-0.024383168667554855,
0.06684073060750961,
0.026447009295225143,
0.0015593633288517594,
-0.014099286869168282,
-0.041446950286626816,
0.03915915638208389,
0.017235253006219864,
-0.0018762509571388364,
0.06858717650175095,
0.045769382268190384,
-0.022396814078092575,
-0.005504316184669733,
-0.00507392780855298,
0.008606413379311562,
-0.008619964122772217,
-0.01481662131845951,
0.002863144502043724,
0.015678120777010918,
-0.0032762533519417048,
0.02895752526819706,
-0.03416544198989868,
0.01505147386342287,
0.025044027715921402,
-0.03376118093729019,
0.002742455108091235,
0.019819876179099083,
-0.01531627494841814,
0.00995367206633091,
-0.0292466189712286,
0.0455799475312233,
-0.022340547293424606,
0.007723774760961533,
0.04474446177482605,
-0.025612875819206238,
-0.015035498887300491,
0.055773768573999405,
-0.014569643884897232,
-0.024965669959783554,
-0.045149337500333786,
-0.009796209633350372,
-0.009312594309449196,
-0.031282078474760056,
0.017666015774011612,
-0.04008322209119797,
0.021199088543653488,
-0.008990795351564884,
-0.03742064908146858,
-0.02351480722427368,
0.023312650620937347,
0.02008681930601597,
0.05706910043954849,
-0.0072177378460764885,
0.01905777119100094,
0.0051075248047709465,
-0.018905481323599815,
-0.06956596672534943,
-0.047017090022563934,
0.026276959106326103,
0.06346368789672852,
0.015283203683793545,
-0.0001233553048223257,
0.050330840051174164,
-0.019629552960395813,
-0.031854599714279175,
0.012844005599617958,
-0.020902546122670174,
-0.04045802354812622,
0.03728173300623894,
-0.00026267769862897694,
0.028096145018935204,
0.034147586673498154,
0.004484070930629969,
-0.041835542768239975,
0.03946615383028984,
-0.023826466873288155,
-0.03869001567363739,
-0.04523693025112152,
0.03014550730586052,
-0.0014386314433068037,
-0.057724419981241226,
0.0011953889625146985,
-0.016760030761361122,
0.03360578045248985,
-0.013709013350307941,
-0.030722759664058685,
0.038081612437963486,
0.0033075478859245777,
0.010824166238307953,
-0.012489764019846916,
0.03290203586220741,
0.0039019400719553232,
0.03558474779129028,
-0.013832434080541134,
0.0029322761110961437,
-0.05430445447564125,
-0.03902927041053772,
0.0507919006049633,
-0.01703793555498123,
0.05472515523433685,
0.029300622642040253,
0.05524369329214096,
0.00008003468974493444,
0.02274521254003048,
-0.0005704495124518871,
-0.002575768856331706,
0.03635802119970322,
-0.028716720640659332,
0.008947576396167278,
0.02032177895307541,
0.026207221671938896,
0.004493164364248514,
-0.040361542254686356,
-0.014979032799601555,
-0.020205069333314896,
0.04277733713388443,
-0.014185529202222824,
0.028967883437871933,
-0.00566530879586935,
-0.01672191359102726,
-0.024187207221984863,
-0.012920983135700226,
-0.021657021716237068,
0.0068420832976698875,
-0.024710174649953842,
0.03162657096982002,
-0.027539651840925217,
0.006551212631165981,
0.013294056989252567,
0.0673326626420021,
-0.00967248622328043,
0.012718931771814823,
0.05376078188419342,
0.0458429716527462,
-0.00498472573235631,
0.008904561400413513,
-0.03603134676814079,
0.014984464272856712,
-0.04677624627947807,
0.0045384899713099,
0.03404843807220459,
-0.018410339951515198,
0.030909301713109016,
0.007394763641059399,
0.004708835855126381,
-0.02841542661190033,
-0.01756005734205246,
-0.03713250905275345,
0.02800886146724224,
-0.0275665745139122,
0.012160365469753742,
0.014466268010437489,
-0.02643563039600849,
0.032883159816265106,
-0.006302294321358204,
0.019724899902939796,
0.05128731578588486,
-0.04350042715668678,
-0.029904134571552277,
-0.030988870188593864,
-0.06677435338497162,
0.0768660232424736,
0.021885966882109642,
-0.023344729095697403,
-0.004108100663870573,
-0.05836154520511627,
0.06278306990861893,
0.007188162300735712,
0.033519111573696136,
0.005218496546149254,
0.034866247326135635,
-0.015146663412451744,
0.006612006574869156,
0.004584716632962227,
0.02607523836195469,
0.11396549642086029,
0.04595315083861351,
0.020933298394083977,
-0.02717328816652298,
-0.02511816844344139,
-0.05552364140748978,
0.025918183848261833,
0.007976913824677467,
0.02563275396823883,
0.01996561884880066,
0.022677114233374596,
0.011664134450256824,
0.026135200634598732,
0.02929738536477089,
-0.010304795578122139,
0.03471958264708519,
-0.04699331894516945,
-0.022332189604640007,
0.031032931059598923,
-0.0077757020480930805,
0.01493599358946085,
0.02940976992249489,
-0.03955128788948059,
0.02893228642642498,
-0.03406331688165665,
-0.04860444739460945,
-0.0354406014084816,
-0.019985010847449303,
0.037100840359926224,
-0.029654480516910553,
-0.03558928519487381,
-0.028804516419768333,
-0.018353570252656937,
-0.014441203325986862,
-0.019546210765838623,
0.032861389219760895,
0.0452067106962204,
-0.018118297681212425,
-0.002001302083954215,
-0.033591173589229584,
0.022521337494254112,
0.005686093587428331,
0.008079707622528076,
0.02899213507771492,
-0.02884559892117977,
0.00770626962184906,
-0.024491826072335243,
0.05934327840805054,
-0.044845227152109146,
-0.019508009776473045,
-0.023749055340886116,
0.015349190682172775,
0.008683075197041035,
-0.045012108981609344,
-0.020861878991127014,
-0.015698881819844246,
0.035997696220874786,
0.013287942856550217,
-0.02851465344429016,
-0.009865070693194866,
0.011276441626250744,
-0.01146883238106966,
0.02851942554116249,
0.020508859306573868,
-0.01975238509476185,
-0.008070596493780613,
-0.00047938499483279884,
0.014651617966592312,
-0.032476723194122314,
0.008797569200396538,
-0.013494877144694328,
0.0014011473394930363,
-0.041900552809238434,
-0.00953873060643673,
0.005564048420637846,
0.03875759616494179,
0.03577147424221039,
-0.013334386982023716,
-0.02102118730545044,
-0.03248340263962746,
-0.053294502198696136,
0.02351203002035618,
-0.004068940412253141,
-0.01885390095412731,
-0.020887751132249832,
-0.018053241074085236,
-0.012613995000720024,
0.042763110250234604,
-0.0330192856490612,
-0.02152060903608799,
-0.0017975927330553532,
0.013035046868026257,
-0.009492428973317146,
-0.03811166062951088,
-0.06689611077308655,
0.029378466308116913,
0.012467369437217712,
0.021381905302405357,
0.0005584753816947341,
0.03189187869429588,
-0.013356524519622326,
0.020849525928497314,
0.012794566340744495,
0.025869056582450867,
-0.012319657020270824,
-0.05040637031197548,
0.011217023245990276,
-0.029509948566555977,
0.008446885272860527,
0.018600964918732643,
0.022872978821396828,
-0.026719016954302788,
-0.031503695994615555,
-0.025139139965176582,
-0.007987153716385365,
-0.00008343531226273626,
0.01639525219798088,
0.021414058282971382,
0.010525009594857693,
-0.0487295538187027,
0.002426520688459277,
0.0015942163299769163,
0.0018098574364557862,
-0.06398014724254608,
0.028916627168655396,
0.00898620206862688,
-0.037865061312913895,
-0.0343690924346447,
0.03982410952448845,
-0.03787657618522644,
-0.005809473339468241,
0.04990579932928085,
0.01312689483165741,
-0.03629622235894203,
0.04423098638653755,
0.01580476388335228,
0.002405985724180937,
0.04218646511435509,
0.012036154046654701,
0.00009244859393220395,
0.05131879076361656,
-0.06645388156175613,
-0.03826594352722168,
0.004533381666988134,
-0.008269675076007843,
0.019696051254868507,
0.0189057569950819,
-0.03816812485456467,
-0.01962040737271309,
0.06877274811267853,
-0.024798812344670296,
-0.01316953543573618,
-0.0180346742272377,
0.04973341524600983,
0.008161128498613834,
0.017822207883000374,
0.0005244564381428063,
-0.039854951202869415,
-0.020513184368610382,
0.0790271982550621,
-0.0028682383708655834,
0.007331805303692818,
0.003836000105366111,
-0.018801255151629448,
-0.019866596907377243,
-0.0023828125558793545,
-0.0015485456679016352,
0.03684021160006523,
0.029240209609270096,
0.05273137241601944,
-0.019987020641565323,
0.07959470897912979,
0.02589760720729828,
0.0037115642335265875,
-0.07285798341035843,
-0.026710912585258484,
-0.024759825319051743,
0.03898876532912254,
0.03379909321665764,
-0.0425419844686985,
0.0024087890051305294,
-0.011088097468018532,
-0.1084434986114502,
0.002069341018795967,
0.013974626548588276,
-0.0285785011947155,
-0.0574876144528389,
0.010187826119363308,
-0.044047459959983826,
0.005868586711585522,
0.02507632039487362,
0.05317125469446182,
0.020734546706080437,
0.021768730133771896,
-0.023028917610645294,
-0.00376282911747694,
-0.05327910929918289,
0.03487575054168701,
-0.007262285798788071,
0.001952855265699327,
0.06579577177762985,
-0.002959354082122445,
0.004517735447734594,
0.008701219223439693,
-0.011482302099466324,
0.026608340442180634,
0.030028048902750015,
0.005891937296837568,
-0.00008099625847535208,
0.019911691546440125,
0.004947501700371504,
-0.040533483028411865,
0.010946938768029213,
0.02434612438082695,
0.023289931938052177,
0.0003339905524626374,
-0.018716800957918167,
0.03257032483816147,
0.05255211889743805,
-0.05727237090468407,
-0.024144696071743965,
-0.003730603028088808,
0.0047280569560825825,
-0.027096135541796684,
-0.012386113405227661,
0.046913474798202515,
0.03902874514460564,
-0.025913190096616745,
-0.007669406943023205,
-0.07182299345731735,
-0.019989321008324623,
0.010622131638228893,
0.02282867766916752,
0.01463065855205059,
-0.016321968287229538,
0.007072765380144119,
-0.010396252386271954,
0.005900068674236536,
0.02842838317155838,
-0.008991519920527935,
-0.015356967225670815,
0.004599357955157757,
-0.0029754620045423508,
0.01765667274594307,
-0.003214200958609581,
-0.03339270502328873,
-0.07140333950519562,
0.0180366113781929,
-0.011090262793004513,
0.03764879330992699,
0.033070918172597885,
-0.022884802892804146,
-0.05493685603141785,
-0.07429544627666473,
0.00596242630854249,
-0.04663742333650589,
-0.00414734473451972,
-0.05150790885090828,
-0.019580993801355362,
-0.03001450188457966,
0.040474485605955124,
0.06879019737243652,
0.0000296779671771219,
-0.001869599218480289,
-0.0014155474491417408,
0.01039976067841053,
0.026298724114894867,
-0.03148255497217178,
0.034842297434806824,
-0.04627302289009094,
-0.02245364710688591,
-0.027449361979961395,
0.039328623563051224,
-0.02472437173128128,
0.04454997181892395,
0.009181651286780834,
-0.03275047615170479,
0.002213104162365198,
-0.05470918491482735,
-0.024415187537670135,
0.05473196879029274,
0.019843043759465218,
-0.039904043078422546,
0.041680291295051575,
-0.008540184237062931,
0.02292638272047043,
0.02942216768860817,
-0.0037553124129772186,
-0.028877826407551765,
0.02788432687520981,
-0.03690299391746521,
0.0016946193063631654,
0.03047896735370159,
-0.023597853258252144,
0.011163811199367046,
-0.015530620701611042,
0.003842303529381752,
0.03120083548128605,
-0.03012615442276001,
-0.014580854214727879,
0.0429806187748909,
0.03377753868699074,
0.00720949238166213,
0.042685024440288544,
0.03824299946427345,
-0.009329556487500668,
-0.017206288874149323,
-0.05196847394108772,
0.02868230827152729,
-0.0020056746434420347,
-0.009194166399538517,
0.026168467476963997,
0.051014650613069534,
-0.002853990765288472,
0.010480226948857307,
0.0017175044631585479,
0.06057615578174591,
-0.04179535433650017,
-0.01960853300988674,
-0.007789186201989651,
0.005388136021792889,
-0.023975655436515808,
-0.02768152579665184,
-0.02541985735297203,
0.06689972430467606,
-0.03237267583608627,
0.020068388432264328,
-0.008598235435783863,
-0.03586670383810997,
0.03400687873363495,
0.026905793696641922,
0.04673121124505997,
0.028922943398356438,
-0.01480349525809288,
-0.009393690153956413,
-0.02040800079703331,
0.015456648543477058,
0.05601290240883827,
-0.03938205912709236,
0.00570007273927331,
-0.02504603937268257,
-0.030552469193935394,
0.0018260084325447679,
0.005742231849581003,
0.028129450976848602,
-0.004427052568644285,
0.0187411829829216,
0.05552567541599274,
-0.023460151627659798,
-0.0019888279493898153,
0.010461036115884781,
-0.054016124457120895,
0.049252234399318695,
-0.06322776526212692,
0.0106737669557333,
-0.017046045511960983,
0.043217021971940994,
0.001950382604263723,
0.036253660917282104
] |
<p>If I understand correctly, according to Einstein's General Theory of Relativity, mass results in a distortion in space-time. In turn, the motion of the mass is affected by the distortion. A result of the interplay between mass and space-time is that the 'force' of gravity may be explained away. Masses are not subject to a force, but are merely following a 4-dimensional space-time geodesic; gravity is just geometry.</p>
<p>And yet physicists are searching for exchange particles for the force of gravity, and are trying to unify quantum mechanics with relativity, or to unify the weak/strong/electromagnetic forces with that of gravity.</p>
<ol>
<li><p>What have I missed? Are these different communities of physicists? Does relativity explain only part of the story of masses acting under gravity?</p></li>
<li><p>Is gravity a force or not? Is it only an apparent force or not?</p></li>
<li><p>Can such an apparent force 'generate' exchange particles? Are the exchange particle and geometric models both different views of the same underlying truth?</p></li>
<li><p>A side question might be: why can't the other forces be explained away similarly? Or is that what is happening with all this talk of small extra dimensions?</p></li>
</ol>
<p>I'd appreciate any illumination on this matter, or suggested reading (preferably at the 'popular science' or undergraduate level).</p>
| 10,776 |
[
-0.0019154882756993175,
-0.0039015444926917553,
0.024991484358906746,
-0.05684962496161461,
0.0517965666949749,
0.021154824644327164,
-0.02146811969578266,
-0.023444483056664467,
-0.010237524285912514,
-0.02959677390754223,
0.027314890176057816,
0.007542275823652744,
0.06239740923047066,
0.017380090430378914,
0.003945525735616684,
0.01193083357065916,
-0.001051090657711029,
-0.021975500509142876,
-0.000017515456420369446,
-0.0478559248149395,
0.0072387820109725,
0.023065509274601936,
-0.00390642648562789,
-0.0005504616419784725,
-0.033165935426950455,
0.03173203766345978,
0.0486738458275795,
0.011890972964465618,
0.027689091861248016,
0.06818781793117523,
0.009256351739168167,
0.0027067235205322504,
-0.0023312843404710293,
0.00902294460684061,
0.004195746965706348,
0.008284462615847588,
-0.015618745237588882,
-0.035392243415117264,
0.05797167122364044,
0.01388736255466938,
-0.04748086258769035,
-0.0030797591898590326,
-0.007630350533872843,
0.03131123259663582,
-0.02920670621097088,
0.02109227329492569,
0.029522327706217766,
0.02980477176606655,
0.08036123961210251,
-0.055001407861709595,
0.0648590549826622,
0.023421213030815125,
0.018580075353384018,
-0.019189445301890373,
-0.009164550341665745,
-0.010996283032000065,
0.06204633042216301,
0.056411370635032654,
-0.005114509258419275,
-0.07180363684892654,
-0.010381810367107391,
-0.025707755237817764,
-0.016378970816731453,
-0.023117080330848694,
-0.01344013400375843,
0.036353059113025665,
-0.030391009524464607,
-0.0009141070186160505,
0.022869450971484184,
-0.0009491664823144674,
0.006613972131162882,
0.015077564865350723,
0.02913358062505722,
0.056922607123851776,
-0.017737019807100296,
-0.02644553780555725,
0.014462901279330254,
-0.012512655928730965,
0.03856454789638519,
0.03463805094361305,
-0.02672179788351059,
0.013261974789202213,
0.04259507358074188,
0.0252839382737875,
0.02915893867611885,
0.002468494465574622,
0.058737464249134064,
-0.03793928399682045,
0.0010788210202008486,
0.04043222963809967,
-0.03227035701274872,
0.013135225512087345,
0.054931920021772385,
-0.003242631908506155,
-0.03938743844628334,
0.03130947798490524,
0.01569945178925991,
0.014485524967312813,
-0.0045168097130954266,
0.020022863522171974,
-0.026522180065512657,
-0.00546569749712944,
0.010363423265516758,
0.07216331362724304,
0.0027586696669459343,
-0.016242150217294693,
-0.036040857434272766,
0.01446453481912613,
-0.022596467286348343,
-0.01341051422059536,
-0.01652681641280651,
-0.0065229800529778,
0.01144407782703638,
0.00627613952383399,
0.013225728645920753,
-0.031256671994924545,
0.037692517042160034,
-0.02737342193722725,
0.0767131894826889,
0.06190557777881622,
0.026080748066306114,
-0.062287360429763794,
0.0015487958444282413,
-0.015426802448928356,
-0.06338273733854294,
-0.012140566483139992,
0.05194962024688721,
-0.00476055545732379,
0.0015062644379213452,
0.03225769102573395,
0.017695490270853043,
-0.0018972582183778286,
-0.01010155864059925,
0.03323584049940109,
0.04599711671471596,
0.015212154015898705,
-0.09106633067131042,
-0.05126163735985756,
0.06410881131887436,
-0.005859327968209982,
-0.019694456830620766,
-0.05255861207842827,
-0.033690061420202255,
0.014513721689581871,
0.07497860491275787,
0.016167867928743362,
0.02052859403192997,
-0.009404923766851425,
0.049523450434207916,
0.0283465888351202,
-0.012060803361237049,
0.01417478546500206,
-0.01203838735818863,
-0.029489226639270782,
0.003926635254174471,
-0.07347734272480011,
0.01793629303574562,
0.05009052902460098,
-0.020471228286623955,
-0.002007311675697565,
0.09836681932210922,
0.005732226651161909,
0.011118100956082344,
0.03535844013094902,
0.01115524023771286,
-0.01862451434135437,
0.04415006563067436,
-0.0027196849696338177,
-0.02680351957678795,
0.05259685218334198,
0.024203039705753326,
0.014919701032340527,
0.022249408066272736,
0.019070178270339966,
-0.012660875916481018,
-0.0202089361846447,
-0.02620408870279789,
-0.019003232941031456,
-0.02742443047463894,
0.007863746024668217,
-0.04287033528089523,
-0.039835430681705475,
-0.0232964139431715,
-0.028519436717033386,
0.0047577195800840855,
0.006905138958245516,
-0.01850716955959797,
-0.013974218629300594,
0.013582549057900906,
-0.035534027963876724,
-0.04337810352444649,
-0.07499130815267563,
-0.004949275869876146,
-0.008377709425985813,
-0.016994187608361244,
0.013183576986193657,
0.016288997605443,
0.014415278099477291,
-0.03863808885216713,
-0.03480595722794533,
-0.011053802445530891,
0.04657701030373573,
0.011753064580261707,
0.022580476477742195,
0.0034217573702335358,
0.04050514101982117,
0.025291625410318375,
-0.007642409298568964,
-0.02110518142580986,
0.03597690165042877,
-0.0617765411734581,
0.02656044065952301,
-0.013871664181351662,
0.02199679985642433,
-0.009982411749660969,
0.016933349892497063,
-0.019522644579410553,
-0.012303832918405533,
-0.033974431455135345,
0.03149893879890442,
-0.020024973899126053,
0.06172974780201912,
0.023496270179748535,
-0.008027379401028156,
-0.02299569733440876,
0.08567314594984055,
0.055899765342473984,
0.03484770283102989,
-0.015780974179506302,
-0.02261423133313656,
-0.05168347433209419,
-0.04973633214831352,
0.006902887485921383,
0.04609420895576477,
-0.005262891761958599,
0.05354240909218788,
0.02105950377881527,
0.07093389332294464,
-0.024188080802559853,
0.023942526429891586,
-0.024974405765533447,
-0.03155122697353363,
0.025379272177815437,
0.0034486171789467335,
0.010878683999180794,
0.026844708248972893,
0.028297284618020058,
0.026679914444684982,
-0.018573470413684845,
-0.01710408367216587,
-0.016631612554192543,
-0.0005920696421526372,
-0.015404516831040382,
0.035888493061065674,
0.012366591021418571,
-0.03358902409672737,
0.04922380670905113,
0.006274574436247349,
0.0065300436690449715,
0.02571154572069645,
-0.019253648817539215,
-0.022539174184203148,
-0.030631398782134056,
-0.009059583768248558,
-0.017617451027035713,
0.005318258889019489,
-0.015783142298460007,
-0.030657971277832985,
0.01932222954928875,
-0.06858034431934357,
0.02227349579334259,
-0.03585419803857803,
-0.051859721541404724,
-0.022992068901658058,
-0.005631355568766594,
-0.005711630918085575,
0.03653222694993019,
0.06761982291936874,
-0.03702376037836075,
-0.03801347315311432,
0.028913306072354317,
-0.033324502408504486,
-0.024474194273352623,
0.0319577194750309,
-0.04848121106624603,
0.03370610997080803,
-0.09268241375684738,
0.0007985769188962877,
0.0531187430024147,
-0.010111987590789795,
0.027269449084997177,
0.019753968343138695,
0.011427839286625385,
-0.024251580238342285,
-0.01568811759352684,
-0.025624649599194527,
0.008599171414971352,
-0.03099762462079525,
-0.006683944258838892,
0.04990483075380325,
-0.02549211122095585,
-0.032559968531131744,
0.011769762262701988,
-0.024197883903980255,
-0.024378381669521332,
-0.0379573293030262,
0.026822224259376526,
-0.010980100370943546,
-0.017856432124972343,
0.0006465300102718174,
0.03723369166254997,
-0.019830763339996338,
-0.013179216533899307,
-0.05284258723258972,
-0.03237226605415344,
0.026482123881578445,
-0.005993783939629793,
0.04261861741542816,
0.00827713217586279,
-0.02927977591753006,
0.05905731022357941,
0.02579573169350624,
0.00630216347053647,
-0.0306314155459404,
-0.007488852832466364,
0.007227833848446608,
-0.016812337562441826,
0.04272381588816643,
0.012552441097795963,
0.020382855087518692,
0.0065316567197442055,
0.05184358358383179,
0.04146308824419975,
-0.030006134882569313,
-0.0027592992410063744,
-0.03380388393998146,
-0.007203435059636831,
0.012046273797750473,
-0.017945032566785812,
0.0214946698397398,
0.01831265538930893,
-0.015122901648283005,
-0.013906213454902172,
0.011088419705629349,
0.03595797345042229,
-0.002151651307940483,
-0.0588432140648365,
0.03733619302511215,
0.03323959931731224,
0.003239215351641178,
0.006144619081169367,
0.008709082379937172,
-0.01874917559325695,
-0.02595536969602108,
0.01776449754834175,
-0.011764162220060825,
0.05145935341715813,
-0.00007980149530339986,
0.018130110576748848,
0.048185717314481735,
0.06023332104086876,
-0.030317816883325577,
0.0020331672858446836,
0.005290167406201363,
0.005598119925707579,
-0.00019403098849579692,
-0.04816924035549164,
0.018388301134109497,
0.046140119433403015,
0.04807490482926369,
0.03649323433637619,
0.011902257800102234,
-0.038729242980480194,
-0.020151449367403984,
-0.046865593641996384,
0.01009314227849245,
0.010381192900240421,
0.03698119521141052,
0.0024674287997186184,
0.033459920436143875,
0.020955223590135574,
0.0019635031931102276,
-0.015317696146667004,
0.0046502104960381985,
-0.08218145370483398,
-0.0022716689854860306,
-0.05251311510801315,
0.013197380118072033,
-0.008256408385932446,
-0.007298795040696859,
-0.020344678312540054,
-0.012033888138830662,
-0.02415924333035946,
-0.017649894580245018,
-0.015771079808473587,
-0.056109894067049026,
0.016889996826648712,
-0.08168207854032516,
-0.05540814250707626,
0.007721719332039356,
0.023349231109023094,
0.05499017611145973,
-0.021712174639105797,
-0.025392159819602966,
0.0422491729259491,
-0.052100397646427155,
-0.022587841376662254,
-0.0024675405584275723,
0.011140668764710426,
0.010431545786559582,
0.026062633842229843,
-0.024685639888048172,
-0.0035784756764769554,
-0.02149832621216774,
0.0038416534662246704,
0.03839588165283203,
0.02623826079070568,
-0.012599628418684006,
0.012829978950321674,
-0.04065776243805885,
-0.045496974140405655,
-0.021430540829896927,
0.006702720187604427,
0.04699878767132759,
0.0011311377165839076,
-0.01638752594590187,
0.012177140451967716,
0.014022082090377808,
-0.03579634055495262,
0.07070112973451614,
0.054732535034418106,
0.019613021984696388,
-0.0325324647128582,
-0.021802622824907303,
-0.0036175139248371124,
-0.031722504645586014,
0.001597040449269116,
0.045594166964292526,
-0.015437258407473564,
-0.0375712625682354,
0.01792491413652897,
-0.014345871284604073,
0.018624506890773773,
-0.03628582879900932,
-0.021872559562325478,
-0.03567155450582504,
0.022781917825341225,
-0.017512356862425804,
0.010017593391239643,
0.009114732965826988,
0.020466532558202744,
0.06432940810918808,
0.009839914739131927,
0.025614669546484947,
-0.10506323724985123,
0.00520248943939805,
0.04429866001009941,
0.061572153121232986,
-0.024272939190268517,
-0.02060076780617237,
-0.06291677802801132,
-0.022580809891223907,
0.013082304038107395,
-0.035629287362098694,
-0.011968211270868778,
-0.018950747326016426,
0.01412511058151722,
-0.013121165335178375,
-0.007019643671810627,
-0.01456315815448761,
0.011661708354949951,
-0.012100163847208023,
-0.012944077141582966,
-0.01735113188624382,
0.019466925412416458,
0.0014833688037469983,
0.053126171231269836,
0.03191438317298889,
0.019902369007468224,
0.040981221944093704,
-0.00255386671051383,
-0.006388892885297537,
0.014279340393841267,
-0.060398172587156296,
-0.09549408406019211,
-0.007997133769094944,
0.025566022843122482,
-0.043980881571769714,
0.04688720777630806,
-0.050359729677438736,
-0.061170563101768494,
-0.0431375652551651,
-0.02103322371840477,
0.012885614298284054,
-0.013267511501908302,
-0.04681049659848213,
0.012370876036584377,
0.025628099218010902,
-0.0011264504864811897,
0.025950830429792404,
0.034523796290159225,
-0.04094551131129265,
-0.003034645691514015,
-0.02564987540245056,
0.043546054512262344,
-0.01994745060801506,
0.014649537391960621,
-0.015105817466974258,
-0.011451179161667824,
-0.05119882896542549,
0.02752758376300335,
0.0011770545970648527,
0.0014535957016050816,
-0.0007188675226643682,
-0.03251812234520912,
-0.025198083370923996,
0.04833177104592323,
-0.0028986004181206226,
-0.012402066960930824,
0.0022656465880572796,
0.018388669937849045,
-0.03546345606446266,
0.006813928484916687,
0.019110381603240967,
0.04648907482624054,
-0.021578967571258545,
0.01819477416574955,
0.01987580582499504,
-0.0014465379063040018,
-0.010506154038012028,
0.0004933734307996929,
0.014287997968494892,
-0.06418147683143616,
0.05070589482784271,
0.00006763330748071894,
-0.0013230426702648401,
0.037312690168619156,
-0.04153447598218918,
-0.022389942780137062,
-0.015451931394636631,
-0.007421031594276428,
0.011565187014639378,
-0.009961429052054882,
0.0054289307445287704,
0.019666798412799835,
0.03320581838488579,
-0.07774475961923599,
-0.0524040125310421,
-0.0006787566817365587,
-0.010623396374285221,
0.017527593299746513,
-0.036750465631484985,
0.009916224516928196,
-0.06393551081418991,
-0.0011024829000234604,
0.00165248301345855,
0.05558866634964943,
-0.0472102127969265,
0.005579082760959864,
0.009780734777450562,
0.019254133105278015,
0.050963904708623886,
-0.02643427811563015,
-0.013856085948646069,
0.025008022785186768,
0.03597765788435936,
0.019405027851462364,
0.01342559140175581,
0.05690184608101845,
-0.014339066110551357,
-0.047702375799417496,
-0.008887529373168945,
-0.0015550563111901283,
-0.0028303239960223436,
-0.03464062884449959,
0.01837369240820408,
0.055137600749731064,
0.019852666184306145,
-0.003241162048652768,
-0.0335223414003849,
0.04898499324917793,
-0.003691333346068859,
0.03642413020133972,
-0.0250425823032856,
0.0383831225335598,
-0.010274002328515053,
-0.04148802161216736,
0.04986901581287384,
-0.013033008202910423,
-0.003273179056122899,
0.01589334011077881,
0.014088818803429604,
0.001494583790190518,
-0.002728598890826106,
0.01492340862751007,
-0.03705648332834244,
0.032409604638814926,
-0.0023102648556232452,
0.013663302175700665,
0.015550038777291775,
-0.0009869297500699759,
-0.019899090752005577,
-0.055583540350198746,
-0.012838057242333889,
-0.0069893039762973785,
0.026155726984143257,
-0.01201999094337225,
0.046283744275569916,
0.03173830732703209,
-0.03653606027364731,
-0.0011002618120983243,
-0.02787819318473339,
0.0007239324622787535,
0.012504484504461288,
0.00985774490982294,
0.010975565761327744,
-0.027303483337163925,
0.004665776155889034,
0.03154328092932701,
0.05914483591914177,
-0.01664564572274685,
-0.009998931549489498,
0.028195157647132874,
0.02273363433778286,
0.010799397714436054,
-0.04160831868648529,
-0.007195711135864258,
0.06156843155622482,
-0.028711393475532532,
0.02908662147819996,
0.012837430462241173,
-0.008260084316134453,
0.03853478282690048,
0.016327109187841415,
0.025969810783863068,
-0.015079168602824211,
-0.024801911786198616,
-0.04038166627287865,
0.007040216121822596,
0.012552481144666672,
0.0019278032705187798,
-0.014819207601249218,
-0.012049026787281036,
0.023925883695483208,
0.01764269545674324,
-0.002351954346522689,
0.014188947156071663,
-0.09016071259975433,
-0.02430340088903904,
-0.020989781245589256,
-0.04321460798382759,
0.0313270166516304,
-0.03869928792119026,
-0.03575422242283821,
0.007099530193954706,
-0.05323746055364609,
0.017328090965747833,
0.02282380312681198,
0.033368222415447235,
-0.0636926218867302,
0.04117267578840256,
-0.01373214926570654,
-0.017282238230109215,
-0.024691332131624222,
-0.012902303598821163,
0.1287636160850525,
0.013290799222886562,
-0.007700833957642317,
-0.037196964025497437,
0.007883656769990921,
-0.0275331549346447,
-0.014409409835934639,
-0.01103555504232645,
-0.013139716349542141,
-0.03670712560415268,
0.02243942953646183,
0.004243839997798204,
0.06670720130205154,
-0.02378714084625244,
-0.05419991910457611,
0.06427928060293198,
-0.004376160446554422,
-0.03295157849788666,
-0.024966612458229065,
0.01731129176914692,
0.011491214856505394,
0.017355093732476234,
-0.046392928808927536,
0.05757109075784683,
-0.032205451279878616,
-0.0034274233039468527,
-0.043394092470407486,
-0.020838763564825058,
-0.010599215514957905,
0.004073095507919788,
-0.0816904678940773,
0.008397427387535572,
0.00046852120431140065,
-0.04429192841053009,
-0.006659283768385649,
0.02965950034558773,
0.003169918665662408,
-0.02124863676726818,
0.041509490460157394,
0.02793804369866848,
-0.03182891756296158,
0.003111959435045719,
0.03520149737596512,
0.01635834202170372,
-0.04001183062791824,
-0.033564165234565735,
-0.0006336388760246336,
0.07050350308418274,
-0.001232024049386382,
0.015178314410150051,
0.02416302263736725,
-0.029726667329669,
0.0061620925553143024,
-0.036777857691049576,
-0.01577211171388626,
-0.021794645115733147,
0.03366180136799812,
-0.0010582481045275927,
-0.010903787799179554,
0.011749382130801678,
0.057082194834947586,
-0.00031854744884185493,
0.03272305801510811,
0.0013062735088169575,
0.006923804525285959,
0.02047123946249485,
-0.021315520629286766,
0.03839455172419548,
0.0011072912020608783,
0.0059455824084579945,
-0.04158037528395653,
-0.024511199444532394,
-0.049718987196683884,
-0.019637366756796837,
0.016663329675793648,
0.04254531115293503,
0.02579023875296116,
0.009133286774158478,
-0.020904485136270523,
-0.021323099732398987,
-0.030082939192652702,
0.04240596294403076,
-0.027074918150901794,
-0.022345220670104027,
-0.00820153672248125,
0.005212308373302221,
0.0024764544796198606,
0.017450479790568352,
0.0043553696013987064,
0.017891384661197662,
-0.00577213428914547,
-0.01603802479803562,
-0.024784646928310394,
-0.0029000083450227976,
-0.02293870598077774,
0.008572138845920563,
-0.004025435075163841,
-0.021179603412747383,
-0.003934677690267563,
0.0016956975450739264,
0.03801826015114784,
-0.02897234819829464,
0.008466795086860657,
0.06587143987417221,
-0.004124082159250975,
-0.016567055135965347,
0.03554706647992134,
0.002173804445192218,
0.0049711307510733604,
0.0116334343329072,
-0.0014488118467852473,
-0.0653730258345604,
-0.0139347268268466,
-0.02555529959499836,
-0.013960604555904865,
-0.022510144859552383,
0.05910395830869675,
-0.023298632353544235,
0.03465840965509415,
-0.0011474844068288803,
0.019015047699213028,
-0.03149835392832756,
0.0021163406781852245,
-0.03378378972411156,
0.005567403044551611,
-0.0120920455083251,
-0.035650867968797684,
-0.016675645485520363,
0.01807548850774765,
-0.02741544507443905,
-0.018005773425102234,
-0.013037726283073425,
0.010173209942877293,
-0.04356951266527176,
0.0021529581863433123,
0.019490737468004227,
-0.009539501741528511,
0.06223253905773163,
0.014477560296654701,
-0.04431892931461334,
0.03008861653506756,
-0.03922555595636368,
-0.03296126425266266,
0.033133868128061295,
-0.028898222371935844,
0.024796025827527046,
0.03794771432876587,
-0.01799292489886284,
-0.02533618174493313,
0.030726034194231033,
-0.01394538301974535,
-0.005332031287252903,
-0.022749610245227814,
-0.013346567749977112,
-0.01919562928378582,
-0.024407925084233284,
-0.004259748850017786,
-0.023265548050403595,
-0.024356460198760033,
0.023884229362010956,
0.007385655771940947,
0.008000215515494347,
0.01279531605541706,
0.026227343827486038,
0.00374202779494226,
-0.02240869216620922,
0.015246054157614708,
0.0017664266051724553,
0.005429708864539862,
0.06294440478086472,
-0.04460286349058151,
0.03309953212738037,
0.031027553603053093,
0.033758074045181274,
-0.11534962803125381,
-0.030057892203330994,
0.011556056328117847,
0.0068671260960400105,
0.0456925705075264,
-0.04242943599820137,
0.014813870191574097,
-0.002217998029664159,
-0.081438809633255,
0.052719779312610626,
-0.02093018963932991,
-0.01124939788132906,
0.01291080191731453,
-0.00557980639860034,
0.013756484724581242,
0.04485570639371872,
0.015984050929546356,
0.0804944708943367,
0.0014445694396272302,
-0.012614325620234013,
-0.003539333352819085,
-0.036606721580028534,
0.00039177737198770046,
0.05110524967312813,
-0.009615740738809109,
0.009280385449528694,
0.08842320740222931,
0.008182454854249954,
-0.01985921896994114,
0.05383655056357384,
0.01155276782810688,
0.008698019199073315,
-0.03040962666273117,
-0.02441239170730114,
0.013236182741820812,
0.025875233113765717,
0.020975379273295403,
-0.023749101907014847,
0.0034494372084736824,
0.04408205300569534,
-0.009846672415733337,
0.029240239411592484,
0.014054235070943832,
0.012028537690639496,
0.008746606297791004,
-0.05054552108049393,
0.02948460355401039,
0.013962626457214355,
-0.015823571011424065,
0.005297141149640083,
-0.019782090559601784,
0.029847677797079086,
0.008117297664284706,
-0.01618502475321293,
0.026004580780863762,
-0.04984382912516594,
-0.010173540562391281,
0.018366562202572823,
0.017344649881124496,
0.008153480477631092,
0.03177065774798393,
0.023055309429764748,
0.01025448739528656,
-0.020893380045890808,
-0.008252759464085102,
0.013872873038053513,
-0.04565183445811272,
0.0023307139053940773,
0.02072243019938469,
0.041263699531555176,
-0.0015211458085104823,
-0.021634744480252266,
-0.03788086771965027,
0.05319917947053909,
0.016208112239837646,
0.060020141303539276,
-0.04827199503779411,
-0.05595451965928078,
-0.006362388841807842,
-0.05649592727422714,
0.010970883071422577,
0.03360425680875778,
0.003373952116817236,
-0.04300011694431305,
-0.02563764899969101,
-0.010918375104665756,
0.0165204256772995,
0.05362487584352493,
0.003619413124397397,
-0.005926212295889854,
0.04622931405901909,
0.018300866708159447,
-0.01658247411251068,
-0.036847688257694244,
-0.005672131199389696,
0.013275262899696827,
-0.010673985816538334,
-0.004065823741257191,
0.011893323622643948,
-0.030936915427446365,
0.02729169651865959,
0.015689082443714142,
-0.05023881047964096,
0.030523071065545082,
0.007772669196128845,
-0.06455083191394806,
0.0736646056175232,
0.013433635234832764,
-0.01601240783929825,
0.035907842218875885,
0.00900198519229889,
0.02821498177945614,
0.017631134018301964,
-0.014031853526830673,
-0.01663290522992611,
0.016049550846219063,
-0.025682926177978516,
0.003478558035567403,
-0.029722049832344055,
0.010983412154018879,
0.00949876382946968,
-0.027118051424622536,
0.0011584848398342729,
0.05582283437252045,
-0.022737309336662292,
0.012393755838274956,
0.05335710942745209,
0.030851153656840324,
0.04503120854496956,
0.01251458004117012,
0.006900871638208628,
0.005865143612027168,
-0.021829137578606606,
0.018999462947249413,
0.036793339997529984,
0.024114977568387985,
0.009974663145840168,
-0.0181785449385643,
0.04319396987557411,
-0.01756375841796398,
-0.00021514286345336586,
0.019898662343621254,
0.015849048271775246,
-0.04485009238123894,
-0.00999073963612318,
0.025594137609004974,
0.0011480023385956883,
0.01982513815164566,
0.034191302955150604,
-0.025055162608623505,
0.08411509543657303,
-0.012234294787049294,
-0.012203475460410118,
-0.015957310795783997,
0.0036152848042547703,
0.04816966503858566,
0.002911983523517847,
-0.020264288410544395,
0.03413777053356171,
0.0032016090117394924,
-0.015265196561813354,
-0.0451083667576313,
0.009452982805669308,
-0.002743637887760997,
-0.021841129288077354,
-0.0011202802415937185,
0.0002968884655274451,
0.01114898081868887,
0.005383297801017761,
-0.03179160878062248,
-0.013677766546607018,
-0.024273043498396873,
0.04964563623070717,
0.029812147840857506,
0.031910188496112823,
-0.030350448563694954,
0.02044060081243515,
-0.04404260963201523,
0.04482918605208397,
-0.07170920073986053,
-0.019841495901346207,
-0.021054519340395927,
0.023240474984049797,
-0.030590249225497246,
0.002473796484991908
] |
<p>Can someone summarize, with references if possible, all of the alternatives to the simplest model (that requires only a single scalar Higgs field with the Mexican Hat potential) of spontaneous electroweak symmetry breaking?</p>
| 10,777 |
[
0.005979823414236307,
-0.026486836373806,
0.0353471077978611,
-0.018313348293304443,
0.015603850595653057,
0.005799718201160431,
-0.0069863139651715755,
-0.03350149095058441,
-0.012825052253901958,
-0.016538990661501884,
0.020466182380914688,
0.007776440586894751,
0.03133303299546242,
-0.007690928876399994,
0.02683873288333416,
0.0178325604647398,
0.010090996511280537,
-0.013045870698988438,
-0.023609638214111328,
-0.01492825523018837,
-0.024494187906384468,
0.012074639089405537,
-0.015078066848218441,
0.025329893454909325,
-0.0026729728560894728,
-0.0012221703073009849,
0.03183523938059807,
0.01548389345407486,
0.011011902242898941,
0.07622875273227692,
-0.04522993415594101,
-0.040054403245449066,
-0.03635349124670029,
0.045637745410203934,
0.006008068099617958,
0.0014488092856481671,
0.022809995338320732,
-0.08379971981048584,
-0.012761988677084446,
0.009417310357093811,
-0.023585954681038857,
-0.017045369371771812,
-0.03297126293182373,
0.009709385223686695,
-0.04786840081214905,
-0.0012567536905407906,
-0.03021312691271305,
-0.017456095665693283,
0.07285582274198532,
-0.04411067068576813,
0.059853069484233856,
0.0014748856192454696,
0.027575936168432236,
0.0500125028192997,
0.008296423591673374,
0.016613341867923737,
0.038911499083042145,
0.03418829292058945,
0.032154638320207596,
-0.05970323830842972,
-0.07648693770170212,
-0.022696198895573616,
-0.015184802934527397,
-0.052589450031518936,
-0.016769129782915115,
0.06783099472522736,
-0.01622380129992962,
0.0048120818100869656,
-0.005681561306118965,
0.02551567368209362,
0.016189491376280785,
-0.008766711689531803,
0.012403629720211029,
0.006731788162142038,
0.03215602785348892,
0.002966217929497361,
-0.006974844262003899,
0.0005607650964520872,
0.018840370699763298,
0.037814829498529434,
-0.011212331242859364,
-0.009224939160048962,
0.015484989620745182,
0.04755512997508049,
-0.02939668856561184,
-0.011820489540696144,
0.0706038698554039,
-0.000961692479904741,
-0.02553655579686165,
0.036781296133995056,
-0.036873698234558105,
-0.009753978811204433,
0.0590437613427639,
-0.006743148900568485,
-0.05498985946178436,
0.013416191563010216,
0.009566158056259155,
0.05002662539482117,
-0.027161868289113045,
0.004863171372562647,
0.036707554012537,
-0.006936379708349705,
0.01008465327322483,
0.055956605821847916,
0.0006554235587827861,
-0.040404804050922394,
-0.021982312202453613,
-0.000462017604149878,
-0.008451184257864952,
0.013076438568532467,
-0.017704933881759644,
-0.0029480354860424995,
0.013331240974366665,
0.00013367550855036825,
0.01130537036806345,
-0.022372998297214508,
-0.02112359181046486,
-0.06106966361403465,
0.09224416315555573,
0.07785762846469879,
0.06348611414432526,
-0.046905916184186935,
0.043271370232105255,
-0.05090797692537308,
-0.07864771038293839,
-0.02154308743774891,
0.0057985736057162285,
0.001387688098475337,
-0.03616354987025261,
0.02741319313645363,
-0.018345972523093224,
-0.03042552061378956,
0.026401029899716377,
-0.007345255464315414,
0.06628090888261795,
-0.07071420550346375,
-0.10814169049263,
-0.06121647730469704,
0.039691634476184845,
-0.03265220671892166,
-0.04822320118546486,
-0.05269203335046768,
-0.01981152594089508,
0.006780104711651802,
0.06252230703830719,
-0.01216768380254507,
0.009092850610613823,
-0.006928313989192247,
0.04585343226790428,
0.006498688366264105,
-0.029182225465774536,
0.001163288950920105,
0.019472667947411537,
-0.014488087967038155,
-0.010967745445668697,
-0.07861769199371338,
0.004997414071112871,
0.01982218399643898,
-0.005287875887006521,
-0.0033672694116830826,
0.0655858963727951,
-0.01820879988372326,
0.029708804562687874,
0.005775986704975367,
0.013893010094761848,
-0.013452106155455112,
0.04149302467703819,
-0.026142995804548264,
-0.028194237500429153,
0.01828523725271225,
-0.03470021113753319,
-0.007750669494271278,
-0.0018695605685934424,
0.009963244199752808,
0.014025204814970493,
-0.027344556525349617,
0.007319674361497164,
-0.02461833506822586,
0.041943587362766266,
0.0090455561876297,
-0.04067221283912659,
-0.000016412453987868503,
0.021054813638329506,
0.009429925121366978,
-0.0034141482319682837,
0.03930101543664932,
-0.03088679537177086,
-0.03457217663526535,
0.045147109776735306,
-0.07148458808660507,
-0.06062156707048416,
-0.03928219899535179,
0.005205216351896524,
0.037058450281620026,
-0.006726980675011873,
0.040830984711647034,
0.029190901666879654,
0.042655088007450104,
-0.061955079436302185,
-0.06043035909533501,
-0.014149753376841545,
0.041847944259643555,
0.01648426428437233,
0.011292287148535252,
0.00035777725861407816,
0.028804961591959,
0.03465897962450981,
-0.024842580780386925,
0.03222426399588585,
-0.00035205177846364677,
-0.021518534049391747,
-0.024918925017118454,
-0.0415026992559433,
0.04135239124298096,
0.00963536649942398,
0.017602046951651573,
-0.020846864208579063,
0.011449421755969524,
-0.015547585673630238,
0.02864101529121399,
-0.03966454416513443,
0.04939952492713928,
0.02328460104763508,
0.041484203189611435,
-0.015218832530081272,
0.016737397760152817,
0.011576852761209011,
0.017758043482899666,
-0.02802450582385063,
-0.022435849532485008,
-0.0305044986307621,
-0.002808432327583432,
0.05366823822259903,
0.01748940907418728,
-0.06700024753808975,
0.06873996555805206,
0.01853242516517639,
0.020122898742556572,
0.04630725458264351,
0.024980613961815834,
-0.04196419194340706,
-0.04171055555343628,
0.028446674346923828,
0.012037931941449642,
0.028290821239352226,
0.002264417940750718,
0.005158599000424147,
0.011248520575463772,
0.003738970495760441,
0.014207780361175537,
-0.023978499695658684,
0.013078287243843079,
0.0007676064851693809,
-0.025275632739067078,
-0.04633219540119171,
-0.04148352891206741,
0.04034089669585228,
-0.026335468515753746,
0.059904761612415314,
0.040931686758995056,
-0.0437101386487484,
-0.009516608901321888,
-0.010256879962980747,
-0.015497668646275997,
0.0018060203874483705,
-0.015538332052528858,
0.0016997515922412276,
-0.036571621894836426,
0.026104135438799858,
-0.029486563056707382,
0.018155107274651527,
-0.044397272169589996,
0.002861005486920476,
-0.051318924874067307,
-0.0102697117254138,
0.061358124017715454,
-0.013554971665143967,
0.04664449766278267,
-0.013949071988463402,
-0.03270350396633148,
0.036725953221321106,
-0.022741040214896202,
0.01789318211376667,
0.03469839692115784,
-0.04002225026488304,
0.014292656444013119,
-0.05800650268793106,
-0.0220706295222044,
0.06184381619095802,
0.012915031984448433,
-0.0098792165517807,
0.026179365813732147,
0.017635297030210495,
-0.010151108726859093,
0.005012539215385914,
-0.02928484044969082,
0.023178106173872948,
-0.024546049535274506,
-0.00018111903045792133,
0.03118501603603363,
0.019948778674006462,
-0.035009849816560745,
0.040578775107860565,
-0.04950829967856407,
-0.05347417667508125,
-0.002192860469222069,
0.02585785835981369,
-0.006268955301493406,
-0.050610169768333435,
0.022997207939624786,
0.047690536826848984,
-0.07327070832252502,
0.03265366703271866,
-0.03177833929657936,
-0.019772572442889214,
0.013955515809357166,
-0.011668900027871132,
0.025528820231556892,
0.009623559191823006,
-0.04038736969232559,
0.07784131169319153,
0.04346968233585358,
-0.03479837626218796,
-0.0426926463842392,
0.0069460636004805565,
-0.030922608450055122,
-0.033386360853910446,
0.0056746038608253,
0.030637698248028755,
-0.003806964261457324,
0.0049374718219041824,
0.02456427738070488,
0.03861860930919647,
0.010634160600602627,
0.009009968489408493,
-0.012746719643473625,
0.008660524152219296,
0.012083438225090504,
-0.009212668053805828,
0.03864434361457825,
0.01431775838136673,
-0.02720489725470543,
-0.0446583516895771,
0.021531181409955025,
0.006026864517480135,
0.0051819197833538055,
-0.023649562150239944,
0.07710622251033783,
0.02537933737039566,
0.016558082774281502,
-0.0437779575586319,
0.02156117744743824,
0.003680308349430561,
-0.03544093668460846,
0.007164275739341974,
0.01219040248543024,
0.006753942463546991,
-0.022028829902410507,
0.011666781269013882,
0.011360902339220047,
0.03788335621356964,
-0.03280281648039818,
-0.01659880205988884,
-0.0185665562748909,
0.017029600217938423,
0.004721614066511393,
0.031693968921899796,
-0.03534962981939316,
0.08115655928850174,
0.06227106228470802,
0.027232039719820023,
-0.011199665255844593,
-0.0036721406504511833,
0.003650359343737364,
-0.04372434318065643,
0.028436707332730293,
-0.02591801807284355,
0.0026105204597115517,
0.015702873468399048,
0.032862745225429535,
0.010350457392632961,
-0.007841764949262142,
-0.014636775478720665,
0.0006243307143449783,
-0.06458410620689392,
0.03434078022837639,
-0.05545072630047798,
0.011471467092633247,
-0.003586958395317197,
0.0015116104623302817,
0.001280882046557963,
0.010717347264289856,
-0.02924829162657261,
-0.031493138521909714,
-0.014256062917411327,
-0.036806702613830566,
0.01220184937119484,
-0.02674487978219986,
-0.008766391314566135,
0.0031881071627140045,
0.023766973987221718,
0.04585881903767586,
-0.050506144762039185,
-0.060631077736616135,
0.004750102758407593,
-0.045088037848472595,
0.008594692684710026,
0.01579698733985424,
0.031007928773760796,
-0.008634867146611214,
0.009917376562952995,
0.0473366379737854,
0.0036459174007177353,
-0.03107590042054653,
-0.021315336227416992,
0.027350908145308495,
0.05138367787003517,
0.03412173315882683,
0.01820862665772438,
0.014974062331020832,
-0.05934562906622887,
-0.02363155595958233,
0.004456245806068182,
0.03546291962265968,
-0.008514282293617725,
0.041901905089616776,
0.03899708017706871,
0.04126541316509247,
-0.020700255408883095,
0.039348725229501724,
0.039065659046173096,
-0.011775569058954716,
-0.04283294454216957,
-0.01444071251899004,
-0.022928157821297646,
0.0038321977481245995,
0.0013640634715557098,
0.0189000703394413,
-0.012112725526094437,
-0.021950572729110718,
0.029619112610816956,
0.009812906384468079,
0.014148157089948654,
-0.03673801198601723,
0.0021698172204196453,
0.005408618599176407,
0.012600470334291458,
-0.010308440774679184,
-0.01720461994409561,
-0.0010132018942385912,
0.027564140036702156,
0.0330803208053112,
0.009167042560875416,
-0.0031031733378767967,
-0.06505248695611954,
0.012814832851290703,
0.0658184215426445,
0.01695181429386139,
-0.002209477825090289,
-0.026466017588973045,
-0.053043756633996964,
-0.03640129417181015,
0.0690760612487793,
-0.004510149359703064,
-0.0006168074323795736,
0.0068047079257667065,
-0.000053337957069743425,
-0.03142767772078514,
-0.0121778454631567,
-0.01808686926960945,
0.012074260972440243,
-0.022359441965818405,
0.00034189262078143656,
-0.01628830097615719,
-0.00547291012480855,
-0.025981130078434944,
0.026165831834077835,
0.031912755221128464,
0.03551238775253296,
0.012173743918538094,
0.03027002513408661,
0.02126721665263176,
0.012247596867382526,
-0.011295318603515625,
-0.1072896420955658,
-0.0023048927541822195,
0.02338496968150139,
-0.04764750599861145,
0.03897957131266594,
-0.01016531977802515,
-0.024341821670532227,
0.0051960209384560585,
0.039428915828466415,
0.0017598214326426387,
0.005643603857606649,
-0.037343572825193405,
0.009981616400182247,
0.0360061414539814,
0.01663840562105179,
0.039375364780426025,
0.023188553750514984,
-0.03582368418574333,
-0.014815382659435272,
-0.015095085836946964,
0.020557010546326637,
-0.014546310529112816,
0.0002961232385132462,
-0.040067918598651886,
-0.014353211969137192,
-0.034544266760349274,
0.05469195917248726,
-0.025541123002767563,
0.020585697144269943,
0.022185368463397026,
-0.007258299272507429,
-0.015353329479694366,
0.016833648085594177,
-0.0065894462168216705,
-0.05150463804602623,
-0.019244255498051643,
0.046593014150857925,
0.02854233793914318,
-0.012711504474282265,
0.045183245092630386,
-0.007425583433359861,
-0.0057535977102816105,
-0.021336084231734276,
-0.0200711227953434,
0.013164719566702843,
-0.026617366820573807,
-0.018334826454520226,
0.0398317351937294,
-0.06514230370521545,
0.04120149463415146,
-0.016535764560103416,
0.004230107180774212,
0.0039970772340893745,
-0.06862924993038177,
-0.04080989956855774,
-0.01649758219718933,
-0.0059832059778273106,
0.03743346780538559,
-0.01226347777992487,
0.030127370730042458,
0.00899351853877306,
-0.01711512729525566,
-0.08478017151355743,
-0.058824341744184494,
-0.004782857373356819,
0.0035968548618257046,
-0.01439526118338108,
-0.002514870138838887,
-0.03417372331023216,
-0.04025057330727577,
-0.03397864103317261,
-0.008801979944109917,
0.05361775681376457,
-0.02114570513367653,
0.0490606352686882,
-0.013754461891949177,
0.03353627771139145,
0.013568269088864326,
0.009599062614142895,
-0.011427215300500393,
0.048426706343889236,
-0.013220492750406265,
0.011977290734648705,
-0.0035150398034602404,
0.0651213526725769,
-0.01691356860101223,
-0.018921731039881706,
-0.012014909647405148,
-0.002243708586320281,
0.015947774052619934,
-0.04158010706305504,
0.027231797575950623,
0.05488314852118492,
0.006485950667411089,
-0.012529895640909672,
-0.05327722430229187,
0.0171797014772892,
0.014342698268592358,
0.048723019659519196,
-0.014202402904629707,
0.00026884465478360653,
0.020406503230333328,
-0.07252451777458191,
0.07252123206853867,
-0.009095338173210621,
0.021086204797029495,
0.010003652423620224,
0.027591940015554428,
0.02198837324976921,
-0.02273736335337162,
0.019541414454579353,
-0.050904080271720886,
-0.010010987520217896,
-0.02070174552500248,
0.05983651429414749,
0.015951434150338173,
0.0010540056973695755,
-0.018512951210141182,
-0.06942504644393921,
-0.007705284282565117,
0.009736975654959679,
0.052744217216968536,
-0.0026608232874423265,
0.02463473379611969,
0.03659934550523758,
-0.011740146204829216,
0.002801662776619196,
-0.027134647592902184,
-0.01166886929422617,
0.009732194244861603,
0.021061783656477928,
0.05257098376750946,
0.006615263409912586,
0.007432851474732161,
0.06186673790216446,
0.04421989247202873,
0.01693851314485073,
0.049475643783807755,
0.04632815346121788,
0.02830924652516842,
0.012649117968976498,
0.0004161407705396414,
-0.04231686890125275,
0.06295458972454071,
-0.022463489323854446,
0.034547965973615646,
0.02439170517027378,
-0.02003718540072441,
0.033081576228141785,
-0.02688519097864628,
-0.00748571939766407,
-0.011281766928732395,
-0.048343725502491,
-0.042574480175971985,
0.03364771977066994,
0.0002858856169041246,
0.0011606615735217929,
-0.0011415352346375585,
0.023887787014245987,
0.0006312181358225644,
0.005117198918014765,
0.02082287147641182,
0.028396524488925934,
-0.11034661531448364,
-0.050263747572898865,
0.008435821160674095,
-0.050908494740724564,
0.03315115347504616,
0.028897512704133987,
-0.015071563422679901,
-0.015269125811755657,
-0.02111492119729519,
0.010712121613323689,
-0.01955140382051468,
0.029095500707626343,
-0.010180716402828693,
0.01801695115864277,
-0.002423982135951519,
0.02001391351222992,
-0.0480070598423481,
-0.016368741169571877,
0.11323250085115433,
0.05831003561615944,
0.010356452316045761,
-0.08700388669967651,
0.02465883642435074,
-0.03310694545507431,
-0.0018405801383778453,
-0.03125558793544769,
0.03342151641845703,
0.005704689770936966,
0.015145878307521343,
0.013866114430129528,
0.08228272199630737,
-0.0026886598207056522,
0.0028112069703638554,
0.040352120995521545,
-0.027384482324123383,
-0.06914432346820831,
-0.007100805174559355,
0.03952475264668465,
-0.00550412479788065,
-0.009968595579266548,
-0.030562348663806915,
0.024859046563506126,
-0.027888203039765358,
-0.0007478556362912059,
0.0017053333576768637,
-0.052128225564956665,
0.046599727123975754,
0.044845134019851685,
-0.01718851923942566,
-0.016319317743182182,
-0.020565079525113106,
-0.011556008830666542,
-0.04075693339109421,
0.02312077209353447,
0.004155876114964485,
-0.01401714701205492,
0.03551468625664711,
0.040668439120054245,
0.018309583887457848,
-0.011782489717006683,
0.0231369286775589,
-0.003927983809262514,
-0.0389852449297905,
-0.022049015387892723,
-0.002228581579402089,
0.05433063209056854,
-0.016438191756606102,
0.006761827971786261,
-0.00501558743417263,
0.008742246776819229,
-0.013629220426082611,
0.009508884511888027,
-0.05783994868397713,
-0.028232689946889877,
0.058374520391225815,
-0.013830607756972313,
-0.005670808721333742,
0.004315690137445927,
0.06400785595178604,
-0.014841049909591675,
0.015802109614014626,
-0.01881476864218712,
-0.0011950901243835688,
-0.024459123611450195,
-0.02181292325258255,
0.0010942236986011267,
0.03724518045783043,
-0.0401204489171505,
-0.0075731584802269936,
-0.007226459216326475,
0.004441359546035528,
0.006968309637159109,
0.029497144743800163,
0.035219743847846985,
0.04842296242713928,
-0.0011390196159482002,
0.008446009829640388,
-0.006384124513715506,
-0.0035774766001850367,
0.03823247179389,
-0.007705227006226778,
-0.010527543723583221,
0.011397688649594784,
-0.02310134470462799,
0.0261742752045393,
0.039478152990341187,
-0.015096493065357208,
0.015168649144470692,
-0.019079722464084625,
0.04910922050476074,
-0.0043413895182311535,
-0.03791840001940727,
-0.030055038630962372,
-0.005800026934593916,
-0.015381844714283943,
-0.01597609743475914,
-0.02982853353023529,
0.03455200418829918,
0.03027304820716381,
-0.014416655525565147,
0.0008929827599786222,
0.05073089525103569,
-0.015901461243629456,
0.0013220012187957764,
0.02294672653079033,
-0.03202565386891365,
0.010248263366520405,
0.024566661566495895,
0.004403440747410059,
-0.03679735213518143,
-0.05176650732755661,
-0.01138231996446848,
0.007521898951381445,
0.01535491831600666,
0.01253901794552803,
-0.027427913621068,
-0.006355220451951027,
-0.02313624508678913,
0.018881894648075104,
-0.014416863210499287,
0.02074718475341797,
-0.015053878538310528,
0.024117013439536095,
0.008199529722332954,
-0.017608243972063065,
0.010392324067652225,
0.014688070863485336,
0.0010197319788858294,
0.013120471499860287,
0.015946149826049805,
0.03582075983285904,
-0.006261918693780899,
0.013857696205377579,
0.002503709401935339,
0.04271842911839485,
0.015918651595711708,
-0.00419640401378274,
-0.03406001627445221,
0.03558681160211563,
-0.04723130539059639,
-0.049487050622701645,
0.05237952619791031,
0.008453363552689552,
0.029919574037194252,
0.01144105102866888,
-0.033182643353939056,
-0.040352754294872284,
0.05752710625529289,
-0.021971620619297028,
-0.026771698147058487,
0.010687426663935184,
0.007247286383062601,
-0.0165728610008955,
-0.021089881658554077,
-0.005597013048827648,
-0.000819190579932183,
-0.009595690295100212,
0.007710808888077736,
0.01797131448984146,
0.008006826043128967,
-0.015539809130132198,
-0.02427520789206028,
-0.029485302045941353,
0.048797331750392914,
0.013525398448109627,
0.038130100816488266,
-0.025240972638130188,
0.051982153207063675,
-0.03401309624314308,
0.04089631512761116,
0.01787164807319641,
0.009601528756320477,
-0.08115141838788986,
0.008314651437103748,
-0.0036020867992192507,
0.00040576086030341685,
0.039040613919496536,
-0.07582192867994308,
0.02217145822942257,
0.06414872407913208,
-0.05697322264313698,
0.02093169093132019,
-0.006549555342644453,
-0.0004797479195985943,
-0.013743853196501732,
-0.0351644828915596,
0.00744938338175416,
0.08976251631975174,
0.029825484380126,
0.04563796892762184,
0.00558516476303339,
-0.02125507965683937,
-0.014688204042613506,
-0.0054991599172353745,
-0.040354061871767044,
0.010893198661506176,
0.032712921500205994,
-0.03223930671811104,
0.059350691735744476,
-0.014957006089389324,
-0.03171663358807564,
0.028017351403832436,
0.011402680538594723,
-0.006325410213321447,
0.0010194680653512478,
0.02252945862710476,
-0.009328894317150116,
0.03239784762263298,
0.008157973177731037,
-0.003889508545398712,
0.005064147524535656,
0.00007887622632551938,
0.006759740877896547,
0.023188183084130287,
0.042623355984687805,
0.024438878521323204,
-0.015545052476227283,
-0.03869367018342018,
-0.030702581629157066,
0.031729310750961304,
-0.007388301659375429,
-0.03326058387756348,
0.008244394324719906,
-0.024385666474699974,
0.0442541278898716,
-0.021883666515350342,
-0.012242189608514309,
-0.07128717005252838,
-0.011634038761258125,
0.029037542641162872,
0.02363874763250351,
0.022976810112595558,
0.035702772438526154,
-0.03707583248615265,
-0.014120928011834621,
-0.018551787361502647,
0.02663438580930233,
0.0002628854417707771,
-0.04114086553454399,
0.0068412404507398605,
0.013406412675976753,
-0.010376131162047386,
0.003530419897288084,
0.005743242334574461,
-0.013277013786137104,
0.023969430476427078,
-0.004899879451841116,
0.006563706323504448,
0.009071056731045246,
-0.03985115513205528,
0.006365325767546892,
-0.02545076049864292,
0.03874911740422249,
-0.0008825159748084843,
0.016952360048890114,
0.000944913481362164,
-0.005402215290814638,
0.015145043842494488,
0.01004433911293745,
0.02007235400378704,
-0.03813904896378517,
-0.009078575298190117,
0.01582452468574047,
0.0074679115787148476,
0.013439374044537544,
-0.052089836448431015,
-0.0020446658600121737,
0.0020961901172995567,
-0.007164216134697199,
-0.010594201274216175,
-0.007855568081140518,
0.021568957716226578,
0.026592262089252472,
0.02023019641637802,
-0.005758276209235191,
-0.015841688960790634,
0.01703636720776558,
-0.022225724533200264,
0.04977906122803688,
-0.0275027547031641,
-0.04976958408951759,
0.06021404266357422,
-0.03434891253709793,
0.0011249727103859186,
-0.007733727339655161,
-0.027510758489370346,
0.01026403158903122,
0.037074606865644455,
-0.042605914175510406,
-0.01496395468711853,
-0.014666738919913769,
-0.004677908029407263,
0.004817966837435961,
-0.010331030935049057,
0.014126716181635857,
0.003704535309225321,
0.006094603333622217,
-0.013868807815015316,
0.028518058359622955,
0.004354297183454037,
0.03870999440550804,
0.008948256261646748,
-0.04471058025956154,
0.016501108184456825,
0.03313446789979935,
-0.0027407824527472258,
0.023370321840047836,
0.017109833657741547,
0.0283431988209486,
-0.003605398116633296,
-0.012898814864456654,
-0.05354618653655052,
0.029921235516667366,
0.013151489198207855,
0.017500320449471474,
-0.019757743924856186,
-0.03739234805107117,
0.035197384655475616,
-0.0039033920038491488,
0.018306564539670944,
-0.036955542862415314,
-0.019637608900666237,
0.09207793325185776,
-0.0540144182741642,
0.009802168235182762,
-0.011328683234751225,
0.015529129654169083,
0.010269425809383392,
0.0008111034985631704,
-0.013520478270947933,
0.03914622217416763,
-0.026638910174369812,
-0.005500045605003834,
-0.014733914285898209,
0.039729759097099304,
0.03261853754520416,
-0.08437266945838928,
0.01264797430485487,
-0.01601118966937065,
-0.016593189910054207,
-0.008729662746191025,
-0.012764528393745422,
0.00458702864125371,
0.012895839288830757,
0.009824861772358418,
0.04314504191279411,
0.03212055191397667,
-0.008745920844376087,
-0.016979310661554337,
-0.05251901224255562,
0.046721216291189194,
-0.03758244588971138,
0.013788434676826,
-0.04930249974131584,
0.02674313262104988,
-0.048705969005823135,
0.02066320925951004
] |
<p>What impulse should be applied to an object of mass m, having a known coefficient of friction u to get to a distance d ?</p>
<p>Thanks!</p>
<p>Update 14.02.2011: </p>
<p>I still wasn't able to find an answer to this. Could you please share the solution? I need an "Idiot's solution" for this. I'm not experienced enough to find a formula by myself starting from your clues. I've searched the forums but they take into account other parameters. Thank you !</p>
<p>Update 13.02.2011: </p>
<p>Here is a representation of what I need: <img src="http://i.stack.imgur.com/Pc7qa.png" alt="http://img412.imageshack.us/img412/2192/20110213112259.png"></p>
<p>It's been a long time since I studied the principles of physics, sorry if I did not make myself clear in the first post. </p>
<p>I've tried formulas like:</p>
<p>1)m * a = u * m * g => a = u * g</p>
<p>2)a = v / t</p>
<p>3)d = v * t</p>
<p>So from these three equations, distance = u * g * t^2</p>
<p>The impulse p = m*v , so I get p= m * u * g * t</p>
<p>However, the time is not known and it is not important how long it takes for the object to get to target.</p>
<p>Does this formula (p= m * u * g * t) seem right? The mass, u, g are known, but what about time?</p>
| 10,778 |
[
-0.010584836825728416,
-0.028066089376807213,
-0.023190131410956383,
-0.011061342433094978,
0.031204231083393097,
-0.056137990206480026,
-0.053346652537584305,
0.0010296204127371311,
0.009650539606809616,
0.02356787957251072,
0.002924311673268676,
0.07377893477678299,
0.06612077355384827,
0.01821834407746792,
0.011048243381083012,
-0.021382225677371025,
0.00491242203861475,
-0.0337861105799675,
0.03478342294692993,
-0.04378823935985565,
0.03938329219818115,
-0.02570628933608532,
0.02220524661242962,
-0.015213294886052608,
0.013380412943661213,
0.010384457185864449,
0.013946345075964928,
-0.016774913296103477,
0.0037649828009307384,
0.0010919878259301186,
-0.016020413488149643,
-0.0184926837682724,
0.005549325607717037,
-0.022155452519655228,
0.020872032269835472,
0.04029190540313721,
-0.03914901614189148,
-0.02274390496313572,
-0.01890755072236061,
0.006323940586298704,
-0.029205989092588425,
-0.02315736934542656,
-0.008487584069371223,
0.04923715442419052,
-0.03211789205670357,
0.014566054567694664,
0.018232213333249092,
-0.012161322869360447,
0.05364113301038742,
-0.05434470623731613,
0.09335145354270935,
0.015082634054124355,
0.04550826549530029,
0.0017504727002233267,
-0.03476919233798981,
-0.009051200933754444,
0.0731273666024208,
0.09586279839277267,
-0.05670837685465813,
-0.01403326541185379,
-0.008356224745512009,
-0.012706289067864418,
-0.017092972993850708,
-0.014538269490003586,
0.02539176121354103,
0.053431130945682526,
-0.04382744058966637,
-0.020367875695228577,
0.01488241646438837,
-0.007142594549804926,
0.02510109171271324,
-0.010423891246318817,
0.038141705095767975,
0.005963788367807865,
-0.006148406304419041,
-0.01519477367401123,
0.04383004084229469,
0.0007058753399178386,
0.03165378049015999,
0.045205630362033844,
-0.022656574845314026,
0.02543831802904606,
0.04309030622243881,
0.04987864941358566,
0.04704940319061279,
-0.022537585347890854,
0.05139860510826111,
0.00737509410828352,
0.01018945500254631,
0.010405437089502811,
-0.041915733367204666,
0.003031430533155799,
0.02043995074927807,
0.02666936255991459,
0.02810394950211048,
0.03958404064178467,
0.006500188261270523,
0.06197327747941017,
0.014244732446968555,
-0.011892867274582386,
-0.004007453098893166,
-0.0005115651874803007,
-0.002389410510659218,
0.08798030018806458,
0.0028595414478331804,
-0.0031258868984878063,
-0.03513577952980995,
0.017463935539126396,
0.0028183208778500557,
0.005776159930974245,
-0.02045351266860962,
0.05101625993847847,
-0.01542587298899889,
-0.017290713265538216,
0.005471966695040464,
-0.015177261084318161,
-0.025884658098220825,
-0.010187583044171333,
0.016544237732887268,
0.022048205137252808,
0.035640131682157516,
-0.06469584256410599,
0.038389720022678375,
-0.04974742606282234,
-0.02407987229526043,
-0.022455478087067604,
0.03784843906760216,
-0.022831812500953674,
0.011710084974765778,
0.007405809126794338,
-0.009836584329605103,
-0.043963294476270676,
0.018847933039069176,
-0.012751256115734577,
0.014430207200348377,
-0.028548868373036385,
-0.0941033586859703,
-0.07791063189506531,
0.024853339418768883,
0.028697198256850243,
-0.035349007695913315,
-0.08526408672332764,
-0.018286747857928276,
0.041979797184467316,
0.05238112062215805,
0.02848530188202858,
-0.03697172924876213,
0.005572176072746515,
0.049174144864082336,
-0.012380264699459076,
0.002249854151159525,
-0.0256830845028162,
-0.01369961816817522,
-0.03493068739771843,
0.03846537321805954,
-0.05484248325228691,
0.022004157304763794,
-0.001074593048542738,
0.006316571496427059,
-0.018072819337248802,
0.06993429362773895,
-0.023367026820778847,
-0.018079349771142006,
0.023000504821538925,
0.0018257376505061984,
0.007024749182164669,
0.06085802614688873,
0.03161080554127693,
-0.02529175765812397,
0.03237808868288994,
0.03920583426952362,
0.0039028008468449116,
-0.006988690700381994,
-0.001928881392814219,
0.05545475333929062,
-0.04894126579165459,
-0.03301448002457619,
0.013645336963236332,
-0.031542640179395676,
-0.0057632396928966045,
-0.02459000051021576,
-0.09080082178115845,
0.027293384075164795,
-0.009006529115140438,
0.027961276471614838,
0.03631813824176788,
0.025748666375875473,
0.03893395885825157,
-0.03342519700527191,
0.02579486556351185,
-0.04441462829709053,
-0.07008244097232819,
0.024547681212425232,
-0.0030963795725256205,
0.04042619466781616,
0.008090553805232048,
-0.016728414222598076,
-0.0033407986629754305,
-0.012681510299444199,
-0.014207589440047741,
0.01792355626821518,
0.018378358334302902,
0.009534819982945919,
-0.011637835763394833,
-0.03446885198354721,
0.08199536800384521,
0.03740084171295166,
-0.02253606729209423,
0.0007138449000194669,
-0.01889578066766262,
0.02665448747575283,
-0.002942554885521531,
-0.022623220458626747,
0.019475433975458145,
0.010357806459069252,
0.036886680871248245,
0.0629141554236412,
-0.01531626470386982,
0.00810778234153986,
0.014461521059274673,
-0.0034961227793246508,
0.0743439719080925,
0.07625158131122589,
0.05499124154448509,
0.004340335726737976,
0.029520582407712936,
-0.029640402644872665,
0.05988997966051102,
0.03414405137300491,
-0.05042349174618721,
-0.019164234399795532,
-0.004463750869035721,
-0.008647475391626358,
0.006992977112531662,
-0.038194410502910614,
0.030768709257245064,
0.05726175382733345,
0.029563387855887413,
0.030696002766489983,
0.036137353628873825,
-0.0017373349983245134,
-0.014498962089419365,
0.021350670605897903,
0.006302394438534975,
-0.02642645500600338,
0.000664981605950743,
-0.010051787830889225,
0.026132509112358093,
-0.005606603343039751,
-0.004463227931410074,
0.012498542666435242,
0.0221585500985384,
0.010356978513300419,
0.01974191702902317,
0.0007469849660992622,
-0.03980543836951256,
0.06134350970387459,
0.005545163992792368,
-0.004092243034392595,
0.06348910182714462,
0.029128728434443474,
-0.012571258470416069,
-0.029369089752435684,
-0.012123760767281055,
0.005856887903064489,
-0.0020418893545866013,
-0.011575526557862759,
-0.026170555502176285,
0.019727082923054695,
-0.025049742311239243,
-0.015000502578914165,
-0.006406372878700495,
0.021571606397628784,
-0.03122219629585743,
0.004210830666124821,
0.010208730585873127,
0.04646887257695198,
0.01818896271288395,
0.001636697445064783,
-0.02686350606381893,
0.022874876856803894,
-0.022613324224948883,
-0.0010190927423536777,
0.009184029884636402,
-0.02766943722963333,
0.008752281777560711,
-0.052319105714559555,
-0.04404151439666748,
0.07508153468370438,
-0.0016782181337475777,
-0.0035958511289209127,
0.0310721006244421,
0.011593651957809925,
-0.04671367630362511,
-0.009065160527825356,
-0.02347530797123909,
-0.0035233269445598125,
-0.024684052914381027,
0.002517801709473133,
0.05211474746465683,
0.015025652013719082,
-0.03883519396185875,
0.005620661191642284,
-0.02662471868097782,
-0.03276532143354416,
-0.02970368042588234,
0.004107480403035879,
0.014761226251721382,
-0.042557619512081146,
0.03806816041469574,
0.0037698091473430395,
0.017425108700990677,
0.03604946285486221,
-0.06028485298156738,
-0.013205865398049355,
0.007239524740725756,
0.04399259760975838,
0.07519552856683731,
0.005805748514831066,
-0.0322941355407238,
0.06233978644013405,
0.019187480211257935,
-0.0367744117975235,
-0.05362999066710472,
-0.01467793621122837,
0.025021957233548164,
-0.02239881455898285,
-0.004797917325049639,
0.020795593038201332,
-0.035581592470407486,
-0.01275188010185957,
-0.0017730238614603877,
0.005459595937281847,
0.037006545811891556,
0.003145744325593114,
0.02821517176926136,
-0.0033151705283671618,
0.021711250767111778,
-0.033692602068185806,
0.027839696034789085,
0.022692089900374413,
-0.032614417374134064,
0.05170884355902672,
-0.026730475947260857,
0.02552690915763378,
0.014781991019845009,
-0.04591452330350876,
0.01781517080962658,
-0.010454647243022919,
-0.019416362047195435,
-0.007044196594506502,
0.03669296205043793,
0.0053106555715203285,
-0.02366696111857891,
0.019384946674108505,
0.03747667372226715,
0.04472104087471962,
-0.017186902463436127,
0.013531247153878212,
0.037955109030008316,
0.015667812898755074,
-0.02042071707546711,
-0.05054298788309097,
-0.007941033691167831,
-0.018330859020352364,
0.03182464465498924,
-0.013900430873036385,
0.020365623757243156,
0.021839188411831856,
-0.017368948087096214,
0.04634518921375275,
0.021695446223020554,
-0.03239158168435097,
0.009912966750562191,
-0.08595621585845947,
-0.0053609455935657024,
-0.014069322496652603,
0.05456772446632385,
-0.006764011923223734,
0.03962681069970131,
0.03448258340358734,
0.030730966478586197,
-0.0007189378375187516,
0.02169095166027546,
-0.08566391468048096,
0.05555618554353714,
-0.055441997945308685,
-0.05494622141122818,
-0.007431387901306152,
0.008605778217315674,
-0.06934935599565506,
0.004509883001446724,
-0.004660777747631073,
0.027976470068097115,
-0.005721104331314564,
-0.07240413874387741,
0.01770826242864132,
-0.05112404376268387,
-0.019321903586387634,
0.013388643972575665,
0.008503052406013012,
0.015845032408833504,
0.009487541392445564,
-0.005118181928992271,
0.05846058204770088,
-0.01767667382955551,
-0.015654750168323517,
-0.00847768783569336,
-0.031456153839826584,
-0.0011277779703959823,
0.06684870272874832,
-0.013706052675843239,
0.022006787359714508,
-0.016788706183433533,
0.012624516151845455,
-0.02626955695450306,
0.028769854456186295,
-0.0052014184184372425,
-0.029514197260141373,
-0.07652647793292999,
-0.08330003172159195,
-0.006523167714476585,
0.0325620174407959,
0.03735216706991196,
-0.01472178753465414,
0.006016179453581572,
0.027203679084777832,
-0.014662246219813824,
0.0159301795065403,
0.024132847785949707,
0.04892410710453987,
-0.0052476851269602776,
-0.03180601820349693,
-0.07609914988279343,
-0.012518993578851223,
-0.019196752458810806,
-0.019668560475111008,
0.011846315115690231,
0.0069720991887152195,
0.01318273600190878,
-0.013274804688990116,
0.010558550246059895,
0.02062559500336647,
-0.0016520872013643384,
0.014876029454171658,
-0.005371568724513054,
0.007532760966569185,
-0.010670047253370285,
-0.016143515706062317,
-0.005823255050927401,
0.03721224144101143,
0.045029181987047195,
-0.02582724764943123,
-0.02284061349928379,
-0.05865764990448952,
-0.0010018207831308246,
0.026964884251356125,
0.03488680720329285,
-0.016215503215789795,
0.005741629749536514,
-0.032569535076618195,
-0.03749142214655876,
0.053121600300073624,
-0.05666195973753929,
0.042240969836711884,
-0.01893325336277485,
0.01589101180434227,
0.009238872677087784,
-0.03711780533194542,
-0.022979509085416794,
0.017569825053215027,
-0.0050324383191764355,
-0.012588344514369965,
-0.014285962097346783,
-0.027785681188106537,
0.006014172453433275,
0.00910012237727642,
0.05306662619113922,
0.05976751446723938,
0.02185976505279541,
-0.017308514565229416,
-0.01235162653028965,
-0.03154800087213516,
-0.039690010249614716,
-0.05228673294186592,
-0.02391146309673786,
-0.02193712815642357,
-0.02755642496049404,
0.010271341539919376,
-0.05264480039477348,
-0.019462594762444496,
0.047725047916173935,
-0.0009314774069935083,
0.0068788486532866955,
0.008191481232643127,
-0.009752797894179821,
-0.018214264884591103,
0.04283982142806053,
-0.01699480228126049,
0.02001393586397171,
0.03245758265256882,
-0.01673463173210621,
-0.013604026287794113,
-0.02793729491531849,
0.004013232421129942,
0.009770780801773071,
-0.03282551467418671,
-0.027486659586429596,
0.02097231335937977,
-0.04766598343849182,
0.02685188688337803,
0.0003194090095348656,
0.021363861858844757,
-0.018833249807357788,
-0.039408084005117416,
-0.03958681598305702,
0.01851499453186989,
0.005146812181919813,
0.02414194867014885,
0.02951422706246376,
0.018791349604725838,
-0.0016081650974228978,
-0.006998460274189711,
-0.0007581041427329183,
0.010441075079143047,
0.017477095127105713,
0.04618356376886368,
-0.01234338991343975,
0.02769884280860424,
-0.02322879433631897,
-0.0036464021541178226,
0.029988421127200127,
-0.06157488748431206,
0.059098388999700546,
-0.01002211682498455,
-0.00021067389752715826,
0.05194144695997238,
-0.04687574505805969,
-0.03336969017982483,
0.0046726735308766365,
0.027215728536248207,
0.0625024065375328,
-0.08169526606798172,
0.01654236763715744,
-0.017171883955597878,
0.05246804654598236,
-0.028824102133512497,
-0.024434970691800117,
0.04903843626379967,
0.01706726849079132,
-0.01904289796948433,
-0.03505447134375572,
-0.009628723375499249,
-0.026103399693965912,
-0.02341294102370739,
-0.010036352090537548,
0.07723408192396164,
0.01596209593117237,
-0.007968353107571602,
0.01460664626210928,
0.013763519003987312,
0.03590419888496399,
0.023158200085163116,
0.007059851195663214,
-0.013964163139462471,
-0.010601458139717579,
-0.011407984420657158,
0.01756119914352894,
0.07259835302829742,
-0.051128093153238297,
-0.026827819645404816,
-0.005316560156643391,
-0.001879723509773612,
0.029263807460665703,
-0.029744602739810944,
0.03807844594120979,
0.024667853489518166,
0.04557179659605026,
-0.0004732722300104797,
-0.035700246691703796,
0.04860145226120949,
0.008381230756640434,
-0.020773401483893394,
-0.019125914201140404,
0.005153195466846228,
-0.03511509299278259,
-0.0026927078142762184,
0.026166513562202454,
0.0051119024865329266,
0.041171442717313766,
-0.01891307160258293,
0.03223612159490585,
-0.014510411769151688,
-0.004669480957090855,
0.05109710991382599,
0.012806731276214123,
0.06229868531227112,
-0.005936987232416868,
-0.03238359093666077,
0.025488194078207016,
-0.03647294640541077,
-0.02603374794125557,
-0.00930765736848116,
-0.024063672870397568,
0.014545857906341553,
0.06945755332708359,
-0.0630185604095459,
0.07992659509181976,
0.012039556168019772,
0.031285688281059265,
-0.028044475242495537,
-0.00323193590156734,
-0.01207054778933525,
-0.0033295731991529465,
0.04269741103053093,
0.0023686708882451057,
0.0023016296327114105,
-0.004832296632230282,
0.044646408408880234,
-0.009619025513529778,
0.008245481178164482,
0.0015825912123546004,
-0.001972956582903862,
0.02074403502047062,
0.004761705175042152,
-0.04076585918664932,
-0.0026206793263554573,
0.008514263667166233,
-0.03689131885766983,
0.033204495906829834,
0.005386009346693754,
-0.01679743453860283,
0.044902071356773376,
0.012386809103190899,
-0.028091955929994583,
-0.03477177768945694,
0.022385060787200928,
-0.0357995443046093,
-0.015985684469342232,
0.03258945420384407,
0.008731067180633545,
0.005028650630265474,
0.03155825287103653,
0.035069577395915985,
0.005600165110081434,
0.024045415222644806,
-0.012787898071110249,
-0.04786321520805359,
-0.03899111971259117,
-0.04396457225084305,
-0.06776648759841919,
0.029366210103034973,
0.0058809746988117695,
-0.016340257599949837,
0.011947535909712315,
-0.01060450728982687,
-0.016704324632883072,
0.009680086746811867,
0.04026586934924126,
-0.0027497969567775726,
0.1134047731757164,
0.007482361979782581,
-0.012182490900158882,
-0.03694457933306694,
-0.00621370691806078,
0.1106875017285347,
0.0304124616086483,
0.021989889442920685,
-0.016190215945243835,
0.01340851467102766,
-0.028458118438720703,
-0.016312560066580772,
-0.022781848907470703,
0.014896550215780735,
-0.006188712548464537,
-0.018227893859148026,
0.02341238595545292,
0.03129877150058746,
-0.0012893843231722713,
0.020605560392141342,
0.03633713722229004,
-0.00852424930781126,
-0.02153579704463482,
-0.0033639254979789257,
-0.0009816919919103384,
0.01713736727833748,
-0.0007762135355733335,
0.016966454684734344,
0.045226555317640305,
-0.0048734345473349094,
0.003530202666297555,
0.00024884441518224776,
-0.036535706371068954,
0.022168243303894997,
-0.00733539741486311,
-0.01871493272483349,
0.023183666169643402,
0.015339208766818047,
-0.04151064157485962,
-0.030785562470555305,
0.051567934453487396,
-0.0006803489523008466,
-0.025503113865852356,
0.00574369914829731,
0.01524514053016901,
0.03657124191522598,
0.025551190599799156,
0.006980625446885824,
0.00717645650729537,
-0.03413494676351547,
-0.006514893379062414,
-0.022064777091145515,
0.027626844123005867,
-0.008783252909779549,
0.013632145710289478,
0.0011009746231138706,
0.014049053192138672,
-0.006927224341779947,
-0.06075112521648407,
-0.023363985121250153,
0.0002513086947146803,
0.040039096027612686,
-0.0021190715488046408,
-0.0013086112448945642,
-0.013397389091551304,
0.020370328798890114,
0.002924900036305189,
0.011967087164521217,
-0.03064676560461521,
0.027396805584430695,
0.007203270681202412,
-0.023839052766561508,
0.04191620647907257,
-0.02840236760675907,
-0.022176187485456467,
-0.005307766143232584,
-0.042235150933265686,
-0.03227141499519348,
-0.017576752230525017,
-0.016777386888861656,
0.036796171218156815,
-0.01595507562160492,
-0.014889461919665337,
-0.004549568984657526,
-0.04506932944059372,
-0.03467189893126488,
0.02707003988325596,
-0.033188190311193466,
-0.0215526781976223,
-0.029994184151291847,
-0.02213703840970993,
0.00856343749910593,
0.027343636378645897,
-0.0010940616484731436,
0.01005005557090044,
-0.010241260752081871,
0.031963083893060684,
0.006713962182402611,
-0.016678374260663986,
-0.008157080970704556,
0.00835331529378891,
-0.010557993315160275,
0.057043444365262985,
0.01878408156335354,
0.03047681227326393,
0.020645469427108765,
-0.01840965822339058,
0.006201418116688728,
-0.013891610316932201,
-0.036247368901968,
0.029270987957715988,
0.014603954739868641,
-0.03191937878727913,
-0.03761377930641174,
-0.0016256857197731733,
-0.004361410159617662,
-0.030101949349045753,
-0.010880200192332268,
-0.03742475062608719,
-0.025164712220430374,
-0.03051883913576603,
0.022433677688241005,
-0.02349819429218769,
0.02932574413716793,
-0.03606676310300827,
0.025311443954706192,
-0.04865496978163719,
0.04013363644480705,
-0.009899700991809368,
0.015978502109646797,
-0.019780300557613373,
-0.026338810101151466,
-0.03353249654173851,
0.0018345045391470194,
-0.044955331832170486,
0.014866950921714306,
-0.00044450588757172227,
0.002387233776971698,
0.013971865177154541,
0.013808663003146648,
-0.002933613955974579,
-0.027591126039624214,
0.033788684755563736,
0.012532854452729225,
-0.005319429095834494,
0.02797083929181099,
-0.05927073583006859,
-0.038597188889980316,
0.058423034846782684,
0.006071065086871386,
0.056835416704416275,
0.014599892310798168,
-0.017020316794514656,
0.005099226720631123,
0.1249627098441124,
-0.018128223717212677,
-0.011774178594350815,
0.011618498712778091,
-0.044936876744031906,
-0.019415773451328278,
-0.02286786213517189,
0.016280917450785637,
-0.019292112439870834,
-0.00937109999358654,
-0.009743550792336464,
-0.02204025723040104,
0.003775157732889056,
0.0003707697906065732,
0.035532642155885696,
-0.0042660110630095005,
-0.011325710453093052,
0.025557732209563255,
0.012668265961110592,
0.02413191646337509,
0.050063084810972214,
-0.005957616493105888,
0.005259733181446791,
0.020043015480041504,
0.0015060664154589176,
-0.09910308569669724,
-0.001953201135620475,
0.0010908476542681456,
0.0069721778854727745,
0.07931254804134369,
-0.05778948590159416,
0.018426835536956787,
0.03837765008211136,
-0.058145713061094284,
0.000991307315416634,
-0.0652455985546112,
-0.01605343259871006,
0.005477642174810171,
-0.01544464286416769,
0.035266220569610596,
0.029132217168807983,
0.014679642394185066,
0.006611830089241266,
0.03245692700147629,
0.01427233312278986,
-0.05754883587360382,
-0.023538870736956596,
0.04309030994772911,
0.08176165074110031,
0.010482667945325375,
0.01258151326328516,
0.05382288619875908,
-0.016845088452100754,
0.009771657176315784,
0.02880975417792797,
-0.020277569070458412,
0.030816739425063133,
-0.018010061234235764,
0.024024242535233498,
-0.008594177663326263,
0.005208233837038279,
0.025590645149350166,
0.0063174087554216385,
0.009006955660879612,
0.030178388580679893,
-0.014857948757708073,
0.015384826809167862,
-0.037370018661022186,
-0.00128854566719383,
0.030937843024730682,
-0.006308559328317642,
-0.03424597904086113,
-0.0252083633095026,
-0.014051784761250019,
-0.0351247675716877,
-0.0021328222937881947,
-0.014605480246245861,
-0.00018133707635570318,
-0.07064603269100189,
-0.054719265550374985,
-0.02990211360156536,
0.009226858615875244,
0.06365976482629776,
-0.04810827225446701,
0.004901351407170296,
0.033783283084630966,
-0.034272465854883194,
-0.005211162380874157,
-0.005393957253545523,
-0.022127320989966393,
-0.010622279718518257,
-0.06926090270280838,
-0.019045211374759674,
0.024599676951766014,
-0.0068715400993824005,
-0.024274829775094986,
-0.0245964452624321,
0.01075917948037386,
0.04190252348780632,
0.016191640868782997,
-0.008111818693578243,
0.023181848227977753,
0.037757400423288345,
-0.03579946979880333,
-0.06955628842115402,
0.006724625825881958,
0.0009295262861996889,
-0.04583636298775673,
-0.03343130648136139,
-0.030616920441389084,
0.024006983265280724,
0.0046664150431752205,
0.0589551106095314,
-0.04751288518309593,
-0.01626673713326454,
0.02667412906885147,
-0.03315366432070732,
-0.008708775043487549,
-0.038087986409664154,
-0.029228385537862778,
-0.0020167832262814045,
-0.0019655702635645866,
-0.025147810578346252,
0.012169618159532547,
-0.0005304192891344428,
-0.03393135964870453,
-0.01594352349638939,
0.011817879974842072,
0.02198476530611515,
0.018498647958040237,
-0.023892881348729134,
0.0010077948682010174,
0.022357456386089325,
-0.0036496156826615334,
0.04425453394651413,
-0.023605145514011383,
0.01292535848915577,
0.004614740144461393,
-0.02856971137225628,
-0.03385712951421738,
0.04407501593232155,
-0.039985258132219315,
-0.01751265674829483,
-0.01974225975573063,
-0.024644264951348305,
0.018982544541358948,
-0.09453029185533524,
0.0022668547462671995,
0.016753682866692543,
-0.013808821327984333,
-0.011719871312379837,
0.022289488464593887,
0.017321527004241943,
0.06802274286746979,
-0.007601916324347258,
0.04157843440771103,
0.02476763166487217,
-0.030401179566979408,
-0.02250160276889801,
0.01891973242163658,
0.015564908273518085,
-0.0024522568564862013,
-0.017565350979566574,
0.019081059843301773,
0.0015224820235744119,
0.01776611991226673,
0.02467811293900013,
0.018614141270518303,
0.007659822702407837,
-0.006253786385059357,
-0.0005144415190443397,
-0.029446613043546677,
-0.0077248308807611465,
0.025261325761675835,
-0.029797881841659546,
0.05148681253194809,
-0.0052221836522221565,
0.005131571553647518,
-0.014737462624907494,
0.03192157670855522,
-0.030871853232383728,
0.01104807946830988,
-0.023163216188549995,
0.0054042828269302845,
-0.039790596812963486,
0.004569848533719778,
0.013844335451722145,
0.013785510323941708,
0.0359426848590374,
0.017048900946974754,
0.018569698557257652,
0.011817662976682186,
-0.009479070082306862,
-0.03024238534271717,
-0.030534856021404266,
-0.03412109240889549,
-0.01258597057312727,
0.05218375846743584,
0.024320270866155624,
-0.005261335056275129,
-0.009215245023369789,
0.005433537065982819,
-0.010884950868785381,
0.07331222295761108,
-0.08136190474033356,
-0.016261566430330276,
-0.03930424898862839,
0.013351378031075,
-0.0031617647036910057,
0.0049141691997647285
] |
<p>Stephen Wolfram in his book <em>A New Kind of Science</em> touches on a model of space itself based on automata theory. That it, he makes some suggestions about modelling not only the behaviour of matter through space, but the space itself in terms of state machines (a notion from computing). Here, the <a href="http://en.wikipedia.org/wiki/General_topology" rel="nofollow">general topology</a> of space arises from a small-scale connection lattice. </p>
<p>I wondered whether any theoretical work is being undertaken along these lines within the physics community.</p>
<p>The reason for my interest in this regards one of the mysteries of quantum mechanics, that of quantum entanglement and action at distance. I wondered whether, if space is imagined as having a topology that arises from a notion of neighbourhood at a fine level, then quantum entanglement might be a result of a 'short circuit' in the connection lattice. That is two points at a distance through 'normal' space might also still be neighbours at a fundamental level; there might be a short strand of connectivity in addition the all the long strands relating the two.</p>
<p>(I think Richard Feynman also alluded to this sort of model with his take on quantum electro-dynamics.)</p>
| 10,779 |
[
0.006593621801584959,
0.022455910220742226,
0.026212364435195923,
-0.055960312485694885,
0.008516189642250538,
0.018091745674610138,
-0.037458065897226334,
0.01833486743271351,
0.02188258059322834,
-0.03601639345288277,
0.005189558956772089,
0.011042381636798382,
0.024725547060370445,
0.044399749487638474,
-0.0019276310922577977,
0.014405627734959126,
0.0017922193510457873,
-0.032630302011966705,
-0.05064212530851364,
-0.04452488198876381,
0.055190857499837875,
-0.017645955085754395,
-0.012070829048752785,
-0.013913863338530064,
-0.013865608721971512,
0.0022030496038496494,
-0.01598355919122696,
-0.04050886631011963,
0.00044544151751324534,
0.046913206577301025,
0.02425427734851837,
-0.04259442910552025,
-0.013374421745538712,
-0.0034845401532948017,
0.018001753836870193,
-0.023282308131456375,
-0.013803289271891117,
-0.04408016800880432,
0.03061983361840248,
-0.0018668632255867124,
-0.022834867238998413,
-0.018440278246998787,
-0.03708868473768234,
0.061104193329811096,
-0.04739512875676155,
0.03830181062221527,
0.0024543702602386475,
-0.013088223524391651,
0.052821382880210876,
-0.046185627579689026,
0.03711836785078049,
0.007765981834381819,
0.012911271303892136,
-0.007310147397220135,
0.0002242280897917226,
-0.0037219293881207705,
0.07139120250940323,
0.052881769835948944,
-0.005054481327533722,
-0.03502432629466057,
-0.02177615649998188,
-0.0029917333740741014,
-0.000841701403260231,
-0.010536625050008297,
-0.024247318506240845,
0.018647240474820137,
-0.04812680929899216,
-0.04095200076699257,
0.008095485158264637,
0.0018348993035033345,
-0.03343028947710991,
0.04885387793183327,
0.04296346381306648,
0.010374613106250763,
0.050069309771060944,
0.015801550820469856,
-0.001084846560843289,
-0.002268186304718256,
0.02755611762404442,
0.022273819893598557,
-0.00666277389973402,
-0.005802577827125788,
0.007210055831819773,
0.01180597860366106,
0.0019548640120774508,
-0.010499156080186367,
0.06346140056848526,
-0.07915672659873962,
-0.041618116199970245,
0.04732522740960121,
-0.006806739140301943,
0.012489723972976208,
0.05389436334371567,
0.003594288369640708,
-0.032374583184719086,
0.04781024530529976,
0.0023364934604614973,
0.017131119966506958,
0.01300040539354086,
0.014207758009433746,
-0.025306595489382744,
-0.05225806683301926,
-0.012750874273478985,
0.06680550426244736,
-0.03202744945883751,
-0.020536178722977638,
0.00577589962631464,
0.03717323765158653,
-0.0000045597284952236805,
-0.001065791235305369,
-0.06863995641469955,
0.016332920640707016,
0.02161346562206745,
0.03924735262989998,
-0.007097848225384951,
-0.01913488283753395,
0.015046786516904831,
-0.025249101221561432,
0.02144770696759224,
0.08235400170087814,
0.02227184921503067,
-0.020107677206397057,
0.0024859262630343437,
-0.022246941924095154,
-0.05543561279773712,
0.035315532237291336,
0.03428642079234123,
-0.03619341179728508,
-0.023975007236003876,
-0.002598654944449663,
0.0010681480634957552,
0.008303028531372547,
0.01080396119505167,
0.0031256447546184063,
0.05530545860528946,
0.015611506067216396,
-0.0811571478843689,
-0.040216606110334396,
0.06137210130691528,
0.043625812977552414,
-0.007978273555636406,
-0.04307396337389946,
0.04398554190993309,
0.005044679157435894,
0.09427225589752197,
0.0051005687564611435,
-0.011445318348705769,
-0.014515222981572151,
0.007887423038482666,
0.000054213662224356085,
-0.02822094038128853,
-0.02470020018517971,
0.01766052655875683,
-0.039443593472242355,
0.004873453173786402,
-0.046082690358161926,
0.04441522806882858,
0.05532081052660942,
-0.0031693419441580772,
0.011576649732887745,
0.08213277161121368,
-0.005135368090122938,
0.015453865751624107,
-0.00009003264858620241,
-0.03222588077187538,
-0.05320683494210243,
0.06309298425912857,
-0.011454550549387932,
0.00844203308224678,
0.03956783562898636,
0.0016749018104746938,
0.005232343450188637,
-0.0096825510263443,
0.010734183713793755,
0.020116126164793968,
-0.038164012134075165,
-0.0072825076058506966,
0.018462490290403366,
-0.010426228865981102,
-0.011558694764971733,
-0.04391563683748245,
-0.005862814839929342,
-0.016458116471767426,
0.027560845017433167,
-0.009713338688015938,
0.007073644082993269,
-0.03182151913642883,
-0.05599115416407585,
0.019123315811157227,
-0.004637277219444513,
-0.010060516186058521,
-0.05882958322763443,
0.006917543709278107,
-0.06417626142501831,
-0.002656050492078066,
-0.006025495007634163,
-0.007966747507452965,
-0.01609310507774353,
-0.015341528691351414,
-0.053732093423604965,
-0.021322011947631836,
0.0064250510185956955,
0.03211290016770363,
0.0027558698784559965,
0.0064494553953409195,
0.06062838435173035,
0.010171742178499699,
-0.016859939321875572,
0.026434406638145447,
-0.02479843981564045,
-0.033396534621715546,
0.0005404838011600077,
-0.02270728349685669,
0.07314887642860413,
0.0019572630990296602,
-0.008576120249927044,
0.018998853862285614,
0.00989168044179678,
-0.03524860739707947,
0.030326446518301964,
-0.025899147614836693,
0.06301133334636688,
0.021563464775681496,
0.018924107775092125,
-0.01838511973619461,
0.061394043266773224,
0.034189753234386444,
0.02342284470796585,
-0.007033308036625385,
-0.02101389691233635,
-0.0924067348241806,
0.003950713202357292,
0.03411872312426567,
-0.0024227965623140335,
-0.000908301561139524,
-0.003867396153509617,
0.014081559143960476,
0.06315429508686066,
-0.004227071069180965,
0.011250397190451622,
-0.030083078891038895,
-0.012124216184020042,
-0.027011679485440254,
-0.009442702867090702,
0.0410594642162323,
-0.01821940205991268,
-0.0011827634880319238,
0.01122677605599165,
0.00814202893525362,
-0.04283592849969864,
-0.032472483813762665,
0.0424472950398922,
-0.03560855612158775,
0.033416926860809326,
0.0008968056063167751,
-0.01591143198311329,
0.051861174404621124,
-0.021920092403888702,
0.006313018500804901,
-0.007855501025915146,
-0.004827954340726137,
-0.011248277500271797,
-0.05006527528166771,
-0.03647761419415474,
0.004739413503557444,
-0.001750304363667965,
-0.007839715108275414,
-0.01042537298053503,
0.036062587052583694,
-0.012951849959790707,
0.03263550624251366,
-0.010715475305914879,
0.011433150619268417,
-0.018738461658358574,
0.003547184867784381,
0.03859857842326164,
-0.005470300558954477,
0.009502741508185863,
-0.028604241088032722,
-0.031201817095279694,
0.03217177465558052,
0.008859659545123577,
0.005929923616349697,
0.04248069226741791,
-0.03860659524798393,
0.016410227864980698,
-0.012944309040904045,
-0.028279319405555725,
-0.01726367697119713,
-0.008991532027721405,
0.014942350797355175,
-0.026680009439587593,
-0.003830394707620144,
-0.011414646171033382,
-0.012605881318449974,
-0.06282222270965576,
0.0205557718873024,
-0.017630569636821747,
0.03720014542341232,
0.059754256159067154,
0.013689255341887474,
-0.07802745699882507,
-0.006862453185021877,
-0.03495405986905098,
-0.028965342789888382,
-0.02110634557902813,
-0.025664106011390686,
0.009727178141474724,
-0.03045959211885929,
-0.004693389870226383,
0.06357739120721817,
-0.045007433742284775,
-0.01017855666577816,
-0.06404880434274673,
-0.05554872751235962,
0.0394786112010479,
-0.014887670055031776,
0.05530324578285217,
0.004294294863939285,
-0.0015904344618320465,
0.0838356539607048,
0.02149437740445137,
-0.0186401829123497,
-0.019854143261909485,
0.01455984078347683,
-0.02473859116435051,
-0.03778255730867386,
0.017221879214048386,
0.03907331824302673,
0.003940118942409754,
0.006741704419255257,
0.03696807101368904,
0.033332161605358124,
0.03000129573047161,
0.0008304641814902425,
-0.014964090660214424,
0.005160818807780743,
0.0032479052897542715,
-0.01588454097509384,
0.04190594702959061,
0.004529288969933987,
-0.02946840599179268,
-0.012486737221479416,
-0.01826479658484459,
-0.0008746169041842222,
0.05137995630502701,
-0.03522935509681702,
0.03977226838469505,
0.00443786196410656,
0.015063735656440258,
0.000323598476825282,
0.002570307580754161,
-0.020051270723342896,
-0.03597278892993927,
0.010366089642047882,
0.05915331467986107,
0.04185304045677185,
0.0318579226732254,
-0.0001617578964214772,
0.016742603853344917,
0.07069149613380432,
-0.04173250496387482,
-0.010202830657362938,
-0.011234981939196587,
0.021013598889112473,
0.019668152555823326,
-0.03355500474572182,
-0.02644445188343525,
0.039785534143447876,
0.031919628381729126,
0.002699886914342642,
0.054450057446956635,
-0.055375777184963226,
-0.028093839064240456,
-0.0704379752278328,
-0.021210577338933945,
-0.0318155474960804,
0.03586256504058838,
0.027070611715316772,
-0.015421581454575062,
0.023700203746557236,
-0.007445833645761013,
-0.026828840374946594,
0.01157728023827076,
-0.09709719568490982,
-0.03387858718633652,
-0.03147348761558533,
-0.041176628321409225,
0.016369624063372612,
-0.0017232568934559822,
0.005938244517892599,
-0.007291288115084171,
-0.06949152052402496,
-0.0071478490717709064,
0.024974407628178596,
-0.13091550767421722,
0.010788669809699059,
-0.04295782372355461,
-0.03519101440906525,
-0.01400382537394762,
0.020939335227012634,
0.08483234792947769,
0.003261098638176918,
-0.025761030614376068,
-0.008398568257689476,
-0.011803802102804184,
-0.018431028351187706,
0.011884842067956924,
0.006210096180438995,
0.030380718410015106,
-0.004753257147967815,
-0.003966416697949171,
0.022576814517378807,
-0.05408259108662605,
0.019014183431863785,
0.018750380724668503,
0.005751136224716902,
-0.008534845896065235,
-0.017069417983293533,
0.005293387454003096,
-0.047348085790872574,
-0.0227202121168375,
0.0021939037833362818,
0.06269525736570358,
-0.002033543772995472,
0.04676467180252075,
0.010980596765875816,
0.01697182096540928,
-0.049222011119127274,
0.02609127014875412,
0.03128257393836975,
-0.008878736756742,
-0.04045603796839714,
-0.010819660499691963,
-0.02157656103372574,
0.0012683557579293847,
-0.01702401600778103,
0.010027854703366756,
0.007373720407485962,
-0.042077962309122086,
0.02945179119706154,
0.010751334950327873,
0.026279248297214508,
-0.03999385982751846,
0.000435236026532948,
-0.032574612647295,
-0.035681888461112976,
-0.01859794184565544,
-0.005487856455147266,
0.008353137411177158,
-0.018199250102043152,
0.03085784614086151,
0.02125643379986286,
0.02305653505027294,
-0.12615889310836792,
-0.008689374662935734,
0.04885789379477501,
0.014543777331709862,
0.057414837181568146,
-0.002509558806195855,
-0.05578871816396713,
-0.04391760006546974,
0.015883326530456543,
0.01219568494707346,
0.04816193878650665,
-0.01000868622213602,
-0.031570497900247574,
-0.03096054494380951,
-0.02940823882818222,
0.03775368630886078,
-0.016028081998229027,
0.004037025850266218,
0.03501557186245918,
0.0030817484948784113,
0.002049320377409458,
-0.0415186733007431,
0.014689512550830841,
0.006972448900341988,
0.005990828387439251,
0.02643084153532982,
0.021556517109274864,
-0.024465516209602356,
0.010430688038468361,
-0.017447400838136673,
-0.09241756051778793,
0.03248026221990585,
0.027221912518143654,
-0.024165598675608635,
0.03843732178211212,
-0.01952156238257885,
0.006959899328649044,
0.018054569140076637,
-0.035853542387485504,
0.005147463642060757,
0.013010979630053043,
0.007049985229969025,
0.0723295509815216,
0.019574783742427826,
0.006241999566555023,
0.014830943197011948,
0.03390230983495712,
-0.05014202371239662,
0.0070310598239302635,
0.022405026480555534,
0.02581067383289337,
-0.008666564710438251,
0.0464198961853981,
-0.02917405404150486,
0.001702671404927969,
-0.008725058287382126,
0.041958995163440704,
0.002293088473379612,
-0.01846916787326336,
0.0020484202541410923,
-0.07799597829580307,
-0.027087664231657982,
-0.006429452449083328,
-0.01440124399960041,
-0.009354121051728725,
-0.016516411677002907,
0.050798434764146805,
0.021391307935118675,
0.007655526045709848,
0.029952440410852432,
0.011350603774189949,
0.02707439474761486,
0.030166510492563248,
-0.021868878975510597,
0.003351891180500388,
-0.04714160040020943,
-0.015175609849393368,
0.029535962268710136,
-0.05532592162489891,
0.029130512848496437,
0.0012243743985891342,
-0.00788841675966978,
0.037348270416259766,
-0.04653608798980713,
-0.017265137284994125,
0.010019329376518726,
-0.04691890627145767,
-0.03710160404443741,
0.024906940758228302,
0.009016272611916065,
-0.004026548471301794,
-0.004388102330267429,
-0.053901027888059616,
-0.05868583917617798,
0.042207710444927216,
0.015621367841959,
-0.013726809993386269,
-0.06045317277312279,
0.01577869802713394,
-0.01749708317220211,
0.0035791019909083843,
0.031436510384082794,
0.03171022981405258,
-0.06381382048130035,
0.030738191679120064,
0.06005837023258209,
0.012680452316999435,
0.018421441316604614,
0.022227715700864792,
0.020133549347519875,
-0.0006732079200446606,
0.026531755924224854,
0.03344260901212692,
-0.012463556602597237,
0.026779597625136375,
-0.05215727910399437,
-0.024738498032093048,
-0.031741801649332047,
0.018191291019320488,
0.02978561446070671,
-0.08052167296409607,
-0.01144286897033453,
0.024886157363653183,
0.03612734004855156,
0.029573755338788033,
0.008114068768918514,
-0.0016372178215533495,
0.011685507372021675,
0.014122377149760723,
-0.011978855356574059,
0.016235163435339928,
0.0005685014184564352,
-0.021111153066158295,
-0.0018906121840700507,
0.02284952998161316,
-0.004013695288449526,
0.039203837513923645,
0.010037761181592941,
0.022637290880084038,
-0.020894749090075493,
0.0356564000248909,
-0.030946101993322372,
0.004080042243003845,
-0.03960096463561058,
0.010564845986664295,
0.021002251654863358,
0.0050846291705966,
-0.02136637270450592,
-0.05231757462024689,
-0.01454627700150013,
-0.024411510676145554,
0.008539547212421894,
0.021120639517903328,
0.035886868834495544,
0.038622837513685226,
-0.03675860911607742,
-0.012015314772725105,
-0.0037194194737821817,
0.008501681499183178,
0.009481821209192276,
-0.011088327504694462,
0.0205211341381073,
-0.04724860191345215,
0.020014848560094833,
0.0275588259100914,
0.05450132489204407,
-0.04311791807413101,
-0.007874232716858387,
0.03217269852757454,
0.025743763893842697,
0.04205076023936272,
-0.030710330232977867,
-0.022041866555809975,
0.053110864013433456,
-0.030595513060688972,
0.01617933064699173,
0.051066845655441284,
-0.004749765153974295,
0.01866968348622322,
0.03104950115084648,
0.0379154272377491,
-0.005199848674237728,
0.001883864519186318,
-0.059155259281396866,
0.02295827493071556,
-0.003961692564189434,
0.028354311361908913,
-0.0024061710573732853,
-0.0065753767266869545,
0.04402785003185272,
-0.012205873616039753,
-0.014666158705949783,
0.02189771644771099,
-0.042035941034555435,
0.013847464695572853,
-0.025628630071878433,
-0.039801377803087234,
0.04342219606041908,
0.001471034251153469,
-0.03863948583602905,
0.0085609657689929,
-0.029780462384223938,
0.045251041650772095,
0.023226488381624222,
0.039229582995176315,
-0.011679143644869328,
0.05644790828227997,
-0.019071312621235847,
0.016500504687428474,
-0.052056074142456055,
0.023635772988200188,
0.1275947093963623,
0.020485904067754745,
-0.01925557292997837,
-0.03806154057383537,
0.02404732070863247,
-0.018839385360479355,
0.0421643890440464,
-0.03491665795445442,
-0.0008444118429906666,
0.03702942281961441,
0.005202640313655138,
0.028330743312835693,
0.05236528068780899,
0.021080587059259415,
-0.04130196198821068,
0.05535224452614784,
-0.03866184130311012,
-0.026789391413331032,
0.011475480161607265,
-0.01759514771401882,
-0.005964410025626421,
0.020246054977178574,
-0.026029692962765694,
0.021254928782582283,
-0.004326019436120987,
0.008864104747772217,
-0.02321465313434601,
0.004137071780860424,
0.012417877092957497,
0.0360463447868824,
-0.031555913388729095,
-0.005271147936582565,
-0.01720159687101841,
-0.017701182514429092,
0.00012916822743136436,
0.015353819355368614,
0.02689763531088829,
0.024926958605647087,
0.013149025849997997,
0.04297852888703346,
-0.001655077445320785,
-0.0048070428892970085,
-0.012963521294295788,
0.0310188140720129,
-0.05994849652051926,
-0.048989538103342056,
-0.018326541408896446,
0.034957803785800934,
-0.020211121067404747,
0.01416125986725092,
0.012976273894309998,
-0.008791591040790081,
0.04612934589385986,
-0.0177917443215847,
-0.012104523368179798,
-0.010954263620078564,
0.013092183507978916,
-0.013678867369890213,
-0.0005959763075225055,
-0.00984263140708208,
0.024537840858101845,
-0.01036505401134491,
0.017672650516033173,
-0.003989831544458866,
-0.0006740338285453618,
-0.010897349566221237,
0.004437688272446394,
0.0355043038725853,
-0.01547904685139656,
-0.015178551897406578,
-0.06109258159995079,
0.009637373499572277,
-0.049683935940265656,
-0.029397660866379738,
0.027385342866182327,
0.03858856111764908,
0.025562351569533348,
-0.006397987250238657,
-0.006719592027366161,
0.03140435740351677,
-0.02472912147641182,
-0.011296428740024567,
-0.04040491208434105,
0.005415452644228935,
0.0025905859656631947,
0.012465152889490128,
0.031198924407362938,
0.027020519599318504,
-0.01767510548233986,
-0.025067873299121857,
0.009545162320137024,
0.007922464050352573,
0.03837474063038826,
-0.010592295788228512,
0.0063113197684288025,
-0.014807235449552536,
-0.030217032879590988,
0.017289157956838608,
0.0031435845885425806,
0.003128987969830632,
0.004598564933985472,
-0.007256106939166784,
0.0015460350550711155,
0.03998337686061859,
0.013102809898555279,
0.006338952109217644,
0.014240066520869732,
-0.02556759864091873,
-0.015455525368452072,
-0.015480443835258484,
0.02527710236608982,
-0.027971817180514336,
-0.001256203860975802,
-0.012828460894525051,
0.004455896560102701,
0.008294613100588322,
0.04180391877889633,
-0.045946672558784485,
-0.0011638235300779343,
0.011386841535568237,
0.03369157761335373,
-0.021144578233361244,
0.0013020685873925686,
-0.04711887985467911,
-0.03767192363739014,
-0.04011792317032814,
-0.005686300806701183,
0.029419509693980217,
0.02254558727145195,
-0.01024411991238594,
-0.0090513676404953,
0.01856142282485962,
0.013767348602414131,
-0.038525037467479706,
0.0013110206928104162,
0.01648140326142311,
0.029826443642377853,
0.061414726078510284,
-0.01055814791470766,
-0.04805236682295799,
-0.0010482972720637918,
-0.020175177603960037,
-0.07587561011314392,
0.02188805490732193,
-0.05743873864412308,
0.0028638034127652645,
0.05140894278883934,
-0.020837891846895218,
-0.021513722836971283,
0.027516230940818787,
0.007373829837888479,
0.0017246560892090201,
0.023538287729024887,
0.021215034648776054,
0.008024238981306553,
-0.005861320067197084,
0.018424028530716896,
-0.01734023168683052,
0.011352135799825191,
-0.021877944469451904,
0.019146503880620003,
0.003684456693008542,
-0.006039117928594351,
0.013207577168941498,
-0.07689382135868073,
-0.005871680099517107,
0.005617893300950527,
0.010632283054292202,
0.017490312457084656,
0.025923816487193108,
-0.011148353107273579,
0.041747577488422394,
0.057486627250909805,
-0.014712552540004253,
-0.07866118103265762,
-0.014707090333104134,
0.033765558153390884,
-0.012869217433035374,
0.04259977862238884,
-0.03799661621451378,
0.021600570529699326,
0.013871707022190094,
-0.10763800144195557,
0.05386817082762718,
0.014816973358392715,
0.005488064605742693,
-0.03795833885669708,
-0.0015107616782188416,
-0.040176406502723694,
0.06290819495916367,
-0.007342554163187742,
0.05898682773113251,
0.01550301630049944,
0.038052525371313095,
-0.01525946520268917,
-0.022130828350782394,
-0.024028019979596138,
0.0037096140440553427,
-0.04054880887269974,
0.02326047234237194,
0.04106809198856354,
-0.029110580682754517,
0.008590553887188435,
-0.01497819647192955,
-0.03037145361304283,
-0.0038820018526166677,
-0.03214562311768532,
-0.0015421098796650767,
0.054373834282159805,
0.0041612982749938965,
0.028230922296643257,
-0.02165394090116024,
0.015112902969121933,
0.002691603498533368,
0.0011247516376897693,
0.006705010309815407,
-0.013542667962610722,
-0.016767678782343864,
0.03164190798997879,
-0.028939908370375633,
-0.0225700493901968,
-0.020034488290548325,
-0.018809232860803604,
0.042410433292388916,
-0.00924620870500803,
0.026068653911352158,
-0.006527189165353775,
-0.009493072517216206,
-0.004607386887073517,
-0.03947686403989792,
-0.007602408528327942,
0.017803966999053955,
-0.0010017018066719174,
-0.0070265959948301315,
0.026195814833045006,
-0.03228916600346565,
-0.009324506856501102,
0.007890291512012482,
0.003513561561703682,
0.003936778288334608,
-0.03981497138738632,
-0.05842176824808121,
-0.001902432763017714,
0.04042045399546623,
0.02568279393017292,
-0.03641844540834427,
-0.0025519945193082094,
0.05124460533261299,
0.00002830380981322378,
0.04513905942440033,
-0.0028356309048831463,
-0.02173881232738495,
0.008529264479875565,
-0.025179831311106682,
0.02275875024497509,
0.007886211387813091,
0.07768166065216064,
0.002031896263360977,
-0.026601040735840797,
0.029601257294416428,
-0.01517847366631031,
0.0662226602435112,
0.0027497655246406794,
0.022355590015649796,
-0.008243924006819725,
0.015100225806236267,
0.033516474068164825,
0.031303081661462784,
-0.01948598027229309,
-0.040077608078718185,
-0.0011954810470342636,
-0.00023158137628342956,
-0.046767015010118484,
-0.030377471819519997,
0.012865019962191582,
0.025731271132826805,
-0.013091294094920158,
-0.021423256024718285,
-0.049643661826848984,
-0.0677880346775055,
0.06866966187953949,
0.011642372235655785,
0.004577995277941227,
0.04684378206729889,
-0.003741201711818576,
0.038919080048799515,
0.02536592446267605,
-0.025995587930083275,
-0.005423669703304768,
0.023162202909588814,
-0.03174187242984772,
-0.0085220942273736,
-0.013705817051231861,
-0.01577077805995941,
0.04889967292547226,
-0.009776904247701168,
-0.04959693178534508,
0.03135610371828079,
-0.01787649653851986,
-0.004515574313700199,
0.07255379855632782,
-0.011431149207055569,
0.028861237689852715,
-0.020958589389920235,
0.018250804394483566,
0.03458708897233009,
0.010424256324768066,
-0.021106017753481865,
0.04004400968551636,
0.05642210692167282,
0.012373355217278004,
0.0022142655216157436,
0.04738767817616463,
0.012288328260183334,
0.05199217423796654,
0.014190268702805042,
0.01866321824491024,
-0.025194313377141953,
0.01044713705778122,
0.027301879599690437,
0.005055648740381002,
0.000135032954858616,
0.04287770390510559,
-0.049197036772966385,
0.10015495866537094,
-0.012725370936095715,
-0.007845050655305386,
-0.0032430358696728945,
0.021538469940423965,
-0.04063629359006882,
0.012963883578777313,
-0.006130244117230177,
0.023442190140485764,
-0.0031727461609989405,
0.01307272631675005,
-0.011801397427916527,
0.013047637417912483,
0.0043680500239133835,
-0.030371425673365593,
0.01397375762462616,
-0.029108764603734016,
0.029156921431422234,
0.0298809502273798,
-0.0006017233827151358,
-0.02583639696240425,
-0.03246203809976578,
0.03416815027594566,
0.05704079568386078,
0.006372807547450066,
-0.002949661109596491,
0.011174912564456463,
0.005903166253119707,
0.07947875559329987,
-0.06571049988269806,
-0.016192350536584854,
-0.03327373042702675,
0.026777371764183044,
-0.05737346410751343,
-0.0035589488688856363
] |
<p>or a phenomenon where we can only measure the standard deviation ($\sigma_w$) of a variable $w$ and not the mean $\overline{w}$</p>
| 10,780 |
[
-0.0281179528683424,
-0.010874813422560692,
0.002988782012835145,
-0.047148142009973526,
0.025410255417227745,
0.040726084262132645,
-0.00592446094378829,
-0.015466242097318172,
-0.0010175976203754544,
-0.02127338945865631,
0.040959663689136505,
-0.0015412739012390375,
0.08160248398780823,
-0.007962607778608799,
0.038798533380031586,
0.02290363982319832,
-0.03847408667206764,
0.04120447486639023,
-0.015850847586989403,
-0.019603250548243523,
-0.0058171628043055534,
0.022684544324874878,
0.019204031676054,
0.0016477488679811358,
-0.01997538097202778,
0.02107488550245762,
0.018260834738612175,
-0.009861609898507595,
0.013244425877928734,
0.05606207996606827,
-0.03684400022029877,
-0.02519850805401802,
0.038981158286333084,
0.02483816258609295,
0.03620067983865738,
-0.005159864202141762,
0.019303830340504646,
-0.008341958746314049,
-0.002842488931491971,
0.013964047655463219,
-0.028586992993950844,
-0.0010820069583132863,
0.011987943202257156,
0.0015552156837657094,
-0.024487538263201714,
0.010130371898412704,
-0.012363716959953308,
-0.08083195984363556,
0.02702961675822735,
-0.0254175066947937,
0.04050874337553978,
-0.007078113034367561,
0.01908450573682785,
0.0172036811709404,
0.004057032987475395,
0.03737941011786461,
0.08174674212932587,
0.05640041083097458,
-0.019164443016052246,
-0.08858930319547653,
-0.04373648390173912,
0.01852172426879406,
0.020616354420781136,
0.010851397179067135,
-0.026172896847128868,
0.005241455044597387,
-0.003249605419114232,
-0.0315081812441349,
0.04469967260956764,
0.007256960496306419,
-0.020294643938541412,
0.02433481626212597,
0.016062265262007713,
0.008402880281209946,
0.03947174921631813,
-0.031963855028152466,
-0.002924552420154214,
-0.00817488506436348,
0.025137219578027725,
0.052265603095293045,
0.0619875006377697,
-0.022485867142677307,
0.025442365556955338,
-0.0038459422066807747,
0.024293191730976105,
-0.03907012939453125,
0.06678559631109238,
-0.007086725439876318,
-0.006197288632392883,
0.02698460780084133,
-0.0033294649329036474,
-0.007392429281026125,
0.05037899315357208,
-0.029442371800541878,
-0.04539387300610542,
0.050163596868515015,
-0.002238736255094409,
-0.0088913319632411,
0.0034738865215331316,
-0.031189801171422005,
0.013999556191265583,
-0.04035009816288948,
0.020812947303056717,
0.0787259191274643,
-0.023735111579298973,
-0.014065645635128021,
-0.013041814789175987,
0.025865880772471428,
-0.023134861141443253,
0.002528396202251315,
-0.00992564857006073,
0.009132268838584423,
0.024837322533130646,
0.03938013315200806,
0.02303372509777546,
0.03277048468589783,
-0.01509651355445385,
0.0011293221032246947,
0.027678262442350388,
0.08619175851345062,
0.05087275803089142,
-0.030220450833439827,
0.0019931739661842585,
0.009749632328748703,
-0.06790308654308319,
0.06543286889791489,
0.03721388056874275,
0.0006008587079122663,
-0.04210171848535538,
0.003272923408076167,
0.022069821134209633,
-0.014496219344437122,
0.07185637950897217,
-0.00750591279938817,
0.023330306634306908,
-0.004279534798115492,
-0.08766866475343704,
-0.04835972189903259,
0.05246131122112274,
-0.006444418802857399,
-0.02561238780617714,
-0.04757852107286453,
0.003538262564688921,
0.022225791588425636,
0.021585950627923012,
0.050129663199186325,
0.04821796715259552,
0.014875008724629879,
0.021856874227523804,
0.008877545595169067,
-0.0008341755601577461,
-0.017378317192196846,
0.03871789574623108,
-0.04315396398305893,
0.016567550599575043,
-0.040104545652866364,
0.011079815216362476,
0.00825029332190752,
-0.03591436147689819,
0.020320625975728035,
0.00538709806278348,
-0.018865155056118965,
0.009657477959990501,
0.0008932158234529197,
0.027547037228941917,
-0.02571280673146248,
0.05718319118022919,
0.0279664508998394,
0.02873378060758114,
0.0047590360045433044,
0.01602996326982975,
0.03397337347269058,
0.006876684725284576,
0.05603255331516266,
0.0589018240571022,
-0.031067848205566406,
-0.033592358231544495,
-0.0013518311316147447,
0.008961999788880348,
0.018923630937933922,
-0.06367305666208267,
-0.01762043870985508,
0.01711614429950714,
0.03674136474728584,
0.004577827639877796,
0.04875257983803749,
0.006366501562297344,
0.0056357234716415405,
0.03381519764661789,
-0.04019622877240181,
-0.01902676187455654,
-0.04370905086398125,
0.0030672866851091385,
0.006192365661263466,
-0.04089551791548729,
0.02207755297422409,
0.02949920855462551,
0.0005559796118177474,
-0.03611745312809944,
-0.058659669011831284,
-0.005741557572036982,
0.04530946910381317,
0.031767841428518295,
-0.0527149960398674,
-0.010858647525310516,
0.05580682307481766,
0.05986268073320389,
0.006466517690569162,
0.05502207949757576,
-0.01828625239431858,
-0.060742735862731934,
-0.020142164081335068,
-0.025756077840924263,
0.0176453348249197,
-0.02211982011795044,
-0.030117306858301163,
0.026424726471304893,
-0.011239149607717991,
-0.008897429332137108,
0.06263945251703262,
-0.020118199288845062,
0.01883271336555481,
0.05051904544234276,
0.014907123520970345,
-0.015963952988386154,
-0.002156505361199379,
0.017503909766674042,
0.012238583527505398,
-0.03326844796538353,
-0.0010079166386276484,
-0.0021572192199528217,
-0.0017453741747885942,
0.021455256268382072,
0.02798871509730816,
-0.032018616795539856,
0.0003325916186440736,
0.04540963098406792,
0.02237899973988533,
0.002668058965355158,
0.028221827000379562,
-0.00828114990144968,
-0.04041452333331108,
-0.03660750761628151,
0.0175448227673769,
0.05521027371287346,
0.021367104724049568,
-0.009140266105532646,
0.013857552781701088,
0.0012706088600680232,
0.023380976170301437,
-0.0026947609148919582,
0.0388229563832283,
0.005570672918111086,
0.01657892018556595,
0.014968937262892723,
-0.018671294674277306,
0.006716887000948191,
-0.031925689429044724,
0.024597205221652985,
0.05319515988230705,
-0.003804991254583001,
0.006332755088806152,
0.011735551990568638,
-0.00973529927432537,
0.020546656101942062,
0.022487109526991844,
-0.004588012583553791,
0.0032435215543955564,
0.04026305675506592,
-0.02091153897345066,
-0.004151308909058571,
-0.015576205216348171,
-0.022157153114676476,
-0.016734654083848,
-0.009011519141495228,
0.05696242302656174,
0.00031804016907699406,
0.055355384945869446,
-0.002935498720034957,
-0.04962123930454254,
0.004689937923103571,
-0.02672687917947769,
-0.007758710533380508,
-0.029956789687275887,
-0.0062500606290996075,
-0.0030215114820748568,
-0.025835400447249413,
-0.02526668645441532,
0.012618749402463436,
-0.042412661015987396,
0.01026771031320095,
0.03752589598298073,
-0.00345406006090343,
-0.0150124067440629,
0.011978656984865665,
-0.046551115810871124,
0.017690937966108322,
-0.018815509974956512,
-0.013297189958393574,
0.038599271327257156,
-0.01064111664891243,
-0.05099689960479736,
0.04368850588798523,
-0.0382276251912117,
-0.06557371467351913,
-0.048738736659288406,
-0.04040515422821045,
0.036322541534900665,
-0.02216426655650139,
0.04220655560493469,
0.0216617863625288,
-0.07171262055635452,
-0.025974201038479805,
-0.03988248109817505,
-0.05349799990653992,
0.02055809274315834,
-0.01151929423213005,
0.014549159444868565,
-0.02115759253501892,
-0.005877171643078327,
0.07467580586671829,
0.013285143300890923,
-0.008424736559391022,
-0.0216806773096323,
0.02486230991780758,
-0.02203160896897316,
-0.03830546885728836,
-0.0017439726507291198,
0.00019726602477021515,
0.012673824094235897,
0.053671784698963165,
0.01721344143152237,
0.03292810544371605,
0.03625181317329407,
-0.006194154731929302,
-0.027793806046247482,
0.0017728625098243356,
-0.02786239981651306,
0.004038974177092314,
0.040655165910720825,
-0.019528010860085487,
-0.03234430029988289,
-0.0006358953542076051,
0.019906556233763695,
0.055779799818992615,
0.04478909820318222,
-0.02798967808485031,
0.04135579615831375,
-0.0025230657774955034,
0.030509620904922485,
-0.028962265700101852,
0.05555335059762001,
0.031201422214508057,
0.00594918429851532,
-0.035472169518470764,
0.01111594121903181,
0.020956534892320633,
-0.014906675554811954,
0.021225351840257645,
0.01581127569079399,
0.009318702854216099,
-0.04034007713198662,
-0.014135497622191906,
-0.014132018201053143,
-0.00354360812343657,
0.015696734189987183,
-0.015661396086215973,
-0.05255034938454628,
0.058001045137643814,
0.07372715324163437,
-0.02660752274096012,
-0.011145277880132198,
-0.05225829407572746,
0.010536047630012035,
-0.06418029218912125,
-0.02320263534784317,
-0.030139900743961334,
0.04164115712046623,
0.01746963895857334,
0.03282275050878525,
0.03339740261435509,
0.01089116744697094,
-0.004007099196314812,
-0.02182694524526596,
-0.056974735110998154,
-0.0016435811994597316,
-0.03767136111855507,
-0.024133142083883286,
-0.013859597966074944,
-0.02603003941476345,
0.022357413545250893,
-0.02905323915183544,
0.02375008538365364,
-0.026151705533266068,
0.021748190745711327,
-0.03473091125488281,
-0.004822210408747196,
0.0196493249386549,
-0.010764149017632008,
-0.025588281452655792,
0.016837993636727333,
0.03421265259385109,
-0.037460245192050934,
0.03455280512571335,
0.01014305092394352,
-0.0006048385403119028,
-0.034859515726566315,
-0.05576130002737045,
0.001325830933637917,
0.01957126148045063,
0.043517835438251495,
0.011001229286193848,
0.029551222920417786,
-0.04324064403772354,
0.030256833881139755,
0.024304421618580818,
0.03646191954612732,
0.026796972379088402,
0.0209504347294569,
-0.017163220793008804,
-0.020692167803645134,
-0.021071435883641243,
0.010146362707018852,
0.0157458558678627,
0.03415181115269661,
0.01165094319730997,
0.03373881056904793,
0.009551966562867165,
-0.060497403144836426,
0.01965678110718727,
0.03843387961387634,
0.03858676925301552,
-0.01651758700609207,
0.01445874385535717,
0.0019387524807825685,
-0.004881768021732569,
-0.020939676091074944,
0.013415196910500526,
0.010438891127705574,
0.012958331033587456,
-0.018115170300006866,
0.021650174632668495,
0.014835131354629993,
-0.027256641536951065,
-0.041805416345596313,
-0.01660074107348919,
-0.015756472945213318,
-0.032037049531936646,
-0.020751213654875755,
0.02095942571759224,
0.02488408237695694,
0.03724363446235657,
0.03142261505126953,
-0.002370959147810936,
-0.06433102488517761,
0.022141743451356888,
0.04951922595500946,
0.003477142658084631,
-0.019505290314555168,
0.014345419593155384,
0.0003570724802557379,
0.018335066735744476,
0.02460159733891487,
-0.014158865436911583,
0.024092119187116623,
-0.0509820394217968,
-0.0028070637490600348,
-0.009088191203773022,
-0.018718130886554718,
-0.03237665817141533,
0.020358964800834656,
-0.006438915617763996,
0.005772207863628864,
-0.007583273574709892,
0.006714880932122469,
-0.0363176204264164,
-0.0538175068795681,
0.03726164996623993,
0.059255219995975494,
0.01118509192019701,
-0.01124462578445673,
0.010964536108076572,
0.06374558806419373,
-0.015054583549499512,
-0.10188493132591248,
-0.006235713604837656,
0.027010731399059296,
0.001277437200769782,
0.05078984424471855,
0.001166010508313775,
-0.05389461666345596,
0.03398537635803223,
-0.02206752635538578,
-0.02728058397769928,
0.019334599375724792,
0.0004984725383110344,
0.044303134083747864,
0.06718115508556366,
0.039299726486206055,
0.056906089186668396,
0.021427275612950325,
-0.010143311694264412,
-0.01684069260954857,
-0.022653093561530113,
0.0379936657845974,
-0.05320064723491669,
-0.057321157306432724,
-0.05499724671244621,
-0.03185949847102165,
-0.009360436350107193,
0.019144272431731224,
0.008809217251837254,
-0.0005968896439298987,
-0.010147946886718273,
-0.03794214501976967,
-0.029241017997264862,
-0.025354325771331787,
0.006924696732312441,
-0.026931891217827797,
-0.010782568715512753,
0.02194969542324543,
0.006075168959796429,
-0.015594275668263435,
0.018476400524377823,
-0.0007839893805794418,
-0.003043172648176551,
0.02642626315355301,
-0.04730001464486122,
-0.0052852937951684,
-0.05451083555817604,
-0.04369146004319191,
0.03775057941675186,
-0.010686801746487617,
0.030831631273031235,
-0.03201780468225479,
0.008565016090869904,
-0.003989781718701124,
-0.02727244235575199,
-0.043174728751182556,
0.02441559173166752,
0.01190383080393076,
-0.0006118133314885199,
-0.04862331226468086,
0.014120311476290226,
0.026349665597081184,
-0.006710870657116175,
-0.07837565988302231,
-0.029555844143033028,
-0.003664839081466198,
0.011244721710681915,
-0.0012401919811964035,
-0.004032945726066828,
-0.0053890664130449295,
-0.011894825845956802,
-0.05649566277861595,
-0.03931846842169762,
0.025794867426156998,
-0.009408988989889622,
-0.02548062987625599,
-0.020651154220104218,
0.047250330448150635,
0.051064152270555496,
-0.02766590006649494,
0.0035193839576095343,
0.025063496083021164,
-0.013431742787361145,
0.021126367151737213,
0.0374314971268177,
0.035369399935007095,
-0.026746109127998352,
-0.0014949694741517305,
-0.010547537356615067,
-0.0571100227534771,
-0.016847815364599228,
-0.0324050672352314,
-0.017725219950079918,
-0.004662015940994024,
0.03037804737687111,
-0.018174396827816963,
0.003669168334454298,
0.05473807826638222,
-0.009152677841484547,
0.03910183161497116,
0.0017776897875592113,
-0.021152377128601074,
-0.027706526219844818,
-0.014616838656365871,
0.009007340297102928,
0.05314110964536667,
-0.05461669713258743,
0.007838957011699677,
0.06569942831993103,
-0.024518094956874847,
-0.01179511658847332,
-0.0027904475573450327,
-0.02254888229072094,
0.02052070014178753,
0.013698793016374111,
0.023493362590670586,
-0.0006691391463391483,
0.046398602426052094,
-0.025157421827316284,
-0.020588034763932228,
-0.027596572414040565,
-0.01759125478565693,
0.0594550296664238,
-0.020555146038532257,
0.061156537383794785,
0.043778274208307266,
-0.026376327499747276,
0.036022551357746124,
-0.05817301571369171,
-0.013208174146711826,
0.02624030038714409,
-0.013314493000507355,
0.04778462275862694,
-0.0025082535576075315,
0.041085585951805115,
0.03381134569644928,
0.05546989291906357,
-0.025587303563952446,
0.038562025874853134,
-0.007633506786078215,
0.02715200185775757,
0.004254790022969246,
-0.04854170233011246,
-0.04814465343952179,
0.05233946815133095,
-0.03565177321434021,
0.006325398106127977,
-0.03672853857278824,
-0.0024285155814141035,
0.02472851425409317,
-0.022500891238451004,
-0.014105704613029957,
-0.042728979140520096,
0.023513998836278915,
-0.046636100858449936,
-0.01954253762960434,
0.0015242478111758828,
-0.011059941723942757,
0.03132719174027443,
-0.030385678634047508,
0.031901899725198746,
-0.02482517436146736,
0.0065238201059401035,
-0.01716083101928234,
-0.08342837542295456,
-0.04384057596325874,
-0.017946138978004456,
-0.035535793751478195,
0.06571424752473831,
-0.02418476901948452,
-0.04989665746688843,
-0.0013544008834287524,
-0.026103496551513672,
0.03150315582752228,
0.033981963992118835,
0.012426672503352165,
-0.01710597053170204,
0.04446715861558914,
0.014997477643191814,
0.017689639702439308,
-0.0000568153518543113,
0.008070188574492931,
0.11385057866573334,
0.03779824078083038,
0.0693456158041954,
-0.023462045937776566,
0.021419670432806015,
-0.03200925514101982,
0.0003694561019074172,
-0.03465423360466957,
0.04082940146327019,
-0.02370539680123329,
0.023287296295166016,
-0.007499140687286854,
0.0569000169634819,
0.06093919277191162,
-0.026759328320622444,
0.031015103682875633,
-0.04137652739882469,
-0.014687025919556618,
0.012384273111820221,
-0.01200818456709385,
0.007782104890793562,
-0.005797953344881535,
-0.0408790148794651,
0.014962921850383282,
0.012689776718616486,
0.0051702880300581455,
-0.024663394317030907,
-0.017221631482243538,
-0.01481157448142767,
0.019456421956419945,
-0.04522332921624184,
0.010552800260484219,
0.03171193599700928,
0.02156529389321804,
-0.04104761779308319,
-0.018429085612297058,
0.05471343174576759,
-0.03059832938015461,
-0.005434134975075722,
0.026251524686813354,
0.01021276880055666,
0.014066335745155811,
0.002730665495619178,
0.00977937038987875,
-0.05719307065010071,
-0.02207602933049202,
0.008839956484735012,
0.029706254601478577,
0.006615892518311739,
0.027018683031201363,
-0.03960804268717766,
0.0006800279952585697,
0.006217561196535826,
0.00684171449393034,
0.009957268834114075,
-0.014328555203974247,
-0.01590489037334919,
-0.018664874136447906,
-0.028709588572382927,
0.015419283881783485,
0.0029387162066996098,
-0.029230089858174324,
0.036172639578580856,
0.02071375772356987,
-0.02511199377477169,
-0.009271804243326187,
0.05084758996963501,
0.051839910447597504,
0.010781408287584782,
-0.012692123651504517,
0.025030212476849556,
0.007635531015694141,
-0.009584316052496433,
-0.0026101740077137947,
0.01673397421836853,
-0.01425615418702364,
0.011912875808775425,
-0.013623814098536968,
-0.026826804503798485,
-0.057022951543331146,
-0.05898258090019226,
0.019362054765224457,
-0.034943703562021255,
-0.003509905654937029,
-0.03347652032971382,
-0.012121970765292645,
0.028131689876317978,
0.03212973475456238,
0.03515588492155075,
-0.0376635305583477,
0.011781773529946804,
0.1076800599694252,
0.010706709697842598,
-0.0344465933740139,
-0.0028852333780378103,
-0.012955992482602596,
0.0025802182499319315,
-0.009334162808954716,
0.016787944361567497,
0.0410025380551815,
0.06749910861253738,
0.03097807615995407,
-0.03465033695101738,
0.03983265161514282,
-0.014237823896110058,
0.0020622245501726866,
0.04933171346783638,
-0.0032387576065957546,
-0.025445589795708656,
0.012579986825585365,
0.014723794534802437,
-0.020346393808722496,
-0.007328295614570379,
-0.026621434837579727,
-0.026498638093471527,
-0.013182779774069786,
0.0172331053763628,
-0.028016896918416023,
-0.011157079599797726,
0.00002143809433619026,
0.03647225350141525,
-0.013343258760869503,
-0.0499691516160965,
-0.04362228140234947,
-0.024334071204066277,
0.01486176811158657,
0.007162321824580431,
-0.025913460180163383,
0.031157830730080605,
0.003700065892189741,
-0.0027471326757222414,
0.0006874245591461658,
0.03303306922316551,
-0.0026243922766298056,
0.010183784179389477,
0.0003335078654345125,
0.0014707781374454498,
0.028371866792440414,
-0.013388780876994133,
0.013413900509476662,
0.06282466650009155,
-0.04800546541810036,
-0.030978446826338768,
0.053143590688705444,
-0.00917008612304926,
0.046666666865348816,
-0.004920835141092539,
-0.01134672574698925,
-0.007603675592690706,
0.004631975200027227,
-0.021686458960175514,
-0.01616349071264267,
-0.033396411687135696,
-0.013676363043487072,
-0.015157878398895264,
0.0037455593701452017,
0.02478848211467266,
0.02593132108449936,
-0.01891728863120079,
-0.016202863305807114,
0.048499368131160736,
-0.01613069884479046,
-0.01647709310054779,
0.056758515536785126,
-0.004796185065060854,
0.014908692799508572,
-0.002402651822194457,
0.008320147171616554,
-0.021565739065408707,
0.01518201269209385,
-0.04682489484548569,
0.028112227097153664,
-0.005925861187279224,
0.008454703725874424,
-0.07833465933799744,
-0.04321630299091339,
0.02413047105073929,
-0.02116619050502777,
0.04911435395479202,
-0.05023351311683655,
0.00040491970139555633,
0.024968814104795456,
-0.10097912698984146,
0.015178953297436237,
-0.025377601385116577,
-0.041352465748786926,
-0.045576248317956924,
0.0005519862752407789,
-0.013360102660953999,
0.05160108208656311,
-0.0002656512660905719,
0.021038198843598366,
0.033572059124708176,
0.05612469092011452,
-0.015274874866008759,
-0.023802202194929123,
-0.03992690145969391,
0.006446614395827055,
-0.008764391764998436,
-0.08728593587875366,
0.019152598455548286,
-0.029568683356046677,
-0.011151835322380066,
0.02819470688700676,
0.013873323798179626,
0.0032060344237834215,
-0.033164817839860916,
0.016254516318440437,
0.005682865157723427,
0.01740320399403572,
0.03188985586166382,
-0.01134311594069004,
-0.01965133473277092,
0.010561840608716011,
0.0008707143133506179,
0.035236015915870667,
-0.00021152164845261723,
-0.02319137379527092,
0.0136070866137743,
-0.017614370211958885,
-0.058299679309129715,
0.0011173783568665385,
-0.024906134232878685,
-0.03212062269449234,
0.033679842948913574,
0.010795668698847294,
-0.009627871215343475,
-0.04594426602125168,
0.027632342651486397,
-0.023744218051433563,
0.024673055857419968,
0.002264728071168065,
0.022163718938827515,
-0.045814428478479385,
0.03240484744310379,
0.00037067930679768324,
-0.02381790429353714,
0.020456161350011826,
-0.00045630650129169226,
-0.03129754215478897,
-0.06701387465000153,
-0.026895105838775635,
-0.050864264369010925,
0.006702388636767864,
-0.005638364236801863,
-0.01333028357475996,
-0.04834160581231117,
0.04580054432153702,
-0.018139714375138283,
0.0062926593236625195,
-0.03913769870996475,
-0.02824571542441845,
0.013884447515010834,
-0.07550756633281708,
0.07456839829683304,
0.014051505364477634,
0.02321094460785389,
-0.0050786458887159824,
-0.008694246411323547,
-0.04571971669793129,
-0.014175843447446823,
0.06760163605213165,
0.016984470188617706,
0.0008230226812884212,
-0.006099140737205744,
0.0348823107779026,
-0.009752778336405754,
-0.05489838123321533,
0.017359059303998947,
-0.024481121450662613,
-0.005699628498405218,
0.0017448124708607793,
-0.04505251348018646,
0.015796223655343056,
-0.033455610275268555,
0.03298862650990486,
-0.014860371127724648,
-0.01735912449657917,
0.007286387495696545,
-0.025190256536006927,
0.044791027903556824,
0.01018216647207737,
-0.020998215302824974,
0.02992848865687847,
-0.0027047614566981792,
0.005397499538958073,
0.006314356345683336,
-0.003397864755243063,
-0.05992581695318222,
0.03351733833551407,
0.004661449231207371,
0.0044696396216750145,
-0.04444913938641548,
0.026102568954229355,
-0.013188169337809086,
-0.01929427497088909,
-0.03378669545054436,
0.04539533331990242,
-0.03323571756482124,
-0.01759062521159649,
0.050640810281038284,
0.03522725775837898,
0.004671207629144192,
-0.0049540321342647076,
-0.013457329012453556,
-0.026010403409600258,
-0.016892611980438232,
0.020144987851381302,
0.033173564821481705,
0.03148631751537323,
0.010289480909705162,
0.04662863165140152,
0.013064468279480934,
0.0029453642200678587,
0.026115067303180695,
-0.006083773914724588,
0.024933164939284325,
-0.01074987929314375,
-0.031118119135499,
-0.007554200943559408,
-0.0074151852168142796,
0.06405331939458847,
0.01199523825198412,
0.0026796956080943346,
0.0729871615767479,
-0.017343206331133842,
0.008533895015716553,
-0.05906576290726662,
-0.011636411771178246,
-0.01610548608005047,
-0.04767998680472374,
0.02335203066468239,
0.02478456310927868,
-0.014598097652196884,
-0.03499652072787285,
-0.010028643533587456,
0.0463702566921711,
-0.011564390733838081,
-0.015329722315073013,
0.06302709877490997,
-0.012881292030215263,
0.0235245693475008,
-0.039614688605070114,
0.0007002415950410068,
-0.025750573724508286,
0.024996811524033546,
0.017577070742845535,
0.0485309362411499,
0.06838563829660416,
0.03215828910470009,
-0.03188594803214073,
-0.015422925353050232,
0.022155893966555595,
-0.061631668359041214,
-0.03209344670176506,
-0.02619343437254429,
0.041759319603443146,
-0.011892909184098244,
-0.016699617728590965
] |
<p>Is there a certain frequency of sound/noise that will cause gunpowder to explode?</p>
| 10,781 |
[
-0.04624983295798302,
-0.038628362119197845,
0.003674157429486513,
-0.02884034439921379,
0.05074745789170265,
-0.011588565073907375,
-0.013746321201324463,
-0.025511668995022774,
0.033113688230514526,
-0.03606142848730087,
0.014378017745912075,
0.06888989359140396,
0.04438856616616249,
0.025229481980204582,
-0.003914372064173222,
-0.013740930706262589,
-0.019234109669923782,
-0.009175127372145653,
-0.01654079370200634,
-0.028162717819213867,
-0.028135066851973534,
0.005560032092034817,
-0.009685337543487549,
-0.002518425229936838,
-0.01738044060766697,
0.031417641788721085,
0.06639043986797333,
0.016755882650613785,
0.03447059169411659,
0.021273180842399597,
0.016897112131118774,
-0.029603740200400352,
0.00976987648755312,
0.045104701071977615,
0.06217937916517258,
0.006369353272020817,
-0.007277575321495533,
-0.021488690748810768,
-0.029899269342422485,
-0.004027794115245342,
-0.02336079813539982,
-0.027544386684894562,
0.03807517886161804,
0.024579275399446487,
-0.04496749863028526,
0.009761421009898186,
-0.0353606715798378,
-0.08178012818098068,
0.044604506343603134,
-0.07116222381591797,
0.07727032154798508,
0.00787778478115797,
0.010731455869972706,
0.026823222637176514,
0.006569644436240196,
0.009793574921786785,
0.0811459943652153,
0.07368343323469162,
-0.040926434099674225,
-0.03514312952756882,
-0.00679598655551672,
-0.008983799256384373,
-0.01928963139653206,
-0.02765849605202675,
-0.040023259818553925,
0.06191070377826691,
-0.004517636727541685,
-0.0398239865899086,
0.022064482793211937,
0.017837315797805786,
-0.028849350288510323,
-0.029061945155262947,
0.043466925621032715,
-0.022126944735646248,
-0.02467222884297371,
-0.02992515079677105,
0.042630407959222794,
0.015207831747829914,
0.006842972245067358,
0.061223581433296204,
-0.03402647376060486,
-0.0212613083422184,
0.01040744036436081,
-0.009567655622959137,
0.04960225522518158,
-0.026768043637275696,
0.06884177029132843,
-0.0037323320284485817,
0.010271118022501469,
0.015318299643695354,
-0.028203988447785378,
0.012780727818608284,
0.03040459007024765,
0.002817604225128889,
-0.030737727880477905,
0.03057149425148964,
0.005829229019582272,
0.057979073375463486,
0.025795316323637962,
-0.06916898488998413,
0.04218178614974022,
0.004375481978058815,
0.03996497765183449,
0.06509429961442947,
-0.01325844507664442,
-0.04166393354535103,
-0.036485232412815094,
0.020283401012420654,
-0.029478108510375023,
-0.004744363948702812,
-0.04153672978281975,
0.0156012661755085,
-0.024471763521432877,
-0.03711705654859543,
-0.004971636924892664,
0.01465859729796648,
0.0058005014434456825,
-0.014881192706525326,
0.020647669211030006,
0.03514045476913452,
0.04015982896089554,
-0.006120729260146618,
0.04718984663486481,
-0.014097277075052261,
-0.023335091769695282,
-0.006748071406036615,
-0.01824987307190895,
-0.023069173097610474,
-0.0030492725782096386,
0.04154914990067482,
0.017608150839805603,
-0.036357615143060684,
0.017203975468873978,
-0.0038763585034757853,
0.014814610593020916,
-0.036394063383340836,
-0.0873291864991188,
-0.07354732602834702,
0.04215455427765846,
-0.030520176514983177,
0.0008453134796582162,
-0.07652074843645096,
-0.003166030626744032,
-0.006112678907811642,
-0.011650395579636097,
-0.006814579479396343,
-0.01983896642923355,
-0.015692465007305145,
0.02336704730987549,
0.021999146789312363,
-0.003069512080401182,
-0.013693545013666153,
-0.009243099950253963,
-0.01911425217986107,
0.027945538982748985,
-0.05007714033126831,
0.041725028306245804,
0.01027077715843916,
0.014323712326586246,
-0.028737008571624756,
0.0029174238443374634,
-0.02920784428715706,
-0.03921891748905182,
0.030120667070150375,
0.03212719038128853,
-0.03322633355855942,
0.04829297587275505,
0.04482150822877884,
-0.03974582254886627,
0.040761519223451614,
0.034345775842666626,
0.0066774701699614525,
0.03401035815477371,
0.004038577433675528,
0.03021598979830742,
-0.05922331288456917,
-0.023382171988487244,
-0.0494900681078434,
0.04722227901220322,
0.005184326786547899,
-0.032088372856378555,
-0.01053270511329174,
-0.0032711017411202192,
-0.0006220185896381736,
0.021265016868710518,
0.03808191791176796,
0.01253077294677496,
0.008944057859480381,
0.0034759382251650095,
-0.026953211054205894,
0.01735513098537922,
-0.056400101631879807,
0.0732344388961792,
-0.0001722463930491358,
-0.021560944616794586,
0.001431433716788888,
-0.016504401341080666,
0.050893522799015045,
-0.05761678144335747,
0.016874616965651512,
0.015840820968151093,
0.04091239348053932,
0.002425693441182375,
-0.025717804208397865,
-0.00124825828243047,
0.053717710077762604,
-0.022140812128782272,
0.0021258636843413115,
0.08510726690292358,
-0.01571076363325119,
-0.037238709628582,
-0.013607612811028957,
-0.00792856328189373,
0.01042176317423582,
-0.029753224924206734,
0.0007033412693999708,
0.049776867032051086,
-0.006476994138211012,
0.005851084366440773,
0.00811158400028944,
-0.02858545072376728,
0.06614162772893906,
0.014752589166164398,
-0.011186697520315647,
-0.007796693127602339,
0.024959547445178032,
0.03926149010658264,
0.0018349565798416734,
0.019668733701109886,
-0.04258070886135101,
-0.05854363366961479,
0.0071556768380105495,
0.039891019463539124,
0.009024042636156082,
-0.022900966927409172,
0.03808071091771126,
0.041477497667074203,
0.037385452538728714,
0.03651231527328491,
0.04741291701793671,
-0.009681609459221363,
-0.027462873607873917,
-0.010262089781463146,
0.009628750383853912,
-0.015100902877748013,
0.018751496449112892,
0.02503725327551365,
0.03489141911268234,
0.002489932347089052,
-0.03901694715023041,
-0.01666792668402195,
0.02705897018313408,
-0.0036517600528895855,
0.0029147479217499495,
0.014460539445281029,
-0.04815094918012619,
0.001076333224773407,
-0.02145937830209732,
0.03703420236706734,
-0.015330757014453411,
0.02334924042224884,
-0.003695039078593254,
0.005669259931892157,
-0.012074151076376438,
-0.006319605279713869,
-0.005627348553389311,
-0.02201761119067669,
-0.0045903087593615055,
0.050431493669748306,
-0.05779418721795082,
-0.010101188905537128,
0.011156235821545124,
0.026337983086705208,
0.020343001931905746,
-0.0024113175459206104,
0.04194331541657448,
0.025129370391368866,
0.04136407747864723,
-0.02048211358487606,
-0.051003970205783844,
0.005425877869129181,
-0.04833889752626419,
-0.029650000855326653,
-0.01490398496389389,
-0.0003084685595240444,
-0.00446655647829175,
0.009706944227218628,
-0.04049468785524368,
0.02394185960292816,
-0.03729604184627533,
0.014741725288331509,
0.06957118213176727,
-0.0542273074388504,
-0.043252769857645035,
0.009663736447691917,
-0.049958355724811554,
0.005285701714456081,
-0.027006616815924644,
0.00225361087359488,
0.0341680645942688,
0.0013301772996783257,
-0.015940405428409576,
0.015276670455932617,
0.008292289450764656,
-0.00813435297459364,
-0.02629372477531433,
-0.021760065108537674,
0.03931846097111702,
0.00397114222869277,
0.010148153640329838,
0.01986422762274742,
-0.047589126974344254,
0.007669676560908556,
-0.025600891560316086,
-0.030084246769547462,
0.02374812588095665,
0.020074564963579178,
0.06097263842821121,
-0.017824461683630943,
-0.03500834479928017,
0.053800616413354874,
0.03456084057688713,
-0.024875398725271225,
-0.012988206930458546,
-0.05036645010113716,
0.00010455819574417546,
-0.04431989789009094,
0.016306938603520393,
0.029048291966319084,
0.008172386325895786,
0.024404184892773628,
0.020925190299749374,
-0.00835371483117342,
0.03603657707571983,
-0.007551365997642279,
0.019521046429872513,
0.010901244357228279,
0.01099795289337635,
0.02944333106279373,
-0.009072922170162201,
0.017938517034053802,
-0.03245244920253754,
0.03399849310517311,
-0.006145987659692764,
0.03387921676039696,
0.02468184567987919,
-0.01505246851593256,
0.018611976876854897,
0.013726914301514626,
-0.0196850523352623,
-0.039545293897390366,
0.038831453770399094,
-0.019029855728149414,
-0.0038821487687528133,
-0.013953502289950848,
0.014556041918694973,
0.04723299294710159,
0.0028445664793252945,
0.018317675217986107,
0.002612315583974123,
0.03541328012943268,
-0.019059566780924797,
-0.01333148404955864,
0.01999814249575138,
0.012265713885426521,
0.008129298686981201,
0.004189752507954836,
0.0266555342823267,
0.02679290436208248,
-0.01458232756704092,
0.04927075281739235,
0.009965501725673676,
-0.019957395270466805,
0.0558457151055336,
-0.05165392905473709,
0.0033121320884674788,
-0.026132211089134216,
0.004765529651194811,
-0.00955593679100275,
0.09817592054605484,
0.020301809534430504,
0.010528967715799809,
0.02755003422498703,
0.005795611999928951,
-0.10178717970848083,
0.027196072041988373,
-0.03686772659420967,
-0.03261047601699829,
-0.03329500928521156,
-0.021445773541927338,
-0.06540519744157791,
0.015512758865952492,
-0.040882740169763565,
-0.02414064109325409,
-0.0045392271131277084,
-0.07114623486995697,
0.029327163472771645,
-0.010410192422568798,
-0.0242846067994833,
0.021608462557196617,
0.05284373462200165,
0.015367806889116764,
0.030453165993094444,
0.033140525221824646,
0.0064327893778681755,
-0.01064696442335844,
0.02812276966869831,
-0.00043705577263608575,
0.007846410386264324,
-0.012827279046177864,
0.05867095664143562,
-0.0282947588711977,
0.008577760308980942,
0.021793371066451073,
0.012242370285093784,
0.006354154087603092,
0.05094252526760101,
0.032854530960321426,
0.004898791201412678,
-0.06428997963666916,
-0.04583042860031128,
0.016580868512392044,
0.03189157694578171,
0.03619269281625748,
-0.03550881892442703,
0.004788876976817846,
0.014517239294946194,
-0.014894302934408188,
-0.012791115790605545,
0.04918992891907692,
0.023990072309970856,
0.027325360104441643,
-0.004950849339365959,
-0.005315048154443502,
-0.003459526225924492,
-0.00695091113448143,
0.011168132536113262,
-0.02772950381040573,
0.008083948865532875,
-0.03358441963791847,
0.02410847507417202,
0.014336306601762772,
-0.0016365923220291734,
-0.0042825499549508095,
0.04759746417403221,
0.017800377681851387,
0.007708478253334761,
-0.016858084127306938,
0.012826322577893734,
0.006603563670068979,
-0.006851161364465952,
0.05422541871666908,
-0.01581045240163803,
-0.05314316228032112,
-0.0738627165555954,
0.002414760645478964,
0.06004052236676216,
0.019678663462400436,
-0.023771239444613457,
0.0226594191044569,
-0.06271211057901382,
-0.046626657247543335,
0.034634362906217575,
0.013697843067348003,
-0.02345658279955387,
-0.009706725366413593,
0.012025418691337109,
-0.004547851625829935,
-0.02882317453622818,
-0.020531246438622475,
0.012988442555069923,
0.031179262325167656,
-0.011799410916864872,
-0.016934795305132866,
-0.026903124526143074,
0.00028360661235637963,
0.02400640770792961,
0.05606525391340256,
0.028132786974310875,
0.00683109974488616,
-0.007419758941978216,
-0.023928353562951088,
0.0035202433355152607,
0.014890279620885849,
-0.05270354449748993,
0.014914101921021938,
-0.016990862786769867,
0.0042658173479139805,
0.03347129374742508,
-0.020291415974497795,
-0.03943256661295891,
0.022214379161596298,
0.0249661672860384,
0.007832934148609638,
0.004423057660460472,
-0.020422538742423058,
0.02616749331355095,
0.015973873436450958,
0.0014508635504171252,
0.016496503725647926,
0.027163129299879074,
-0.007967585697770119,
0.014297889545559883,
-0.005143114365637302,
0.03909052535891533,
-0.05702022835612297,
0.009398882277309895,
-0.010339430533349514,
0.033710774034261703,
-0.04167970269918442,
0.029631508514285088,
-0.006284850649535656,
0.011758808977901936,
0.013916109688580036,
-0.005225346889346838,
-0.00621999753639102,
0.03331325948238373,
0.026307201012969017,
0.01596476323902607,
-0.003258408047258854,
0.0327913798391819,
-0.03450031951069832,
0.028971312567591667,
-0.003294752910733223,
-0.0019074241863563657,
0.024025190621614456,
0.014304816722869873,
-0.029153496026992798,
0.014283068478107452,
-0.02633923850953579,
-0.0040755788795650005,
0.028793450444936752,
-0.03412683308124542,
0.10976676642894745,
-0.007608890533447266,
-0.02014683559536934,
0.038454778492450714,
-0.04574129730463028,
-0.02093593031167984,
0.021513283252716064,
0.009140120819211006,
0.10079300403594971,
-0.06356681138277054,
0.05208832770586014,
-0.040878258645534515,
0.010563802905380726,
-0.046014636754989624,
-0.035256266593933105,
0.07329476624727249,
0.02695702761411667,
-0.008053380995988846,
-0.04033671319484711,
0.006075368262827396,
-0.015000684186816216,
-0.011886052787303925,
0.021590258926153183,
0.026880918070673943,
-0.008629086427390575,
0.004440426826477051,
0.022920729592442513,
-0.03463713824748993,
0.04549897089600563,
0.05341435223817825,
-0.0060646384954452515,
0.03560512885451317,
-0.011144225485622883,
-0.0019444169010967016,
-0.034875765442848206,
0.050253938883543015,
-0.01919362135231495,
-0.0020402302034199238,
-0.019983438774943352,
-0.01922166347503662,
0.025062553584575653,
-0.052473168820142746,
0.000047378416638821363,
0.014855493791401386,
0.040657781064510345,
0.004979595076292753,
-0.020021973177790642,
0.0348510816693306,
0.029452914372086525,
0.011097537353634834,
-0.04477696120738983,
-0.011696376837790012,
-0.04304863139986992,
-0.01857275888323784,
-0.007528058718889952,
0.025144150480628014,
0.035885751247406006,
-0.002337692305445671,
0.057234253734350204,
-0.00042333416058681905,
-0.021479278802871704,
-0.006345799658447504,
-0.008921464905142784,
0.05053786560893059,
-0.03169525787234306,
-0.01674722507596016,
0.015645945444703102,
0.009407560341060162,
-0.010908816009759903,
-0.03680003061890602,
-0.016030754894018173,
-0.022272776812314987,
0.04844494163990021,
-0.0502709299325943,
0.025798873975872993,
0.021025096997618675,
0.012806524522602558,
-0.012643139809370041,
-0.028362911194562912,
0.001581351039931178,
0.016842611134052277,
-0.019588379189372063,
-0.020485689863562584,
-0.008627736940979958,
0.04035814478993416,
0.00021652337454725057,
0.035276491194963455,
0.030730314552783966,
0.013068781234323978,
0.04659362509846687,
0.02729436568915844,
0.006804215721786022,
-0.01933284103870392,
-0.05166652798652649,
0.037414759397506714,
-0.05645649507641792,
0.037351094186306,
0.012006021104753017,
-0.0031441564206033945,
0.02362958714365959,
0.032298583537340164,
-0.025805700570344925,
-0.01464693620800972,
0.0014447266003116965,
-0.018855681642889977,
0.01664123870432377,
0.016732705757021904,
-0.019279763102531433,
0.023551074787974358,
0.0020358203910291195,
0.012928715907037258,
0.002615466946735978,
0.00798034481704235,
-0.01060436014086008,
-0.05407200753688812,
-0.00462531391531229,
-0.0014949075412005186,
-0.04165564104914665,
0.026691894978284836,
-0.025378979742527008,
-0.04087774083018303,
0.053164344280958176,
-0.02511204034090042,
0.032352570444345474,
0.004126618150621653,
0.03452766314148903,
-0.002559176879003644,
0.08454745262861252,
0.006208707578480244,
-0.013111320324242115,
-0.029270922765135765,
0.02290068380534649,
0.13209113478660583,
0.02460360899567604,
0.03670879825949669,
-0.026439284905791283,
-0.0033072293736040592,
-0.023453643545508385,
0.007128819823265076,
-0.01653531938791275,
-0.02298128418624401,
-0.0017902592662721872,
0.00783857237547636,
0.018091244623064995,
0.10310514271259308,
0.0049293553456664085,
0.011962410062551498,
0.0420597605407238,
-0.004195460118353367,
-0.03205171227455139,
0.007102865260094404,
0.0301139485090971,
0.008409935049712658,
0.02376500517129898,
-0.017074720934033394,
0.008401029743254185,
-0.05641815438866615,
-0.02480667270720005,
-0.021934621036052704,
-0.04559541121125221,
0.01970350369811058,
0.003682315582409501,
-0.05566868931055069,
-0.013049661181867123,
0.02384812943637371,
-0.03912820667028427,
-0.03328801319003105,
0.034397732466459274,
0.014255613088607788,
0.0014227930223569274,
-0.027273833751678467,
-0.0016255140071734786,
0.03190694749355316,
-0.00434287590906024,
-0.013489749282598495,
-0.0028447972144931555,
-0.036342550069093704,
0.007550040725618601,
-0.009214113466441631,
-0.010157749988138676,
0.01651923358440399,
-0.011159202083945274,
-0.010019064880907536,
0.0014558077091351151,
0.013536985032260418,
-0.040391214191913605,
-0.06502583622932434,
0.009726596996188164,
0.03313352167606354,
-0.017458925023674965,
-0.03788311034440994,
-0.06008027866482735,
-0.001323070377111435,
-0.03388753533363342,
-0.002629326656460762,
-0.0006056378479115665,
0.006745236925780773,
-0.01114032231271267,
-0.013765158131718636,
0.046133626252412796,
0.004226584918797016,
-0.026133432984352112,
0.00884980894625187,
-0.027983440086245537,
-0.04566125199198723,
-0.04224748536944389,
-0.010914474725723267,
0.046807654201984406,
0.03672318533062935,
0.02586180530488491,
-0.012611934915184975,
-0.021905848756432533,
-0.06675858795642853,
0.039229147136211395,
0.010656537488102913,
0.004606302827596664,
-0.04047883301973343,
-0.03964492306113243,
0.017065607011318207,
0.027349140495061874,
-0.03256521746516228,
0.03308335691690445,
-0.04549264907836914,
0.0356038473546505,
0.060937847942113876,
-0.020694227889180183,
-0.007762576919049025,
-0.001328450394794345,
-0.0016011155676096678,
0.011245491914451122,
0.0032163767609745264,
0.0529327318072319,
0.0010608641896396875,
0.00013499554188456386,
0.0504002720117569,
-0.016023904085159302,
-0.03190009295940399,
-0.021532924845814705,
-0.013790810480713844,
-0.0164765827357769,
-0.028773266822099686,
0.039321403950452805,
0.0444723479449749,
-0.01882391981780529,
-0.052057474851608276,
-0.0467543751001358,
0.00814735796302557,
-0.008369400165975094,
0.04637812077999115,
0.0005204891203902662,
0.022118516266345978,
-0.016229329630732536,
0.00976647436618805,
-0.023643694818019867,
-0.007123177405446768,
-0.0033780771773308516,
-0.01890217326581478,
0.0005861568497493863,
-0.028848795220255852,
-0.0021418065298348665,
-0.0005901891272515059,
-0.02783442847430706,
-0.010518833063542843,
-0.003661294002085924,
-0.0023586733732372522,
-0.006283424329012632,
-0.004581728018820286,
-0.0047265528701245785,
-0.0064115505665540695,
0.06171709671616554,
-0.024306965991854668,
-0.06461077928543091,
0.04757862165570259,
-0.05691412836313248,
-0.08334793895483017,
0.03791935741901398,
-0.023618416860699654,
0.0324946753680706,
0.04216884821653366,
0.005397597327828407,
0.024990474805235863,
0.08601760119199753,
0.004554207436740398,
0.021279623731970787,
0.020156236365437508,
0.03348422423005104,
0.026232704520225525,
0.03409565985202789,
0.002309816423803568,
-0.0011300267651677132,
-0.0031908047385513783,
0.05187206342816353,
0.030138954520225525,
0.013834115117788315,
0.031004274263978004,
0.0587339848279953,
-0.0559081993997097,
0.03948930278420448,
0.010237484239041805,
0.01832314394414425,
0.018296735361218452,
-0.005167809780687094,
0.0031440004240721464,
-0.004482214339077473,
0.02444184385240078,
-0.017821643501520157,
-0.1295487880706787,
0.0007575987256132066,
-0.00498227821663022,
-0.013632265850901604,
0.010228751227259636,
-0.03743075206875801,
0.006141099613159895,
0.02755456231534481,
-0.07510297000408173,
-0.028162190690636635,
-0.006737746298313141,
-0.0542459674179554,
-0.046591855585575104,
-0.02187350206077099,
0.008237877860665321,
0.016800623387098312,
0.010102558881044388,
0.01566830649971962,
0.013506517745554447,
0.029383396729826927,
-0.04479781165719032,
0.007259005680680275,
0.05055929347872734,
-0.007273206487298012,
0.039499688893556595,
-0.009089027531445026,
0.06990782916545868,
-0.04969796538352966,
-0.0004591050383169204,
-0.007849414832890034,
-0.009507563896477222,
0.011629456654191017,
0.0036441527772694826,
0.022247496992349625,
0.019485455006361008,
0.03882253170013428,
-0.006708880420774221,
-0.014738562516868114,
-0.0012837458634749055,
0.06059356778860092,
-0.0086217587813735,
0.024001648649573326,
-0.05739353224635124,
0.012796998955309391,
-0.007140754256397486,
-0.035843051970005035,
-0.01953836902976036,
-0.009876142255961895,
-0.03761432319879532,
-0.024159563705325127,
0.007841410115361214,
0.008209091611206532,
0.0012723555555567145,
-0.028740009292960167,
-0.000939072750043124,
-0.013771549798548222,
-0.006802225019782782,
0.014989743940532207,
0.0503869466483593,
-0.013904149644076824,
0.020205602049827576,
0.00679774908348918,
-0.044825442135334015,
-0.015215196646749973,
0.016055719926953316,
-0.048165012151002884,
-0.05968707799911499,
0.003909400198608637,
0.004871598444879055,
0.03943847119808197,
0.013049213215708733,
-0.002835068618878722,
-0.0040594469755887985,
0.06005511432886124,
0.002088273176923394,
0.004183734767138958,
-0.008144363760948181,
-0.037624698132276535,
-0.04455230385065079,
-0.034600913524627686,
0.0229591503739357,
0.009778684005141258,
0.0018838215619325638,
-0.05895034968852997,
-0.06173665076494217,
0.01602163538336754,
-0.007139578927308321,
0.057901542633771896,
-0.02225198596715927,
-0.038479167968034744,
0.029147859662771225,
-0.0200324896723032,
-0.011335015296936035,
-0.04450808838009834,
0.019958598539233208,
-0.002174417255446315,
-0.0054569789208471775,
-0.03962871432304382,
-0.01978495344519615,
-0.03544072434306145,
-0.008546316996216774,
0.007888702675700188,
0.013397714123129845,
-0.003787825582548976,
-0.008721213787794113,
-0.006313141901046038,
0.047569356858730316,
0.045254431664943695,
-0.011356234550476074,
0.04849611967802048,
-0.01378332357853651,
-0.03197568655014038,
-0.0008521871059201658,
-0.006621968932449818,
-0.06535528600215912,
0.02921963669359684,
0.0006588110118173063,
0.010232580825686455,
0.01651599258184433,
-0.00528309540823102,
-0.014903716742992401,
-0.017023157328367233,
0.0039768218994140625,
0.054847534745931625,
-0.02343365177512169,
-0.023054223507642746,
0.04418989270925522,
0.012340008281171322,
0.04326242208480835,
-0.02675832062959671,
0.013618280179798603,
0.021513165906071663,
0.0069872173480689526,
-0.014642407186329365,
0.02348327822983265,
-0.007088052574545145,
-0.030715707689523697,
-0.013134722597897053,
0.019684728235006332,
-0.035117313265800476,
-0.014267505146563053,
0.05306205898523331,
0.01432032324373722,
-0.0439613051712513,
-0.03382924571633339,
0.019237397238612175,
-0.04549796134233475,
0.006940727587789297,
0.018829919397830963,
-0.04206496477127075,
0.07173559814691544,
0.004632464610040188,
0.01483190804719925,
-0.03733041509985924,
0.02873968705534935,
-0.016114884987473488,
0.006193618755787611,
-0.013037501834332943,
-0.009633521549403667,
-0.046203628182411194,
0.007307879161089659,
0.000721332267858088,
0.009850635193288326,
0.04642069339752197,
-0.07616012543439865,
-0.011393466033041477,
-0.010876381769776344,
0.0017131129279732704,
-0.050765860825777054,
0.013337201438844204,
-0.0447421669960022,
-0.017307497560977936,
0.028110072016716003,
0.027316661551594734,
-0.0007549708825536072,
0.011360608972609043,
-0.02658323384821415,
-0.03598702326416969,
0.015262989327311516,
-0.026611855253577232,
0.021700015291571617,
-0.016127098351716995,
0.032768614590168,
-0.029381683096289635,
0.013917210511863232
] |
<p>I’ve been studying electricity lately and it has been quite hard to understand the terminology, and picturing it in my mind. After struggling to understand what each property of electric currents meant, I found an analogy that related electric current to water flow. I am not sure if this analogy is 100% accurate, but it sure has helped me understand the complex (at least for young, starter scientist like me) topic of electricity. This far I have managed to relate in the analogy that:</p>
<p>-----Electricity-------------------------Water------------</p>
<p>Current (Amps)(A)-------Flow rate (Volume/Time)</p>
<p>Resistance (Ohms)(Ω)----pipe size (Inches)</p>
<p>Voltage (Volts)(V)------Water pressure (psi)</p>
<p>But I am still missing properties like charge. What properties am I missing? How could it be related to water flow? If it can’t be related, can you please give me a short definition and explanation to better grasp the concept? Please include units in both sides of the analogy. Also, please keep the answer short and simple for us, the inexpert scientist (including me) that struggle to grasp the concept.</p>
<p><strong>Thanks a bunch for your expert help</strong></p>
<p>It is kind of discussed in these articles:</p>
<p><a href="http://physics.stackexchange.com/questions/10373/flow-of-water-and-flow-of-electrons-how-this-analogy-works">Flow of water and flow of electrons, how this analogy works?</a></p>
<p><a href="http://physics.stackexchange.com/questions/66629/power-in-hydraulic-analogy">Power in hydraulic analogy</a></p>
<p>But I couldn’t find (or understand) the answer provided in them.</p>
| 10,782 |
[
-0.0052308449521660805,
-0.004087366163730621,
0.01771547645330429,
-0.01305364165455103,
0.027232971042394638,
-0.014516104012727737,
0.005591364577412605,
-0.008976510725915432,
0.03612309694290161,
0.0004711463989224285,
0.043598074465990067,
0.018938429653644562,
0.057808540761470795,
0.00030607098597101867,
0.012478199787437916,
0.023538341745734215,
0.024538367986679077,
-0.017379865050315857,
0.021815525367856026,
-0.03344479203224182,
0.011952918022871017,
0.0027003311552107334,
0.006500639487057924,
0.04479833319783211,
-0.014792718924582005,
0.07542156428098679,
0.03653644025325775,
-0.02274421416223049,
-0.011508173309266567,
0.022625485435128212,
0.013707347214221954,
-0.05318668112158775,
0.01867774687707424,
0.018360065296292305,
0.008231994695961475,
0.008044416084885597,
-0.05874840170145035,
-0.03153296932578087,
0.004224093165248632,
0.034347716718912125,
-0.0009658750495873392,
0.0028657354414463043,
0.026389531791210175,
0.016203908249735832,
-0.0638926774263382,
0.01345143560320139,
0.006353302393108606,
-0.05268656089901924,
-0.0020309360697865486,
-0.04254060611128807,
0.036318711936473846,
0.026622142642736435,
0.06968817859888077,
0.02900918759405613,
0.02755027264356613,
-0.01196904294192791,
0.08328928798437119,
0.06905495375394821,
-0.029677938669919968,
-0.06689251959323883,
-0.0041273548267781734,
0.008634965866804123,
-0.02219957299530506,
-0.046344608068466187,
-0.0140604292973876,
0.011184760369360447,
-0.015223673544824123,
-0.013184905983507633,
-0.017061660066246986,
0.018650900572538376,
0.041405558586120605,
0.011572865769267082,
0.020803380757570267,
0.005632557440549135,
0.01818207837641239,
-0.021838940680027008,
-0.00899595022201538,
-0.004972864408046007,
0.032091643661260605,
0.05619560927152634,
-0.03610141947865486,
0.006029181182384491,
0.022541888058185577,
0.031131619587540627,
0.023777777329087257,
-0.055519137531518936,
0.050620198249816895,
-0.02540217898786068,
0.011088686063885689,
-0.015974778681993484,
-0.021859653294086456,
0.03001725673675537,
-0.011086746118962765,
0.008500723168253899,
-0.00857329461723566,
-0.0056370338425040245,
-0.030562028288841248,
0.028419634327292442,
0.038740623742341995,
0.022756459191441536,
0.012343521229922771,
-0.03471880406141281,
0.052335962653160095,
0.07424817979335785,
0.013710934668779373,
-0.04200737550854683,
0.00484020309522748,
0.0042649246752262115,
-0.03693043813109398,
0.002049764385446906,
-0.043316300958395004,
0.03498109430074692,
0.05240095406770706,
0.02525622583925724,
-0.02153940126299858,
-0.010226481594145298,
0.030177457258105278,
-0.013988635502755642,
0.04651512950658798,
0.013416483998298645,
0.019451651722192764,
-0.044291164726018906,
0.020143568515777588,
-0.019414134323596954,
-0.07210081070661545,
0.030676115304231644,
-0.022241786122322083,
-0.008044580928981304,
-0.033851686865091324,
0.039400603622198105,
-0.01976030506193638,
-0.007589178625494242,
0.013855322264134884,
0.009489919990301132,
0.07114554196596146,
-0.008331656455993652,
-0.10596511512994766,
-0.05452396720647812,
0.016171589493751526,
0.01682589016854763,
-0.04721469804644585,
-0.09395065903663635,
0.03059048391878605,
0.019389230757951736,
0.037187814712524414,
-0.024725794792175293,
-0.028048044070601463,
-0.0147800138220191,
0.006302631925791502,
0.031143082305788994,
0.005180560052394867,
0.03249942511320114,
0.02186969481408596,
0.0029267340432852507,
0.025589950382709503,
-0.021752968430519104,
0.00904510822147131,
0.0052013336680829525,
0.0033373082987964153,
-0.01031352486461401,
0.03873840719461441,
0.002230099868029356,
-0.00297211273573339,
0.005929021630436182,
-0.0043998840264976025,
-0.026509331539273262,
0.06397722661495209,
-0.012568238191306591,
0.00014259199087973684,
0.037291187793016434,
0.0004984315601177514,
-0.004878877196460962,
0.01383507251739502,
-0.001820737379603088,
0.04071876034140587,
-0.025840789079666138,
-0.030490266159176826,
-0.05472134053707123,
-0.012195182964205742,
0.02454475313425064,
-0.03821112588047981,
-0.07161299884319305,
-0.017369424924254417,
0.026640987023711205,
0.024782221764326096,
0.026675337925553322,
0.027970587834715843,
-0.013906536623835564,
-0.021945210173726082,
-0.015393005684018135,
-0.03635985776782036,
-0.04969557747244835,
0.0385625958442688,
-0.026464194059371948,
-0.0008034040802158415,
0.023232651874423027,
-0.04141226410865784,
-0.016673624515533447,
-0.03147413954138756,
0.009760566055774689,
0.018388770520687103,
0.02148890309035778,
-0.0004570458841044456,
-0.026049552485346794,
0.008985732682049274,
0.04347087815403938,
0.04198332875967026,
-0.0024987736251205206,
-0.004253638442605734,
0.014759394340217113,
0.006966735236346722,
-0.027962088584899902,
-0.0371687076985836,
0.04850136861205101,
0.011552582494914532,
0.0003953625855501741,
0.020681068301200867,
-0.007309457287192345,
0.021635906770825386,
0.03611963242292404,
-0.027506016194820404,
0.05085287615656853,
0.05772921070456505,
-0.010993490926921368,
0.0011340263299643993,
0.023321086540818214,
-0.013558952137827873,
-0.0024649156257510185,
-0.01601896807551384,
0.00990307331085205,
-0.03950569033622742,
0.0408238023519516,
0.0411728136241436,
0.01940900646150112,
-0.005156368017196655,
-0.0028355445247143507,
-0.0009972831467166543,
0.027911921963095665,
0.03385213389992714,
-0.00539126992225647,
-0.02122248150408268,
-0.010118234902620316,
-0.0003008735366165638,
0.02790127880871296,
-0.005343408789485693,
0.02605639211833477,
0.004540059249848127,
0.01701446995139122,
0.03244723379611969,
-0.03249426558613777,
0.009922279976308346,
0.044822778552770615,
0.008014120161533356,
0.03234132006764412,
-0.0010526631958782673,
-0.033893242478370667,
0.03664706274867058,
-0.03782756254076958,
-0.021818123757839203,
0.025399936363101006,
0.0051544439047575,
0.027646800503134727,
-0.06036555394530296,
-0.0031413636170327663,
-0.02107609435915947,
-0.023418115451931953,
0.018099073320627213,
-0.04452323913574219,
0.008620469830930233,
-0.05321202427148819,
0.024895399808883667,
-0.004926701541990042,
-0.005725267808884382,
-0.046793971210718155,
-0.00977726373821497,
0.005751794669777155,
0.018385211005806923,
0.030172251164913177,
-0.04456469416618347,
-0.044528406113386154,
0.00580943888053298,
0.004218372516334057,
-0.01494855247437954,
0.007338295225054026,
-0.009478427469730377,
0.022631477564573288,
-0.0367102287709713,
-0.01887604407966137,
0.04554460942745209,
0.0060722786001861095,
-0.01622586138546467,
0.0019633204210549593,
-0.005987715907394886,
-0.017605487257242203,
0.026293590664863586,
-0.030809106305241585,
0.032755620777606964,
-0.024036260321736336,
-0.00019942052313126624,
0.08345314860343933,
-0.012248207814991474,
-0.03258300945162773,
-0.009678159840404987,
-0.033327482640743256,
-0.038833342492580414,
-0.009899746626615524,
0.012272513471543789,
0.0022877026349306107,
-0.00161545944865793,
0.02496497891843319,
0.030708838254213333,
-0.07901675254106522,
-0.04224755987524986,
-0.02333647757768631,
-0.06221793219447136,
0.02547694928944111,
0.02463534101843834,
0.07384435832500458,
0.012400973588228226,
-0.07414186745882034,
0.039317160844802856,
0.004963880870491266,
-0.0578266941010952,
-0.016095545142889023,
-0.018283380195498466,
-0.037449248135089874,
-0.045507289469242096,
0.02403191663324833,
0.10437388718128204,
-0.034336384385824203,
-0.024493291974067688,
0.018771475180983543,
0.06824839115142822,
0.027537574991583824,
0.008507880382239819,
0.03178808093070984,
0.019034283235669136,
-0.0010112050222232938,
0.027150005102157593,
0.045971840620040894,
-0.006077435798943043,
-0.04163515567779541,
0.03268204256892204,
-0.026930131018161774,
0.027241909876465797,
0.03296467661857605,
-0.025817669928073883,
0.03308338299393654,
0.0017293503042310476,
-0.008691644296050072,
-0.06768593937158585,
0.025664033368229866,
-0.008695175871253014,
-0.01736575923860073,
0.016199512407183647,
0.0324372798204422,
0.05162501707673073,
0.01173413172364235,
-0.023690244182944298,
0.032361701130867004,
0.056785911321640015,
-0.04087846726179123,
-0.013176490552723408,
-0.02335037663578987,
0.016865761950612068,
0.013506248593330383,
-0.016268067061901093,
0.0026895401533693075,
0.060427408665418625,
0.002132127294316888,
0.014701666310429573,
0.01832578144967556,
-0.024794137105345726,
-0.015013768337666988,
-0.07180614024400711,
-0.022560013458132744,
-0.023379182443022728,
0.05284722149372101,
0.009188273921608925,
0.10701371729373932,
0.01287638396024704,
0.03538814187049866,
-0.01719757169485092,
0.007323837839066982,
-0.05633420869708061,
0.003038473427295685,
-0.03603878989815712,
-0.026832187548279762,
-0.022416358813643456,
-0.020226003602147102,
-0.032069411128759384,
-0.03010079450905323,
-0.038426004350185394,
0.0035180039703845978,
-0.016760269179940224,
-0.01895865611732006,
0.03489456698298454,
-0.0008203460602089763,
0.0014060318935662508,
-0.03415263444185257,
0.025856373831629753,
0.013162577524781227,
-0.03484095633029938,
0.020732803270220757,
0.020017018541693687,
-0.006375526078045368,
-0.031612180173397064,
0.02148064225912094,
0.015867099165916443,
0.05995241180062294,
-0.019788531586527824,
0.02642177790403366,
-0.009764247573912144,
-0.023808062076568604,
0.009450280107557774,
0.009359214454889297,
0.05070449039340019,
0.02559514157474041,
-0.014984814450144768,
-0.041261862963438034,
-0.022764334455132484,
-0.0053758565336465836,
0.00641704211011529,
0.0645020604133606,
0.012079021893441677,
-0.005543935112655163,
0.0021994193084537983,
-0.01253520417958498,
-0.017299462109804153,
0.05600053817033768,
0.028345022350549698,
0.0013819121522828937,
-0.0338989719748497,
-0.04774137958884239,
0.016042189672589302,
-0.049886055290699005,
0.008277878165245056,
0.028894970193505287,
0.029030468314886093,
-0.01917618326842785,
-0.027420124039053917,
0.010377444326877594,
-0.03236889839172363,
-0.025674913078546524,
-0.0036910385824739933,
-0.003112642327323556,
-0.008965504355728626,
-0.005675082560628653,
0.000060443788242992014,
0.02320949360728264,
0.03352535516023636,
0.0033345462288707495,
0.011448806151747704,
0.005334209185093641,
-0.10095351189374924,
-0.049506522715091705,
0.02261517010629177,
0.04060501977801323,
-0.004313121549785137,
0.0017817690968513489,
-0.06669487804174423,
-0.021232446655631065,
0.023685600608587265,
-0.026463763788342476,
0.01930265501141548,
-0.011707927100360394,
0.020862579345703125,
-0.03112187050282955,
-0.05839495733380318,
0.005586181301623583,
0.019681034609675407,
-0.012401868589222431,
0.033789969980716705,
-0.04184916615486145,
0.0035102549009025097,
-0.017186099663376808,
-0.01372844073921442,
0.04532555118203163,
0.051665809005498886,
-0.012540820054709911,
0.004761319607496262,
-0.007771956734359264,
0.02575010247528553,
-0.005463858600705862,
-0.10967108607292175,
0.03827516734600067,
-0.020468510687351227,
-0.00035626490716822445,
0.008673734031617641,
-0.03945823758840561,
-0.018240313977003098,
0.039536818861961365,
0.012629435397684574,
0.012195324525237083,
0.010362552478909492,
-0.05818643420934677,
0.061586894094944,
0.035176463425159454,
0.028736364096403122,
0.040694646537303925,
0.03962316736578941,
-0.05159052088856697,
-0.02079835906624794,
-0.014564266428351402,
0.05342889577150345,
-0.018152106553316116,
-0.02932933159172535,
-0.05261366814374924,
0.0176581759005785,
-0.02836136519908905,
0.06421159952878952,
-0.021485913544893265,
0.030416982248425484,
-0.008564972318708897,
-0.04629465192556381,
0.0028976215980947018,
-0.03670526295900345,
-0.003294358029961586,
-0.024795427918434143,
-0.04135138913989067,
0.036790668964385986,
0.01393432728946209,
-0.020118892192840576,
0.0033901554998010397,
0.0012299581430852413,
0.015004710294306278,
0.016222454607486725,
-0.004510935861617327,
-0.014772986993193626,
-0.0205202829092741,
0.0014744632644578815,
0.02537192776799202,
-0.03723723813891411,
0.04651166871190071,
-0.03946104645729065,
-0.0022592819295823574,
0.002839696826413274,
-0.036881137639284134,
-0.05298773944377899,
0.0630916953086853,
0.00130551983602345,
-0.0065992712043225765,
-0.012527368031442165,
0.028043562546372414,
0.04078095778822899,
0.019169624894857407,
-0.03288279101252556,
-0.07931098341941833,
0.04524323344230652,
0.010960692539811134,
0.005373288877308369,
0.005935437045991421,
-0.014472554437816143,
-0.029501089826226234,
-0.055075082927942276,
0.005988436285406351,
0.04383920133113861,
-0.04931379109621048,
0.01188271027058363,
-0.0020842934027314186,
0.01750255562365055,
0.06859178841114044,
-0.003984412178397179,
-0.0037037874571979046,
-0.013244196772575378,
-0.04644932225346565,
-0.0034834237303584814,
-0.03052479773759842,
0.043611496686935425,
-0.037482500076293945,
0.0010695677483454347,
-0.001296492526307702,
-0.0309006217867136,
0.05199404060840607,
-0.029902078211307526,
-0.009601853787899017,
-0.004001288209110498,
-0.0007297931588254869,
-0.06332702189683914,
-0.010175639763474464,
0.01073638815432787,
0.027716193348169327,
0.05494551733136177,
-0.016596388071775436,
-0.012753307819366455,
-0.052091605961322784,
-0.04716041684150696,
0.010746515356004238,
0.01621861569583416,
-0.005698822904378176,
0.00654974952340126,
0.01739119365811348,
-0.06502585858106613,
0.003698007669299841,
0.03802747651934624,
0.0010531492298468947,
0.024753551930189133,
0.021414224058389664,
-0.0001455828605685383,
0.008360004052519798,
-0.007414931897073984,
-0.013051888905465603,
-0.015397806651890278,
-0.052458517253398895,
-0.010924051515758038,
0.030327992513775826,
0.02226336859166622,
0.04659758508205414,
0.010297222062945366,
-0.04149976000189781,
0.004028998780995607,
-0.011344571597874165,
-0.024378331378102303,
0.027599859982728958,
-0.012136086821556091,
0.020282883197069168,
-0.013535568490624428,
-0.027736322954297066,
0.031033366918563843,
0.023333700373768806,
-0.015971995890140533,
-0.018867701292037964,
0.015240366570651531,
0.005447764880955219,
0.00440131826326251,
-0.014322356320917606,
-0.02020803466439247,
0.018184661865234375,
-0.04040985554456711,
0.014641585759818554,
-0.004096330609172583,
-0.0067983223125338554,
0.06623072922229767,
0.002394756069406867,
-0.0356728658080101,
-0.06966660916805267,
0.014928451739251614,
-0.04993654042482376,
0.003560542594641447,
0.03376663848757744,
-0.0012276337947696447,
-0.02283470705151558,
0.04989611729979515,
0.044517263770103455,
-0.03321877121925354,
0.018875140696763992,
0.005235814489424229,
-0.03605584427714348,
0.03141169622540474,
-0.028259553015232086,
-0.04788016527891159,
0.05818827822804451,
0.005568837746977806,
-0.027773264795541763,
-0.011706780642271042,
-0.03216495364904404,
0.018183723092079163,
0.0002054933283943683,
0.005844328552484512,
-0.035716354846954346,
0.0669805184006691,
-0.02890981361269951,
0.018945306539535522,
-0.019524358212947845,
-0.010799882933497429,
0.11595487594604492,
0.04527781531214714,
0.015452522784471512,
-0.026079608127474785,
-0.0009878954151645303,
-0.014739110134541988,
0.010808555409312248,
-0.0025863968767225742,
0.004238273482769728,
-0.014004701748490334,
0.030027424916625023,
0.00515245646238327,
0.027057288214564323,
0.03607778996229172,
0.04009116068482399,
0.05695978179574013,
-0.03604882210493088,
-0.0016174810007214546,
0.002553698606789112,
0.024460753425955772,
-0.046932823956012726,
0.05083658918738365,
-0.05393979698419571,
0.051863718777894974,
-0.042732469737529755,
0.0008600339060649276,
-0.026753541082143784,
-0.01952533610165119,
0.06764919310808182,
-0.008847475051879883,
-0.04832339659333229,
-0.0006307319272309542,
-0.017559237778186798,
-0.04305998235940933,
-0.0026484550908207893,
0.06309204548597336,
0.04491008445620537,
-0.01788020320236683,
0.0014834165340289474,
0.02549055777490139,
0.0423109345138073,
0.005490127019584179,
-0.00887218490242958,
0.03383705019950867,
-0.04310620203614235,
0.0029067147988826036,
-0.043824415653944016,
0.017214709892868996,
0.0061459592543542385,
0.016640691086649895,
-0.0028216077480465174,
0.055256348103284836,
-0.004596507642418146,
-0.07400558143854141,
-0.019832871854305267,
-0.0276314839720726,
0.03485042229294777,
-0.00423962390050292,
-0.00394856370985508,
-0.04709046706557274,
0.025820519775152206,
-0.0445084348320961,
0.032522156834602356,
0.011574218980967999,
-0.006460788194090128,
-0.005114555824548006,
-0.0171517226845026,
-0.008567915298044682,
0.012863745912909508,
-0.019354088231921196,
-0.0038259525317698717,
0.01559847965836525,
-0.03905944898724556,
0.017200002446770668,
0.004486615303903818,
0.04509603604674339,
0.0245332233607769,
0.014305023476481438,
-0.00026256119599565864,
-0.011370445601642132,
-0.06865711510181427,
0.06601116806268692,
0.023744095116853714,
-0.012841238640248775,
-0.005387482233345509,
-0.01702185347676277,
-0.006923398934304714,
0.07094400376081467,
0.007273048162460327,
0.005788356997072697,
-0.002028473885729909,
0.037499867379665375,
0.03793390467762947,
-0.041720855981111526,
-0.011834722012281418,
0.021290242671966553,
-0.026190422475337982,
-0.004560625646263361,
0.04811437055468559,
0.03909452632069588,
0.013718447647988796,
0.016222896054387093,
-0.02132730931043625,
0.026736244559288025,
-0.018849804997444153,
-0.01021103747189045,
0.03247871249914169,
0.0036002732813358307,
-0.02079595997929573,
0.028576908633112907,
-0.0025734873488545418,
-0.01493720430880785,
0.004141077399253845,
-0.03467630594968796,
0.022423995658755302,
-0.0035688825882971287,
-0.007232782430946827,
-0.010377266444265842,
-0.004698308650404215,
-0.0541747584939003,
0.026758776977658272,
-0.02635508030653,
0.004450057167559862,
-0.04783143103122711,
-0.02667231298983097,
-0.0014732953859493136,
-0.003492058953270316,
0.002590214367955923,
0.04567352309823036,
-0.009576772339642048,
-0.010420368984341621,
0.022349989041686058,
-0.007895366288721561,
-0.020708570256829262,
-0.013953705318272114,
0.012256579473614693,
0.004956500604748726,
0.05264805257320404,
-0.029544368386268616,
-0.0235424991697073,
0.03925906866788864,
0.0027601614128798246,
-0.003301643766462803,
0.04315945506095886,
-0.0023223243188112974,
0.014122679829597473,
0.029300913214683533,
-0.007201199885457754,
0.0025155001785606146,
0.04697151109576225,
-0.0018419220577925444,
0.044158920645713806,
-0.022431964054703712,
-0.047180842608213425,
0.00832312647253275,
-0.023124950006604195,
0.03767765685915947,
-0.005454063415527344,
0.03752961382269859,
0.028814667835831642,
0.017504079267382622,
0.0012040019501000643,
-0.011392698623239994,
0.01439269632101059,
0.00264173187315464,
0.016732072457671165,
0.04709398373961449,
0.010741615667939186,
0.00994828436523676,
0.019323932006955147,
-0.05450008064508438,
0.034090761095285416,
-0.01695258542895317,
-0.0017353275325149298,
-0.07914043962955475,
0.021550966426730156,
-0.020809244364500046,
0.006995105650275946,
-0.0075988080352544785,
-0.044880460947752,
-0.03531274572014809,
0.02633294090628624,
-0.07157128304243088,
-0.01818455383181572,
0.008452351205050945,
0.016295835375785828,
-0.024240942671895027,
0.00775058101862669,
-0.012439698912203312,
0.02264634147286415,
-0.0037007518112659454,
0.03803953155875206,
0.003763113170862198,
0.032881829887628555,
0.027975238859653473,
-0.032006751745939255,
-0.031353555619716644,
0.05233687534928322,
0.008823692798614502,
0.011287283152341843,
0.01791463978588581,
-0.047818660736083984,
0.014077572152018547,
0.020435580983757973,
0.000011160174835822545,
0.03405836224555969,
-0.028591010719537735,
0.017544183880090714,
0.033617034554481506,
0.0547030046582222,
0.006716813892126083,
-0.01616065576672554,
-0.03069811686873436,
-0.007637893781065941,
0.03918662294745445,
0.014387264847755432,
0.002813670551404357,
-0.011828476563096046,
0.05834898352622986,
-0.01599203422665596,
-0.019351109862327576,
0.033537641167640686,
-0.02707526832818985,
-0.014766283333301544,
0.04152992367744446,
-0.03972405940294266,
0.011733639054000378,
0.004031667951494455,
-0.005651406012475491,
-0.031978920102119446,
-0.028551431372761726,
0.06995810568332672,
-0.02623307704925537,
0.007920753210783005,
0.009185236878693104,
-0.0027382008265703917,
-0.013440166600048542,
0.020084381103515625,
0.012085353024303913,
0.004146452993154526,
-0.04104932025074959,
0.01100405678153038,
-0.007868028245866299,
-0.0010093688033521175,
0.027926849201321602,
-0.03950629010796547,
-0.001464730012230575,
0.02088775858283043,
0.034698646515607834,
-0.010507206432521343,
0.0038629218470305204,
-0.030394192785024643,
0.018079476431012154,
-0.04797960817813873,
0.04418226331472397,
0.015323933213949203,
-0.035123638808727264,
-0.019789721816778183,
-0.021610073745250702,
0.007441708818078041,
0.051330383867025375,
0.07940416783094406,
0.009508326649665833,
-0.01181662455201149,
0.03235160931944847,
-0.008882121182978153,
0.05496841296553612,
-0.07177548110485077,
-0.025961291044950485,
0.0054803285747766495,
-0.0033212804701179266,
0.03644051030278206,
-0.003729676827788353,
-0.026888146996498108,
0.004141278564929962,
0.04394695907831192,
-0.010192271322011948,
-0.01150427758693695,
-0.04408648610115051,
-0.014913328923285007,
0.002277008257806301,
0.03187045827507973,
-0.014095435850322247,
0.07527836412191391,
-0.03683313727378845,
-0.01647089794278145,
-0.008050134405493736,
-0.014045363292098045,
-0.041583139449357986,
0.003962592221796513,
-0.009867522865533829,
0.039124418050050735,
0.01867925189435482,
-0.04996355250477791,
0.025275183841586113,
-0.062316372990608215,
-0.03919985145330429,
0.03426765650510788,
-0.021135006099939346,
-0.019929567351937294,
0.07458467036485672,
0.012223063968122005,
-0.008237293921411037,
-0.022105390205979347,
0.005508533213287592,
-0.027997620403766632,
-0.018616512417793274,
-0.031242646276950836,
0.008119521662592888,
0.08008933812379837,
-0.0033231135457754135,
-0.008135683834552765,
0.047863371670246124,
0.016182292252779007,
0.0011578212724998593,
0.0018397757085040212,
-0.02354518696665764,
-0.01760850101709366,
-0.04013161361217499,
0.009166586212813854,
-0.022326882928609848,
0.007581382989883423,
0.022002659738063812,
-0.01741737686097622,
0.1025654673576355,
-0.04905974864959717,
-0.0004546611453406513,
-0.0001665950840106234,
0.02037968672811985,
-0.011567938141524792,
-0.0018181130290031433,
-0.006865473464131355,
0.007128460798412561,
-0.026399552822113037,
-0.04020919278264046,
-0.021050987765192986,
-0.028899148106575012,
0.024999674409627914,
-0.03532932698726654,
0.03769833222031593,
0.00798834953457117,
-0.0016346904449164867,
-0.017300257459282875,
0.009192871861159801,
-0.015567740425467491,
-0.030539896339178085,
0.037909526377916336,
-0.006422773469239473,
0.022263210266828537,
0.02861000970005989,
-0.039060164242982864,
0.01601441577076912,
0.0429631844162941,
-0.06188470125198364,
-0.02172740362584591,
0.011419308371841908,
0.016637621447443962,
0.012630335986614227,
-0.03904575854539871
] |
<p>Almost every source I can find online maintains that two 0.5 cm blankets are significantly warmer than a single 1cm blanket due to air trapped between the thin blankets.</p>
<p>However, the thermal conductivities of air and wool are roughly comparable according to <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html">this website</a>. That would seem to mean that air only aids the insulation significantly if the thickness of the air layer is significant compared to the thickness of the blankets, which I would guess it is not.</p>
<p>Further, in order for heat transfer through the air to be dominated by conduction, the air needs to be extremely still, which it seems it would not be around a living, breathing, human. Otherwise the air would mix and not provide significant insulation.</p>
<p>Is there any empirical evidence that two thin blankets are superior? If so, why is that, given the above considerations?</p>
| 10,783 |
[
-0.03542246297001839,
-0.014261123724281788,
-0.006753616034984589,
-0.057505153119564056,
-0.008780455216765404,
0.0016933532897382975,
-0.01932879537343979,
-0.035461947321891785,
0.010617267340421677,
-0.03659669682383537,
0.025638172402977943,
0.040516000241041183,
0.031719621270895004,
0.028883202001452446,
0.01347992941737175,
-0.03985866531729698,
0.006471529137343168,
-0.01829983852803707,
0.017859436571598053,
-0.013405714184045792,
-0.01823718473315239,
0.03057069145143032,
-0.020627742633223534,
0.0018075233092531562,
-0.021975602954626083,
0.06348589062690735,
0.024783005937933922,
-0.04666296765208244,
0.01927768997848034,
0.026806799694895744,
-0.033539459109306335,
0.024105167016386986,
0.018983863294124603,
0.005114469677209854,
0.06476698815822601,
-0.030115939676761627,
-0.041851505637168884,
-0.022288333624601364,
0.02749006263911724,
0.02502908557653427,
0.008604959584772587,
-0.020921790972352028,
0.0006430294597521424,
-0.026847636327147484,
-0.021136045455932617,
0.0017617696430534124,
0.016819972544908524,
-0.06626599282026291,
0.036285627633333206,
-0.10364830493927002,
-0.012302374467253685,
0.0006775123183615506,
0.07273020595312119,
0.02954956889152527,
0.014439661055803299,
0.004153373185545206,
0.045129723846912384,
0.051212575286626816,
0.011928850784897804,
-0.02819424867630005,
-0.013924107886850834,
0.010178708471357822,
-0.04790426418185234,
-0.016010822728276253,
0.0222930945456028,
0.04761428385972977,
-0.005179858300834894,
-0.009137129411101341,
0.021145019680261612,
0.0035933416802436113,
0.054714638739824295,
-0.030674153938889503,
0.04667337238788605,
-0.008910383097827435,
0.04810848832130432,
0.03221505135297775,
0.00420282082632184,
0.021275117993354797,
0.05173491686582565,
0.06271912902593613,
0.005633195862174034,
0.0034703880082815886,
0.08109224587678909,
0.03298375383019447,
0.01779967173933983,
0.0014890377642586827,
0.062007226049900055,
-0.0369877815246582,
0.0037588763516396284,
0.017761366441845894,
-0.0007134025217965245,
0.002651721239089966,
0.048030462116003036,
0.020119957625865936,
0.026384262368083,
0.001021151547320187,
-0.007683160249143839,
0.03892206400632858,
-0.023067599162459373,
-0.04046599566936493,
-0.023139700293540955,
0.036557670682668686,
0.0376969538629055,
0.08269018679857254,
0.03721045330166817,
-0.032477475702762604,
-0.04920260235667229,
-0.010892320424318314,
0.014675548300147057,
-0.0024502112064510584,
-0.03190960735082626,
0.00314530567266047,
-0.00932096503674984,
0.006100496277213097,
0.0052444846369326115,
-0.0368429496884346,
0.008614222519099712,
-0.028136808425188065,
0.07448474317789078,
0.04041669890284538,
0.03474833071231842,
0.00371815194375813,
0.011462181806564331,
-0.0403408445417881,
-0.04434255138039589,
0.015549874864518642,
0.023387081921100616,
-0.01810513623058796,
-0.030490484088659286,
0.049829497933387756,
0.023427555337548256,
-0.00260922615416348,
0.021559838205575943,
-0.01419717539101839,
0.033328890800476074,
-0.01696610450744629,
-0.06606587767601013,
-0.028841087594628334,
0.041867226362228394,
-0.009224265813827515,
0.018943049013614655,
-0.07231982797384262,
-0.02229098603129387,
-0.006838320754468441,
0.02560058981180191,
-0.0034532572608441114,
0.023437822237610817,
-0.061011943966150284,
-0.017639273777604103,
-0.019625907763838768,
-0.030956672504544258,
0.0017680810997262597,
0.009137080051004887,
-0.020387092605233192,
-0.013769022189080715,
-0.055287886410951614,
0.05740422382950783,
0.03135959804058075,
-0.009200739674270153,
0.016046205535531044,
0.028185047209262848,
0.029254866763949394,
-0.028973883017897606,
-0.018015993759036064,
-0.014171172864735126,
-0.01834500953555107,
0.026835661381483078,
-0.0377521775662899,
-0.003102724440395832,
0.02307189255952835,
-0.006134589668363333,
-0.008290464989840984,
-0.009063824079930782,
-0.012612473219633102,
0.011102105490863323,
-0.035600241273641586,
0.024471893906593323,
-0.0111538739874959,
-0.0006500422023236752,
0.02857065014541149,
-0.06530817598104477,
-0.004492339212447405,
-0.009540794417262077,
-0.0023459019139409065,
0.01761074922978878,
0.05818312615156174,
-0.01094944030046463,
-0.04418722540140152,
0.029744582250714302,
-0.01718316227197647,
-0.06679689139127731,
-0.0745716542005539,
-0.03245085850358009,
-0.011247699148952961,
0.00711573613807559,
0.021073853597044945,
0.010455502197146416,
0.018865589052438736,
-0.008300554938614368,
-0.02045445330440998,
-0.007323547266423702,
0.019708499312400818,
0.047271728515625,
0.003331392304971814,
0.022923758253455162,
0.06902699172496796,
0.0341784730553627,
-0.01918216235935688,
0.004400614183396101,
-0.023177793249487877,
-0.06073850765824318,
-0.02061566337943077,
-0.06559156626462936,
0.03629057854413986,
0.03191543370485306,
0.03010389767587185,
0.049584150314331055,
0.012669023126363754,
-0.014132542535662651,
0.019464073702692986,
-0.013945684768259525,
0.08071498572826385,
-0.005627802107483149,
-0.02989453449845314,
-0.01236521452665329,
0.025472385808825493,
0.019854092970490456,
-0.03406612575054169,
0.011519870720803738,
-0.05011143535375595,
-0.08026660978794098,
-0.023394672200083733,
0.08892397582530975,
0.02818325348198414,
-0.026277421042323112,
0.01661977730691433,
-0.0002036915539065376,
0.07070917636156082,
0.017146749421954155,
0.019198689609766006,
0.0057139769196510315,
-0.04349769651889801,
0.014361407607793808,
0.04309834912419319,
0.021935734897851944,
-0.010447447188198566,
0.016894644126296043,
0.013689856976270676,
0.025194576010107994,
-0.008530406281352043,
-0.033083438873291016,
0.015277366153895855,
0.020398465916514397,
0.03867025300860405,
-0.008172133937478065,
0.01965506002306938,
0.04014262557029724,
-0.06101153790950775,
0.004471005871891975,
0.013254707679152489,
0.0023437931668013334,
0.000756546389311552,
-0.046375174075365067,
-0.05375320091843605,
0.02221674844622612,
0.0022144222166389227,
-0.0070265838876366615,
0.007384805008769035,
0.011983714066445827,
-0.060452163219451904,
0.01271709706634283,
-0.036142196506261826,
-0.009770967997610569,
0.015037224628031254,
-0.035899024456739426,
0.02755606919527054,
0.026418272405862808,
0.03169018402695656,
-0.04097466170787811,
-0.028553903102874756,
-0.00826580822467804,
-0.02041342295706272,
0.03278861194849014,
-0.006203800439834595,
-0.0014238691655918956,
0.021037429571151733,
-0.059493355453014374,
-0.005680988077074289,
0.05420758202672005,
-0.03401818498969078,
-0.010061986744403839,
0.032503824681043625,
-0.020438523963093758,
-0.05659718066453934,
0.007568270433694124,
-0.020357834175229073,
0.02843765914440155,
0.006516340654343367,
-0.0011160948779433966,
0.07163909077644348,
-0.002534812781959772,
-0.06621254235506058,
0.03722123056650162,
-0.048898838460445404,
-0.024736173450946808,
0.0009694432956166565,
-0.045421943068504333,
0.0036070088390260935,
-0.0013103866949677467,
0.01986345835030079,
-0.00542821642011404,
-0.026593297719955444,
-0.028884688392281532,
-0.05104224756360054,
-0.04257906600832939,
0.033304933458566666,
-0.014171965420246124,
0.036297962069511414,
-0.020464327186346054,
-0.02254604920744896,
0.07808999717235565,
0.019975367933511734,
-0.024153800681233406,
-0.015240938402712345,
-0.009372814558446407,
-0.026380591094493866,
-0.008082624524831772,
0.029163142666220665,
0.03926040977239609,
0.009805073961615562,
0.028835222125053406,
0.05010833218693733,
0.03439007326960564,
0.07364248484373093,
-0.005731996148824692,
-0.020501932129263878,
0.014060616493225098,
0.016082553192973137,
-0.02796139568090439,
0.03609022498130798,
0.01956336200237274,
0.004415703006088734,
-0.013368148356676102,
-0.024146582931280136,
0.01793978363275528,
0.016383817419409752,
-0.024401362985372543,
0.04397064447402954,
-0.00019038924074266106,
0.041417721658945084,
-0.054273344576358795,
0.0041334801353514194,
-0.006811659317463636,
-0.007591333705931902,
-0.021624119952321053,
0.03834541141986847,
0.021815236657857895,
-0.02395494282245636,
-0.008192825131118298,
0.04097506031394005,
0.08740580826997757,
-0.0023118273820728064,
-0.004987610038369894,
-0.022841976955533028,
-0.013425535522401333,
-0.006056701764464378,
-0.0061192261055111885,
-0.021607019007205963,
0.02844390459358692,
0.05253679305315018,
0.06937139481306076,
-0.005343530792742968,
-0.0533866286277771,
0.006325547117739916,
-0.08893898129463196,
-0.05102274566888809,
-0.03152257949113846,
0.062067992985248566,
-0.03753427788615227,
0.013818076811730862,
0.013964824378490448,
0.029943155124783516,
0.029883945360779762,
0.010297058150172234,
-0.04754926636815071,
-0.009470021352171898,
-0.01623827964067459,
0.01342235691845417,
0.03173210844397545,
-0.016893455758690834,
-0.01602400466799736,
-0.016278348863124847,
-0.010574997402727604,
0.0027842381969094276,
0.036397043615579605,
0.007255615200847387,
0.03277469426393509,
-0.0023361220955848694,
-0.021505404263734818,
-0.005395450629293919,
0.040353477001190186,
0.007678700145334005,
-0.01145140826702118,
0.013593574985861778,
0.013817476108670235,
0.016226116567850113,
-0.006824139039963484,
-0.03888295218348503,
0.06101134791970253,
-0.010002262890338898,
0.016830187290906906,
0.013064730912446976,
-0.0037581867072731256,
-0.03249691426753998,
0.0012695023324340582,
0.017268644645810127,
-0.008123653009533882,
-0.032208506017923355,
0.00813550315797329,
-0.031384214758872986,
-0.037012387067079544,
-0.07116948068141937,
-0.028420401737093925,
-0.0018377917585894465,
0.0013412564294412732,
0.014455310069024563,
-0.015416539274156094,
-0.004191791173070669,
0.023970095440745354,
0.01791146583855152,
0.04053131118416786,
-0.04756934195756912,
-0.03584771975874901,
-0.029734399169683456,
-0.04575425013899803,
-0.033578239381313324,
0.007876528427004814,
0.035763930529356,
0.016522938385605812,
-0.028219180181622505,
-0.018613290041685104,
0.06569252163171768,
-0.014834326691925526,
-0.013716761954128742,
0.02188774012029171,
0.0017101449193432927,
0.00764165073633194,
0.0015052251983433962,
-0.003439325140789151,
-0.009267599321901798,
0.02403942309319973,
0.03468151018023491,
0.04561297595500946,
-0.0324818380177021,
-0.03312545642256737,
-0.018737230449914932,
0.020289501175284386,
0.03547117859125137,
-0.029466500505805016,
0.03643988072872162,
-0.05172793194651604,
0.015102692879736423,
0.050135064870119095,
0.0013638704549521208,
0.046875156462192535,
-0.038063302636146545,
-0.003508352441713214,
-0.013945139944553375,
-0.0013476007152348757,
0.013910855166614056,
0.006829155143350363,
0.021389184519648552,
0.02482243999838829,
-0.0013883586507290602,
-0.02297484688460827,
-0.003899533301591873,
0.03373067080974579,
0.0269915871322155,
0.02391515113413334,
-0.012626363895833492,
0.0437118224799633,
0.02621317282319069,
-0.016155458986759186,
-0.022252021357417107,
-0.06389342993497849,
-0.010068858973681927,
-0.009278946556150913,
-0.017736945301294327,
-0.018412040546536446,
-0.03461970016360283,
-0.014918247237801552,
-0.0023558468092232943,
0.005489235743880272,
-0.04864675551652908,
-0.021170256659388542,
-0.011327996850013733,
0.04805151745676994,
0.021978668868541718,
0.006078767124563456,
0.06326945871114731,
0.024561818689107895,
-0.013785531744360924,
0.019611947238445282,
-0.03208089992403984,
0.03813138231635094,
-0.022177081555128098,
-0.027477888390421867,
-0.02164468914270401,
-0.0030813852790743113,
-0.02479214034974575,
0.014209273271262646,
0.002930055372416973,
0.04962547868490219,
0.014787844382226467,
-0.026542063802480698,
0.024515410885214806,
0.007642507553100586,
-0.0016840435564517975,
-0.014675911515951157,
-0.02853560447692871,
0.04293642193078995,
-0.02923058159649372,
-0.018788468092679977,
0.018870411440730095,
0.009361032396554947,
-0.010921421460807323,
0.032744571566581726,
-0.05053938925266266,
-0.011477413587272167,
-0.011201072484254837,
-0.0016558346105739474,
-0.02975773997604847,
-0.010767991654574871,
0.0625072568655014,
-0.024940531700849533,
0.006486882921308279,
0.018709389492869377,
-0.04489690810441971,
-0.02641196735203266,
0.04858826845884323,
0.002325663808733225,
0.03014153055846691,
-0.03664032369852066,
0.029016487300395966,
0.011395972222089767,
-0.010746336542069912,
-0.04981449618935585,
0.01867845095694065,
0.02113785594701767,
0.04457944259047508,
0.003891030792146921,
-0.07931119203567505,
-0.005103125236928463,
-0.012310019694268703,
-0.03739210590720177,
0.0059072403237223625,
0.05862516909837723,
-0.052116092294454575,
-0.010433459654450417,
-0.00912692490965128,
0.0069587440229952335,
0.0071640899404883385,
0.016465766355395317,
-0.020850930362939835,
-0.010242041200399399,
-0.028749164193868637,
-0.023021027445793152,
0.002939557656645775,
-0.011933023110032082,
-0.029720468446612358,
-0.03745346888899803,
0.016842689365148544,
-0.007451679557561874,
0.022450748831033707,
-0.0027705770917236805,
0.00395978894084692,
0.05724481865763664,
-0.0004906905815005302,
0.009889352135360241,
-0.04281046986579895,
0.048387084156274796,
0.004215423483401537,
0.06401229649782181,
-0.0327003113925457,
0.009113596752285957,
-0.02487925812602043,
-0.018039468675851822,
0.029363354668021202,
0.02686542645096779,
-0.02652890980243683,
0.03266123682260513,
0.07583091408014297,
-0.015252608805894852,
-0.015734940767288208,
0.0009372218046337366,
-0.028096500784158707,
0.00894473772495985,
-0.018983352929353714,
-0.005578447133302689,
-0.010424523614346981,
0.019033629447221756,
-0.02617369219660759,
-0.036255571991205215,
0.01665491983294487,
-0.006665383465588093,
-0.0014589889906346798,
-0.00445506302639842,
0.02255828119814396,
0.013332000933587551,
-0.04393330216407776,
-0.009709455072879791,
0.0068763745948672295,
-0.03685295209288597,
0.025094538927078247,
-0.01900322549045086,
0.021194953471422195,
-0.06196654587984085,
-0.008129356428980827,
0.05130428820848465,
0.003181321546435356,
0.035655222833156586,
0.012899421155452728,
0.028780827298760414,
0.01854245364665985,
0.007843452505767345,
-0.038201749324798584,
-0.009098386391997337,
0.05383912846446037,
-0.049585096538066864,
0.0316903255879879,
-0.014348523691296577,
-0.01607818342745304,
0.04584605246782303,
0.01734740473330021,
-0.006020521745085716,
-0.06671552360057831,
-0.02143782563507557,
-0.015790695324540138,
0.003643750911578536,
0.049811992794275284,
-0.0353890024125576,
0.033961132168769836,
-0.0246664397418499,
0.0322907529771328,
-0.024605566635727882,
-0.003303609322756529,
0.01975204423069954,
-0.050976209342479706,
0.011598851531744003,
-0.019324379041790962,
-0.05616680160164833,
0.06375765055418015,
0.007071161642670631,
-0.05119326338171959,
0.027359355241060257,
-0.010486647486686707,
0.009067961014807224,
0.01770775392651558,
0.00822745356708765,
0.018441302701830864,
0.07168324291706085,
0.008460277691483498,
-0.004872298799455166,
0.002444483805447817,
0.009818938560783863,
0.14084430038928986,
0.02242477610707283,
0.008127120323479176,
-0.050099749118089676,
0.0018341864924877882,
0.003353716107085347,
0.017885539680719376,
-0.03905543312430382,
0.03322695195674896,
-0.026908621191978455,
0.012621373869478703,
0.03211553767323494,
0.06897769123315811,
0.02455585077404976,
-0.018908478319644928,
0.04711301252245903,
-0.02316981367766857,
0.006420950870960951,
0.009696136228740215,
-0.009016919881105423,
0.01053023524582386,
0.00024096551351249218,
-0.006933326367288828,
-0.009001385420560837,
-0.0007607428706251085,
0.03366464748978615,
-0.001718754880130291,
-0.02591133490204811,
0.049965791404247284,
0.0022611902095377445,
-0.06463228166103363,
-0.0029364018701016903,
-0.019159600138664246,
-0.01760253868997097,
-0.031599804759025574,
-0.009594494476914406,
0.04533105716109276,
-0.01415114663541317,
0.009467145428061485,
0.008869508281350136,
0.013136127963662148,
0.011174164712429047,
0.04839908331632614,
0.06196447089314461,
-0.050026170909404755,
-0.039522942155599594,
-0.012707262299954891,
0.021759700030088425,
-0.019821489229798317,
0.005555769894272089,
0.02936643920838833,
-0.013943937607109547,
0.005200822371989489,
-0.010342469438910484,
0.007969789206981659,
-0.018511051312088966,
0.029520807787775993,
-0.02277897484600544,
-0.03962640464305878,
-0.056915268301963806,
0.03806208074092865,
0.01794946938753128,
0.03448541462421417,
0.012529921717941761,
-0.012132858857512474,
-0.062110599130392075,
0.009958647191524506,
0.05303933098912239,
-0.0034553869627416134,
-0.0009386815363541245,
-0.047625135630369186,
-0.013567102141678333,
-0.006379738915711641,
-0.038507480174303055,
-0.0025324742309749126,
0.010481956414878368,
0.07658380270004272,
-0.012200935743749142,
-0.03978797048330307,
-0.013689146377146244,
-0.051442164927721024,
-0.01133900135755539,
0.011521517299115658,
-0.0060849362052977085,
-0.01650986634194851,
-0.03941211849451065,
-0.004661524202674627,
0.012288102880120277,
-0.015665069222450256,
0.00042054709047079086,
0.006986703723669052,
-0.0047354502603411674,
0.0027922114823013544,
-0.029537836089730263,
-0.040322497487068176,
0.0004062062653247267,
-0.03320055082440376,
-0.013425752520561218,
0.00857124850153923,
0.04850497096776962,
0.0051883733831346035,
0.02119002863764763,
0.005928338505327702,
0.010968703776597977,
-0.024127814918756485,
0.004205852746963501,
-0.026442641392350197,
-0.01328011229634285,
-0.017410220578312874,
0.036441102623939514,
-0.01805141754448414,
-0.029104841873049736,
-0.06716358661651611,
-0.029106315225362778,
-0.008038005791604519,
-0.01077587902545929,
0.018133586272597313,
-0.01258155144751072,
0.03285295143723488,
-0.010938119143247604,
0.02048630826175213,
-0.024754561483860016,
-0.021328577771782875,
-0.05753816291689873,
0.01437628734856844,
-0.004067415837198496,
0.014610391110181808,
0.008320978842675686,
0.019771721214056015,
-0.04132827743887901,
-0.009002558887004852,
0.04309699311852455,
-0.02800757624208927,
-0.034288350492715836,
-0.005374489352107048,
-0.0030560593586415052,
0.02438354678452015,
0.05837929993867874,
-0.00299126747995615,
-0.06022297590970993,
0.01307501271367073,
0.0009284680127166212,
-0.052067603915929794,
0.009204048663377762,
-0.002071668626740575,
0.009131478145718575,
0.014367799274623394,
-0.02252005599439144,
-0.03822092339396477,
0.07121917605400085,
-0.038736265152692795,
-0.01104305312037468,
-0.05333750322461128,
-0.01792249269783497,
0.051010068506002426,
-0.02102748677134514,
-0.008640747517347336,
-0.04052381590008736,
-0.020954612642526627,
0.05999439209699631,
0.0009842232102528214,
-0.00654352642595768,
-0.0025931703858077526,
-0.009091336280107498,
-0.011525413952767849,
-0.03424970805644989,
0.02290939725935459,
0.008200063370168209,
0.02213543839752674,
0.04749834164977074,
-0.015047095715999603,
0.030257228761911392,
0.0023735675495117903,
-0.02091033384203911,
-0.08990531414747238,
0.012853636406362057,
-0.023047735914587975,
-0.0035551288165152073,
0.0033255803864449263,
-0.06702131032943726,
0.048110805451869965,
0.02076100930571556,
-0.04816250875592232,
0.014484560117125511,
-0.023114290088415146,
0.01132716704159975,
-0.05503737926483154,
-0.008886181749403477,
-0.06266286224126816,
-0.00931509118527174,
-0.001200591097585857,
0.0122649185359478,
-0.012765337713062763,
0.026241427287459373,
0.0030775198247283697,
-0.02537352591753006,
-0.04446464031934738,
0.03987690433859825,
-0.0035561751574277878,
-0.01660943776369095,
0.06231940910220146,
0.03116106241941452,
-0.006028450094163418,
0.024531297385692596,
-0.014130284078419209,
-0.0023704690393060446,
0.006365636363625526,
0.026541847735643387,
-0.009390783496201038,
0.016341451555490494,
0.019335148856043816,
0.008952033706009388,
0.0010469509288668633,
0.027362070977687836,
0.04514694586396217,
-0.0049891117960214615,
-0.02163502387702465,
-0.0036080325953662395,
0.0426797978579998,
-0.0219753198325634,
-0.01798159070312977,
0.05061966925859451,
-0.014502912759780884,
-0.0021679482888430357,
0.025956619530916214,
0.005769414361566305,
0.06354371458292007,
-0.00008725012594368309,
0.007405078504234552,
-0.06461600214242935,
-0.0023962329141795635,
-0.004473037086427212,
-0.01926080882549286,
-0.009771027602255344,
-0.004729130305349827,
0.004497441928833723,
0.035692982375621796,
0.040750984102487564,
0.010569507256150246,
-0.007169634103775024,
-0.03168438374996185,
-0.016053788363933563,
-0.005911505781114101,
0.03740939125418663,
-0.030293406918644905,
-0.04983789846301079,
-0.02551867999136448,
-0.003416731022298336,
0.0009870105423033237,
0.03591732680797577,
0.011951182037591934,
-0.009544485248625278,
-0.0027922880835831165,
-0.04020760953426361,
0.038160327821969986,
-0.026354508474469185,
0.009556923061609268,
-0.04093308374285698,
-0.03286554664373398,
-0.02166602574288845,
0.01181307528167963,
0.09399538487195969,
0.02597515843808651,
-0.022942926734685898,
-0.020725416019558907,
0.02016131393611431,
0.015829235315322876,
-0.035522911697626114,
0.04152461141347885,
0.014866925776004791,
-0.014528399333357811,
0.015584058128297329,
-0.013349160552024841,
-0.05234825983643532,
0.02450188808143139,
0.06213734298944473,
-0.028155839070677757,
0.04299222677946091,
-0.0128872599452734,
-0.01640947163105011,
0.017773665487766266,
0.06524132937192917,
-0.02071523480117321,
0.03627245873212814,
-0.0021882180590182543,
0.009509129449725151,
-0.011817563325166702,
0.0012618866749107838,
-0.04915626719594002,
0.048082347959280014,
0.029034150764346123,
0.04139541834592819,
-0.025969984009861946,
0.020344797521829605,
0.012348221614956856,
-0.05358569324016571,
0.0029619489796459675,
-0.002824578434228897,
-0.021227598190307617,
0.0053311907686293125,
0.038067370653152466,
0.03327983617782593,
0.0031395377591252327,
-0.05812223255634308,
0.04928883910179138,
0.0026070009917020798,
-0.02208087220788002,
-0.03089054487645626,
0.04196823015809059,
0.0018456700490787625,
-0.004400694742798805,
0.016529977321624756,
-0.0039512524381279945,
0.014171662740409374,
0.04287642613053322,
0.0011764890514314175,
0.024663109332323074,
-0.0006795216468162835,
-0.02020658738911152,
0.04705750197172165,
0.011177366599440575,
-0.07955662906169891,
0.008619141764938831,
-0.018879495561122894,
0.0919298306107521,
0.002078455174341798,
0.010302538052201271,
-0.004786836449056864,
0.021203143522143364,
-0.015464999713003635,
0.03023921325802803,
0.03475518897175789,
0.04494823142886162,
-0.007612837012857199,
0.015846695750951767,
0.011988593265414238,
-0.023461516946554184,
0.03131061792373657,
-0.024065440520644188,
0.016729390248656273,
-0.02507278323173523,
0.028788115829229355,
-0.017233876511454582,
-0.010963200591504574,
0.008198676630854607,
-0.013303296640515327,
0.04170435667037964,
0.050411779433488846,
0.023798150941729546,
0.004045657813549042,
-0.037426020950078964,
-0.007042224518954754,
0.10002347826957703,
-0.04774021729826927,
-0.02769489772617817,
-0.02537032961845398,
0.030963320285081863,
0.01846228912472725,
-0.013347572647035122
] |
<p>The resultant force acting on a body in equilibrium is 0:</p>
<p>$$\iiint_R \rho {\bf b}\ dV + \iint_S {\bf t}^{(n)} ds = 0,$$</p>
<p>in which $R$ is a region inside the body, $\rho {\bf b}$ the body force per unit volume, $S$ the surface of the region and ${\bf t}^{(n)}$ the surface traction.</p>
<p>I am not quite sure what to make of all these parts... for example, let $R$ be a solid cube made from uniform material, resting on a table. In this case $S$ consists of the 6 faces of the cube, and $\rho$ is its (constant) density. </p>
<p>But what are ${\bf t}^{(n)}$ and $\bf b$?</p>
<p>It seems ${\bf t}^{(n)}$ should point upwards (against gravity) on every point on the bottom face of the cube, and be 0 on the other five faces. Also, I think $\bf b$ is the gravitational acceleration $g$... is this correct?</p>
| 10,784 |
[
-0.03251103684306145,
-0.006892468314617872,
-0.03168432414531708,
-0.03489021584391594,
-0.006309012416750193,
-0.003961348440498114,
-0.0062461490742862225,
0.029997605830430984,
-0.003980894107371569,
-0.034045204520225525,
0.016465025022625923,
0.024231381714344025,
0.05054629221558571,
0.06034854054450989,
0.021340757608413696,
-0.043394118547439575,
-0.005160920787602663,
-0.004763840232044458,
0.0015002358704805374,
-0.049087509512901306,
0.03392082080245018,
-0.0027398087549954653,
0.008639455772936344,
-0.011079334653913975,
0.0027034832164645195,
0.03733312338590622,
0.009516649879515171,
-0.037336159497499466,
0.04775987192988396,
0.06661263108253479,
-0.017200743779540062,
-0.0008775312453508377,
-0.02146710455417633,
-0.038151588290929794,
0.024266302585601807,
0.013405968435108662,
-0.04159009829163551,
-0.002547549782320857,
-0.023834586143493652,
0.03396976366639137,
-0.04556084796786308,
0.002553402679041028,
-0.01852690801024437,
0.025909515097737312,
-0.009468307718634605,
0.006650837138295174,
0.05487452447414398,
0.02182065322995186,
0.0291287861764431,
-0.0950213223695755,
0.06112566590309143,
0.028605114668607712,
0.0652584508061409,
0.047238174825906754,
-0.006434375420212746,
-0.03530511632561684,
0.05379759520292282,
0.04282595217227936,
0.013969441875815392,
-0.048997629433870316,
0.0025936723686754704,
-0.01060858741402626,
-0.026713963598012924,
-0.03747928887605667,
-0.029624028131365776,
0.04717910289764404,
-0.03291654214262962,
-0.013874487020075321,
0.041599053889513016,
-0.004858655389398336,
0.011370737105607986,
0.012762031517922878,
-0.005949993617832661,
-0.047649282962083817,
-0.011020313948392868,
-0.018401222303509712,
0.06329971551895142,
0.006536802276968956,
-0.011699745431542397,
-0.005679396912455559,
-0.006677344441413879,
0.03172967955470085,
0.029132569208741188,
0.07432790100574493,
0.01586071401834488,
-0.0017449659062549472,
0.0792238861322403,
-0.00652804272249341,
0.022588398307561874,
0.03560971841216087,
0.004715370014309883,
0.02111901342868805,
0.029118673875927925,
-0.038568656891584396,
-0.03158770874142647,
0.001037620473653078,
0.0166565403342247,
0.04449720308184624,
-0.026444923132658005,
-0.027659939602017403,
-0.023080045357346535,
-0.025858238339424133,
-0.039931073784828186,
0.06719991564750671,
-0.01115386188030243,
-0.026102710515260696,
-0.034285176545381546,
-0.005950404796749353,
0.020134834572672844,
-0.015833742916584015,
-0.03638190031051636,
-0.01357153058052063,
-0.035470377653837204,
-0.032728709280490875,
-0.027913233265280724,
-0.0067440783604979515,
0.0056640757247805595,
0.009954603388905525,
-0.0040134647861123085,
0.028124354779720306,
0.020936056971549988,
-0.016592448577284813,
0.024821022525429726,
-0.006524857599288225,
-0.1182292103767395,
0.01455663237720728,
0.04367872700095177,
-0.05292493477463722,
-0.0049699945375323296,
0.01554802805185318,
0.05483816936612129,
-0.04569418728351593,
0.019118214026093483,
0.019117332994937897,
0.03616056591272354,
-0.0017745912773534656,
-0.07658015191555023,
-0.04800787568092346,
0.052185483276844025,
0.0038985370192676783,
-0.01337410043925047,
-0.05722693353891373,
-0.011532661505043507,
0.04121226817369461,
0.03662819787859917,
-0.01764262653887272,
0.008693606592714787,
-0.012752881273627281,
0.01995372213423252,
-0.014098385348916054,
-0.029725434258580208,
-0.008638500235974789,
-0.0015956510324031115,
-0.05561549961566925,
-0.0024059871211647987,
-0.06567300111055374,
0.02754385769367218,
0.04025432839989662,
0.012891470454633236,
-0.04741400107741356,
0.03857912868261337,
-0.03080947883427143,
-0.02238827757537365,
0.019120220094919205,
-0.032989270985126495,
-0.018460191786289215,
0.031979747116565704,
-0.021606333553791046,
0.01916176825761795,
0.03375623747706413,
0.022292476147413254,
-0.002002008957788348,
0.01753607578575611,
0.03392328694462776,
0.031051017343997955,
-0.03382178023457527,
-0.019818544387817383,
-0.0418851263821125,
0.016216058284044266,
0.006546401418745518,
-0.03790361434221268,
-0.0386132188141346,
0.002536493120715022,
-0.0404328815639019,
-0.014291348867118359,
0.05437863618135452,
-0.024804159998893738,
-0.016502168029546738,
-0.037015851587057114,
-0.018588481470942497,
-0.03338947892189026,
-0.07361304759979248,
0.028554067015647888,
-0.01858776994049549,
0.0020359947811812162,
-0.0015748480800539255,
0.010540897957980633,
0.039086759090423584,
-0.01920367404818535,
0.013674693182110786,
-0.0031700998079031706,
0.026706228032708168,
0.00192827929276973,
-0.015057658776640892,
0.021729862317442894,
0.019718950614333153,
0.050041429698467255,
0.017631342634558678,
-0.0019631453324109316,
-0.009774154983460903,
0.013712243176996708,
-0.020451415330171585,
-0.015461589209735394,
0.03832220658659935,
-0.011297086253762245,
-0.01605117693543434,
0.03814391419291496,
-0.030091295018792152,
0.0042575993575155735,
0.038795631378889084,
-0.03435704857110977,
0.0665883868932724,
0.07404042035341263,
0.014806200750172138,
0.049779001623392105,
0.011128432117402554,
0.011129903607070446,
0.03571561351418495,
0.009122416377067566,
-0.01270265132188797,
-0.04236592352390289,
-0.01435440219938755,
-0.003098269458860159,
0.04530763253569603,
-0.01735582947731018,
0.0484011173248291,
0.02027234248816967,
0.009076327085494995,
0.010920250788331032,
0.014203316532075405,
-0.01516373734921217,
-0.04174729436635971,
0.0531059168279171,
0.012249124236404896,
0.018813397735357285,
0.020738869905471802,
-0.009378919377923012,
0.02988913469016552,
0.03959571570158005,
-0.022279774770140648,
-0.00399858970195055,
0.03370760381221771,
0.018080832436680794,
0.03330624848604202,
-0.022403137758374214,
-0.021573685109615326,
0.04358195886015892,
0.01108345203101635,
-0.001890838728286326,
0.01724427007138729,
0.02195669338107109,
0.0011318958131596446,
-0.06917698681354523,
-0.0298638716340065,
0.038346678018569946,
0.0023029912263154984,
0.0036013515200465918,
-0.052987124770879745,
0.021114407107234,
-0.04205993935465813,
-0.007886415347456932,
-0.00528579531237483,
-0.00019847400835715234,
0.0010416205041110516,
0.0012096997816115618,
0.03013298660516739,
0.0008964039152488112,
0.05241376906633377,
-0.028747674077749252,
0.00777039909735322,
0.02039945498108864,
-0.03152595832943916,
-0.006821848452091217,
0.03036118671298027,
-0.0786856934428215,
-0.019361617043614388,
-0.06478612869977951,
-0.03215107321739197,
0.05172505974769592,
0.019587725400924683,
-0.02211689203977585,
0.055742982774972916,
0.007058762013912201,
-0.029930004850029945,
-0.011485464870929718,
-0.012270261533558369,
0.005272855516523123,
-0.061635877937078476,
0.022767342627048492,
0.05350789800286293,
-0.003070379374548793,
-0.0031642557587474585,
0.03353309631347656,
-0.06097687408328056,
-0.043860651552677155,
-0.014825505204498768,
-0.016174547374248505,
-0.013332298025488853,
-0.019652510061860085,
-0.0031711584888398647,
0.04494776204228401,
-0.01998421549797058,
-0.007596299052238464,
-0.07519356906414032,
-0.030941132456064224,
0.021928653120994568,
-0.01755453087389469,
0.044832970947027206,
-0.0017283970955759287,
-0.06680510193109512,
0.08855142444372177,
0.008395454846322536,
-0.027678517624735832,
-0.00185367779340595,
-0.0321480929851532,
0.015532098710536957,
-0.03942576050758362,
0.0009524234337732196,
0.024149343371391296,
-0.006587795913219452,
-0.016302360221743584,
0.012203716672956944,
0.026994001120328903,
0.027392465621232986,
0.01838822476565838,
0.0031040937174111605,
0.015008428134024143,
0.03364920988678932,
-0.02421332336962223,
0.03961125388741493,
0.010475807823240757,
0.033049438148736954,
-0.004517677240073681,
-0.017914777621626854,
-0.002126444596797228,
0.014371148310601711,
-0.05810203775763512,
0.036393869668245316,
-0.008384240791201591,
-0.004492859356105328,
-0.012181329540908337,
0.01407358143478632,
0.005987777374684811,
-0.013226869516074657,
0.033874016255140305,
0.04604671895503998,
0.02609708160161972,
-0.03665836527943611,
-0.015790482982993126,
0.058525215834379196,
0.03899648040533066,
-0.02849864587187767,
-0.06481005251407623,
0.049728915095329285,
0.012439267709851265,
0.015887143090367317,
0.006752704735845327,
0.014874639920890331,
0.013471272774040699,
0.0081564299762249,
0.030544141307473183,
-0.0021411755587905645,
-0.023528406396508217,
-0.009234397672116756,
-0.06632320582866669,
0.010110467672348022,
0.011030900292098522,
0.06969839334487915,
-0.04365503787994385,
0.018504736945033073,
0.012718137353658676,
0.009254604578018188,
0.02219083346426487,
0.030284564942121506,
-0.07782857120037079,
0.031536366790533066,
-0.011040833778679371,
-0.025967776775360107,
0.017531773075461388,
0.023161055520176888,
0.012173510156571865,
-0.03696225583553314,
-0.02144576795399189,
0.010531269945204258,
0.02178935706615448,
-0.040864262729883194,
0.00813809223473072,
-0.023093819618225098,
-0.03509090095758438,
0.030355149880051613,
0.01954990066587925,
0.014739545062184334,
-0.049420688301324844,
0.01752636395394802,
0.051058292388916016,
0.016396639868617058,
0.001378508284687996,
0.009215573780238628,
-0.01980680413544178,
0.004854858387261629,
0.008655711077153683,
0.008032722398638725,
0.034052375704050064,
0.005985046271234751,
0.00007852548151277006,
-0.0000895870616659522,
0.0451008677482605,
-0.012330714613199234,
-0.01129376795142889,
-0.029830457642674446,
-0.03725973889231682,
-0.04489845782518387,
0.006154476664960384,
0.029595308005809784,
-0.004887966904789209,
-0.007174553349614143,
0.03214900568127632,
0.00833436194807291,
0.01373980101197958,
0.06819180399179459,
0.0635245069861412,
-0.01111024059355259,
-0.028027396649122238,
-0.03255767747759819,
-0.03090617060661316,
-0.0636950433254242,
-0.002542445668950677,
0.07138559967279434,
-0.0060571953654289246,
-0.03141293674707413,
-0.006114528514444828,
0.01976720616221428,
0.010190141387283802,
-0.012358957901597023,
0.017615096643567085,
0.03023136593401432,
0.05939710512757301,
-0.027121977880597115,
-0.000686909887008369,
0.020990634337067604,
0.027855176478624344,
0.01638183929026127,
0.0058968584053218365,
-0.010480000637471676,
-0.05738956481218338,
-0.0007211286574602127,
0.010916558094322681,
0.010318252258002758,
-0.02615046128630638,
0.014127487316727638,
-0.06376512348651886,
0.00013802175817545503,
0.026853840798139572,
-0.007207849062979221,
0.028282077983021736,
-0.0106170903891325,
0.013262767344713211,
0.00826514232903719,
0.010950365103781223,
-0.020871834829449654,
-0.0386832021176815,
-0.013557923957705498,
0.025662951171398163,
-0.021601883694529533,
0.005816812161356211,
0.020010532811284065,
0.025129541754722595,
0.026137281209230423,
0.03311791643500328,
0.007368936203420162,
-0.029204070568084717,
-0.007931416854262352,
0.003726795082911849,
-0.053364116698503494,
-0.0847277119755745,
0.01275869645178318,
0.0004157951334491372,
-0.0031322846189141273,
0.040501900017261505,
-0.010747152380645275,
-0.06991167366504669,
0.04389619454741478,
0.029542427510023117,
-0.00039843664853833616,
0.0167179387062788,
-0.045188795775175095,
0.04638839140534401,
0.046063829213380814,
-0.019607091322541237,
0.014227575622498989,
0.022156434133648872,
-0.0077074128203094006,
-0.007192115765064955,
0.01040438748896122,
0.02269870974123478,
-0.011052104644477367,
0.023219464346766472,
-0.0007311563822440803,
0.010297810658812523,
-0.024637393653392792,
-0.002788897603750229,
0.023451389744877815,
0.01797996461391449,
0.005583442747592926,
-0.024371137842535973,
-0.001931330538354814,
0.02288815565407276,
0.026745630428195,
0.017501119524240494,
0.05158371850848198,
0.03130344673991203,
0.025119176134467125,
-0.03134475275874138,
0.018404511734843254,
0.034724630415439606,
0.01757844351232052,
0.02861323021352291,
-0.004094102419912815,
0.0189518965780735,
-0.011462901718914509,
-0.011705544777214527,
-0.005994097329676151,
-0.07139763236045837,
0.09201429784297943,
0.00811487901955843,
0.02770269103348255,
0.037007447332143784,
-0.03424035757780075,
-0.0017573597142472863,
-0.007930146530270576,
0.0010401472682133317,
0.037015508860349655,
-0.0636051818728447,
0.029503537341952324,
0.03585262596607208,
0.02487664483487606,
-0.0636199563741684,
-0.013003828004002571,
0.04261220619082451,
0.022350408136844635,
-0.017857035622000694,
-0.009855878539383411,
-0.01055287104099989,
-0.012100367806851864,
-0.035344067960977554,
-0.0013349950313568115,
0.05214213207364082,
-0.03485489264130592,
-0.00207762373611331,
0.05262851342558861,
0.03326602652668953,
0.06160171702504158,
-0.00903669185936451,
0.0007078320486471057,
0.003799052909016609,
0.011803291738033295,
0.0038794479332864285,
-0.0005678535089828074,
0.06899531185626984,
-0.007189827039837837,
-0.02005445770919323,
0.00815706979483366,
0.007175023667514324,
0.02532411366701126,
-0.00844308827072382,
0.00004495587563724257,
0.003473375691100955,
0.01936335302889347,
-0.037716954946517944,
-0.005081305745989084,
0.02286587655544281,
0.004682580474764109,
0.028647633269429207,
-0.012983153574168682,
0.01684853434562683,
-0.007399184163659811,
-0.04093299061059952,
-0.006437235977500677,
-0.03446098417043686,
0.027891231700778008,
0.016142677515745163,
0.10639960318803787,
0.013396373949944973,
-0.031968459486961365,
-0.002485053613781929,
-0.03571770340204239,
0.06580035388469696,
0.013371167704463005,
-0.014483489096164703,
0.008164753206074238,
-0.035236161202192307,
-0.01287182979285717,
-0.02456326223909855,
-0.05022876337170601,
0.04146463796496391,
0.11020953953266144,
-0.023316867649555206,
0.08832383900880814,
0.030864670872688293,
-0.008763451129198074,
0.01562768779695034,
-0.00042213991400785744,
-0.010783753357827663,
0.004025425761938095,
0.010344193316996098,
0.035135503858327866,
-0.026701392605900764,
-0.009798615239560604,
0.017299307510256767,
0.008405900560319424,
-0.014541187323629856,
0.04202299565076828,
0.031905483454465866,
-0.003113456768915057,
-0.0021025699097663164,
0.00041922449599951506,
-0.028805069625377655,
0.05254023149609566,
-0.007629146799445152,
0.055212728679180145,
0.008041889406740665,
-0.029609760269522667,
0.05987023934721947,
0.04997856542468071,
0.019164711236953735,
-0.05911072716116905,
-0.038383614271879196,
-0.02711864374577999,
-0.0019092279253527522,
-0.0027395428624004126,
-0.004773144144564867,
-0.02155183255672455,
-0.02486085705459118,
0.031052278354763985,
-0.016023017466068268,
0.014874124899506569,
-0.00808324571698904,
-0.02991979755461216,
0.009442954324185848,
-0.03740904852747917,
-0.026299435645341873,
0.005105966702103615,
0.010075614787638187,
-0.009143182076513767,
0.026911556720733643,
-0.03866780549287796,
0.02667705900967121,
0.05951140075922012,
0.03993294760584831,
0.0164157934486866,
0.08882403373718262,
-0.01571645960211754,
0.006251574959605932,
-0.015760907903313637,
0.033313121646642685,
0.13794675469398499,
0.03687141835689545,
-0.0010794504778459668,
-0.02344588004052639,
0.0014444671105593443,
-0.02657439187169075,
-0.007021066267043352,
-0.03415362164378166,
0.000992845045402646,
-0.002670760964974761,
0.00011945678852498531,
-0.003405708819627762,
0.046057119965553284,
-0.0014379116473719478,
-0.029788509011268616,
0.013819679617881775,
-0.021327465772628784,
-0.047279711812734604,
-0.023523060604929924,
0.023937873542308807,
-0.024521350860595703,
-0.00720554031431675,
-0.03687712550163269,
0.0070101856254041195,
-0.0013363626785576344,
-0.025860711932182312,
-0.025080207735300064,
0.0008358791819773614,
0.0056954058818519115,
0.039786215871572495,
-0.07142835855484009,
0.02882533147931099,
-0.01802460290491581,
-0.026427747681736946,
-0.04743469879031181,
0.026380544528365135,
-0.004766255617141724,
-0.037267208099365234,
0.011949609965085983,
0.03371048346161842,
-0.007586617022752762,
0.02080449089407921,
0.05792384222149849,
0.007868406362831593,
-0.05105400085449219,
0.012449325993657112,
-0.03785283863544464,
0.03640897199511528,
-0.031138161197304726,
0.01735718548297882,
-0.002090464113280177,
-0.018772834911942482,
-0.008886178955435753,
-0.06359480321407318,
0.008298198692500591,
-0.02544335275888443,
0.029877858236432076,
-0.015361364930868149,
-0.03652646765112877,
0.005097313784062862,
0.01149059273302555,
-0.0016397197032347322,
-0.003762290347367525,
0.031400397419929504,
0.007502251770347357,
0.009758077561855316,
-0.020437059924006462,
0.069750115275383,
-0.037709563970565796,
0.01918337680399418,
-0.04970541596412659,
-0.012825063429772854,
-0.05221349000930786,
-0.003533251117914915,
-0.0016620461829006672,
0.05749410390853882,
0.028858445584774017,
0.010066214948892593,
-0.007987531833350658,
-0.03942418098449707,
-0.051240473985672,
0.03261138126254082,
-0.05489761382341385,
-0.01577884517610073,
-0.06262964010238647,
-0.04406377300620079,
0.015586243942379951,
0.018702028319239616,
-0.008085310459136963,
0.0018009759951382875,
0.004181867465376854,
0.03508877754211426,
-0.0016516601899638772,
-0.003563409438356757,
-0.013644877821207047,
0.0142129547894001,
0.019106600433588028,
0.005446815397590399,
0.025548774749040604,
-0.006695257965475321,
0.03873609006404877,
-0.007222465705126524,
-0.004116625990718603,
0.06031215563416481,
-0.012822252698242664,
0.03040277399122715,
-0.003984250593930483,
-0.010228105820715427,
0.0028512324206531048,
0.04902080446481705,
-0.017026593908667564,
-0.04487154260277748,
-0.025519248098134995,
-0.03336244076490402,
-0.015283960849046707,
0.0018678869819268584,
0.026479020714759827,
-0.03561463579535484,
-0.020382413640618324,
-0.0035850047133862972,
0.006358715705573559,
-0.038942985236644745,
0.01392629835754633,
-0.05841314047574997,
-0.02525177411735058,
0.029018966481089592,
0.029199061915278435,
-0.0264147836714983,
0.010535839945077896,
-0.0398135669529438,
0.0021713064052164555,
0.00797371193766594,
-0.013731446117162704,
0.03485293313860893,
-0.025433015078306198,
0.0021966961212456226,
0.005100090987980366,
0.025218795984983444,
0.003988285083323717,
-0.0229546669870615,
0.04649898782372475,
-0.013217857107520103,
-0.07003804296255112,
0.004404967185109854,
0.01891036331653595,
0.03502712771296501,
0.013713167048990726,
-0.01806560717523098,
-0.016647769138216972,
0.07964970916509628,
-0.03397354856133461,
0.026882009580731392,
-0.03060915134847164,
-0.03546589985489845,
-0.047367505729198456,
-0.04095909371972084,
-0.002892017364501953,
-0.008085285313427448,
0.01798090711236,
0.02390505000948906,
0.005180049687623978,
-0.017544183880090714,
-0.0034234127961099148,
0.012308289296925068,
-0.022010425105690956,
-0.02321404032409191,
-0.002541579771786928,
0.008707184344530106,
-0.012516039423644543,
0.02905277907848358,
-0.04384529963135719,
0.03675365447998047,
0.01088031381368637,
0.0026965138968080282,
-0.05829319357872009,
-0.04565460979938507,
-0.02106497250497341,
-0.014235778711736202,
0.043386805802583694,
-0.07368370145559311,
-0.0033995124977082014,
0.022378001362085342,
-0.04366523027420044,
0.031832147389650345,
-0.027163971215486526,
-0.0068297721445560455,
0.01301990170031786,
-0.010103997774422169,
0.010364982299506664,
0.014923467300832272,
-0.01081950031220913,
0.038610804826021194,
0.026260919868946075,
0.02993949130177498,
-0.018231287598609924,
-0.023518020287156105,
0.030266644433140755,
0.04796493053436279,
-0.005995635408908129,
-0.017029043287038803,
0.05884933099150658,
-0.024843405932188034,
-0.03667481616139412,
-0.003106883028522134,
-0.0012991720577701926,
0.0033603350166231394,
-0.015447141602635384,
0.009871360845863819,
-0.009821206331253052,
0.01835385337471962,
-0.001813296927139163,
-0.05252470448613167,
-0.019734052941203117,
0.055748239159584045,
0.004580407403409481,
0.004102416802197695,
-0.01871488243341446,
0.009370892308652401,
0.03884986788034439,
-0.021105661988258362,
-0.02691544033586979,
0.015177966095507145,
-0.0319923497736454,
-0.0018693216843530536,
-0.020156914368271828,
-0.012210335582494736,
0.041719745844602585,
-0.029778242111206055,
-0.008234639652073383,
-0.08613600581884384,
0.022927001118659973,
0.014277072623372078,
-0.0011904289713129401,
-0.025011874735355377,
0.015592074021697044,
0.01496050599962473,
0.0065736486576497555,
-0.015366659499704838,
-0.023998573422431946,
-0.025391217321157455,
-0.0573343001306057,
0.003745493246242404,
0.013046483509242535,
-0.04156315699219704,
-0.03178165480494499,
-0.026518860831856728,
0.008336572907865047,
0.023578232154250145,
0.024314910173416138,
0.02105575241148472,
0.02738921158015728,
-0.057781510055065155,
-0.008848274126648903,
-0.04893835261464119,
0.016985055059194565,
0.009936748072504997,
-0.059356916695833206,
-0.005597521550953388,
-0.020886460319161415,
0.009003140032291412,
-0.011085697449743748,
0.022866174578666687,
0.006881044711917639,
0.0122688515111804,
0.02091163583099842,
0.004016316030174494,
0.0018064663745462894,
-0.04258298873901367,
0.014630487188696861,
0.01596026122570038,
-0.010107425041496754,
-0.006712974049150944,
0.02697913348674774,
0.0076391734182834625,
-0.018354862928390503,
0.022728586569428444,
-0.03231317177414894,
0.02877775765955448,
-0.00811341404914856,
-0.04234931245446205,
0.03362162038683891,
0.02304397150874138,
-0.020555945113301277,
0.09146154671907425,
-0.04519379138946533,
0.008540069684386253,
0.008122137747704983,
-0.02976122312247753,
-0.016271503642201424,
0.04890034347772598,
-0.009545596316456795,
-0.005026177037507296,
-0.029842650517821312,
-0.0052374983206391335,
0.009938771836459637,
-0.015194914303719997,
-0.02311566472053528,
0.008170661516487598,
-0.027430454269051552,
0.00521116005256772,
0.027077438309788704,
0.04979810491204262,
0.028110850602388382,
-0.01752268150448799,
0.003979384899139404,
0.0064121331088244915,
-0.028959570452570915,
-0.020121322944760323,
0.010670878924429417,
0.06111889332532883,
-0.0014316822635009885,
-0.024912547320127487,
0.05813854932785034,
-0.05320863053202629,
0.02713186666369438,
0.027686946094036102,
0.0019712867215275764,
-0.012669187970459461,
-0.035705193877220154,
0.016049828380346298,
-0.014844562858343124,
0.004066240042448044,
-0.013208158314228058,
-0.012443176470696926,
0.09640476107597351,
-0.011187436059117317,
-0.004884222522377968,
-0.01010393537580967,
-0.008467050269246101,
-0.015162093564867973,
0.0353156141936779,
0.010304671712219715,
0.04475296288728714,
-0.02290051430463791,
-0.014680602587759495,
-0.01125529408454895,
-0.012929324060678482,
0.025309622287750244,
-0.000308654474793002,
0.022476939484477043,
-0.009407168254256248,
0.014997213147580624,
-0.006856015417724848,
-0.035172007977962494,
-0.01634664461016655,
-0.009003287181258202,
0.046709902584552765,
0.033535800874233246,
0.009472141973674297,
-0.033858515322208405,
0.028586525470018387,
-0.04867690056562424,
0.04757985845208168,
-0.09015519171953201,
-0.05850546434521675,
-0.019746137782931328,
0.022978462278842926,
0.009944051504135132,
0.012558876536786556
] |
<p>I was concerned about what determines the speed of the bullet coming out from the gun.</p>
<p>Is it determined by the strength of the explosive or how fast does it burn up?</p>
<p>For example if we take the same amount of gun powder and a plastic explosive (probably TNT) in a bullet shell which bullet will go further the one with the plastic explosive or the one with the gun powder</p>
| 10,785 |
[
-0.05158170685172081,
-0.013242071494460106,
0.0013115743640810251,
-0.03852229565382004,
0.02350996620953083,
0.005865361541509628,
-0.01980331353843212,
-0.025772029533982277,
0.023430300876498222,
-0.009854685515165329,
0.018724210560321808,
0.06015589460730553,
0.0600583516061306,
0.018229197710752487,
-0.016326166689395905,
0.008051571436226368,
0.009156589396297932,
0.0008130549686029553,
0.010328060016036034,
-0.03372655063867569,
-0.025314509868621826,
-0.005685755517333746,
-0.005033787339925766,
-0.007522711995989084,
-0.014600470662117004,
0.02868068218231201,
0.04744270443916321,
0.02262074314057827,
0.028996093198657036,
0.013651905581355095,
0.019022133201360703,
-0.03867058455944061,
0.03820698335766792,
0.03300534188747406,
0.018026143312454224,
0.02008945122361183,
-0.05755461007356644,
-0.04830110818147659,
-0.009806429035961628,
0.01310933381319046,
-0.016882117837667465,
-0.010090637020766735,
0.037408508360385895,
0.026358911767601967,
-0.02248799242079258,
0.05817033722996712,
-0.04419080540537834,
-0.0347391776740551,
0.043333034962415695,
-0.0456106960773468,
0.04877769574522972,
0.01162668690085411,
0.03176046535372734,
0.042291805148124695,
-0.010244518518447876,
0.01189389731734991,
0.07097925245761871,
0.0742863118648529,
-0.04150390625,
-0.06074969470500946,
0.0023004505783319473,
-0.002840082161128521,
-0.00315279234200716,
-0.0405808687210083,
-0.001351859187707305,
0.03609223663806915,
-0.02458503097295761,
-0.035207971930503845,
-0.002537334803491831,
-0.02348262257874012,
0.0055570704862475395,
-0.022034430876374245,
0.047832854092121124,
-0.004453888162970543,
0.01404502708464861,
-0.03266977518796921,
0.02796175889670849,
0.048210710287094116,
0.005040715914219618,
0.054609134793281555,
-0.04536287859082222,
-0.013653697445988655,
0.017515331506729126,
0.021399443969130516,
0.030246159061789513,
-0.026697127148509026,
0.06289143860340118,
0.012926378287374973,
-0.0073084961622953415,
0.028964892029762268,
-0.0032846659887582064,
0.013730884529650211,
0.004084781277924776,
-0.008279523812234402,
0.007336448412388563,
0.0376659519970417,
-0.011697208508849144,
0.07241865247488022,
0.037230268120765686,
-0.013192648999392986,
0.00281630945391953,
-0.0036358770448714495,
0.05016430467367172,
0.05957481637597084,
0.013203944079577923,
-0.024428946897387505,
-0.014145824126899242,
-0.009280982427299023,
-0.005091046914458275,
0.025279637426137924,
-0.040162988007068634,
0.03852385655045509,
0.01563558541238308,
-0.016323234885931015,
-0.018162772059440613,
-0.003972403239458799,
0.015886973589658737,
-0.024617645889520645,
0.03919713571667671,
0.00058573397109285,
0.04020087048411369,
-0.018528584390878677,
-0.005491023417562246,
-0.0073712547309696674,
-0.048741985112428665,
-0.027842236682772636,
0.040096648037433624,
-0.02906692773103714,
-0.006594136822968721,
0.0476229190826416,
0.014096814207732677,
-0.041117314249277115,
0.003622916992753744,
-0.014965669251978397,
0.03331247717142105,
0.00015386640734504908,
-0.10870464891195297,
-0.07594484090805054,
0.0507504940032959,
0.00219172821380198,
-0.02236570604145527,
-0.0898895114660263,
-0.006975973956286907,
0.004653265234082937,
0.04631703346967697,
-0.013431616127490997,
0.004244884941726923,
-0.007631312590092421,
0.015674449503421783,
-0.0016767287161201239,
-0.0018796829972416162,
-0.02423418127000332,
0.03327718749642372,
-0.011800148524343967,
0.020797915756702423,
-0.04500672593712807,
0.02552039548754692,
0.028920529410243034,
-0.016327012330293655,
0.0013550252187997103,
0.028206225484609604,
-0.06492454558610916,
-0.0027273886371403933,
0.009851031936705112,
0.024122364819049835,
-0.034826986491680145,
0.0358656570315361,
0.024709858000278473,
-0.027047669515013695,
0.02210315130650997,
0.022872116416692734,
0.040855247527360916,
0.03922567516565323,
-0.02786603383719921,
0.00786819588392973,
-0.037303581833839417,
-0.0316929891705513,
-0.023901386186480522,
-0.016340812668204308,
0.01731226034462452,
-0.04982266202569008,
-0.022876355797052383,
-0.000138397459522821,
0.01519541721791029,
0.06369113177061081,
0.023947175592184067,
0.03507222607731819,
0.02628806047141552,
-0.013658762909471989,
-0.00804432388395071,
-0.01841818541288376,
-0.0975446105003357,
0.06247914955019951,
0.008421896025538445,
-0.015172434970736504,
0.023099912330508232,
-0.021077681332826614,
0.005881538148969412,
0.011800563894212246,
0.024440793320536613,
-0.013783465139567852,
0.02517244592308998,
-0.02729189209640026,
-0.03591665253043175,
-0.01933232694864273,
0.07729727029800415,
-0.0122099993750453,
0.0044374666176736355,
0.044408004730939865,
-0.0006035119295120239,
-0.026511909440159798,
0.018188215792179108,
-0.02115718647837639,
-0.008966945111751556,
0.0015234819147735834,
-0.01687198132276535,
-0.0016949918353930116,
0.007271524518728256,
0.01632068306207657,
0.025945870205760002,
-0.005988795775920153,
0.10367679595947266,
0.049283143132925034,
-0.04358670487999916,
-0.009470789693295956,
0.04182417318224907,
0.0005075655062682927,
0.015087047591805458,
0.013242250308394432,
-0.022468969225883484,
-0.05971003696322441,
-0.029591811820864677,
0.0023793429136276245,
0.013216905295848846,
-0.03256919980049133,
0.015382279641926289,
0.026210594922304153,
0.008460812270641327,
0.016018085181713104,
0.04783789440989494,
-0.029353654012084007,
-0.048837680369615555,
-0.016034895554184914,
0.014949609525501728,
-0.018561771139502525,
0.006416529882699251,
-0.00673125172033906,
0.0005715519073419273,
0.004675416741520166,
-0.028053365647792816,
0.0078041129745543,
0.058926187455654144,
0.014277579262852669,
-0.027540383860468864,
0.01776544190943241,
-0.03923237696290016,
0.019511204212903976,
-0.007481173146516085,
0.03814566507935524,
0.015144620090723038,
0.041089970618486404,
0.03300156444311142,
-0.03176772966980934,
0.0038921150844544172,
0.00218105036765337,
0.01489671878516674,
0.025505306199193,
-0.0007464659865945578,
0.02610265091061592,
-0.05346668139100075,
-0.008320185355842113,
0.006783063057810068,
0.004679495934396982,
-0.023405244573950768,
0.006152694579213858,
0.027073301374912262,
0.03373809903860092,
0.022933032363653183,
-0.01250513643026352,
-0.04931461438536644,
-0.005815420299768448,
-0.05586419254541397,
0.014125132001936436,
-0.025470640510320663,
-0.026814378798007965,
0.005286869592964649,
-0.018633056432008743,
-0.047833152115345,
0.030007226392626762,
-0.01759963668882847,
0.013463032431900501,
0.06166554242372513,
-0.02476903796195984,
-0.06668423116207123,
0.0018915365217253566,
0.011081076227128506,
0.014744887128472328,
-0.0183111485093832,
-0.0005014677299186587,
0.04467180371284485,
-0.0032385585363954306,
-0.03901108726859093,
0.020133426412940025,
-0.014629362151026726,
-0.0251710657030344,
-0.024132153019309044,
-0.008160272613167763,
0.028936443850398064,
0.013543589971959591,
-0.015095323324203491,
0.05560312792658806,
-0.020839013159275055,
-0.005633259192109108,
-0.045321933925151825,
-0.019401218742132187,
0.05909835919737816,
-0.0010445320513099432,
0.06505060940980911,
-0.01193933840841055,
-0.033133093267679214,
0.08256929367780685,
0.05109580233693123,
0.000027801714168163016,
-0.027053266763687134,
-0.03599466010928154,
-0.00719838822260499,
-0.027437662705779076,
0.03965006023645401,
0.039727114140987396,
-0.0008258060552179813,
0.030804071575403214,
0.017882414162158966,
0.06117391213774681,
0.049091991037130356,
-0.02425604686141014,
0.022134793922305107,
0.010715911164879799,
0.005577602423727512,
-0.00011203184840269387,
0.021076761186122894,
0.04021390527486801,
-0.023185258731245995,
0.03707185015082359,
-0.04284257814288139,
0.07448592782020569,
0.018693240359425545,
-0.03658280521631241,
0.02394389919936657,
0.026901166886091232,
-0.05705403909087181,
-0.02154454030096531,
0.0352703221142292,
-0.025541000068187714,
-0.0022902966011315584,
-0.008781987242400646,
0.028865225613117218,
0.038547661155462265,
-0.000532529957126826,
0.016983864828944206,
-0.02235601469874382,
0.045090071856975555,
-0.025563009083271027,
-0.016054833307862282,
0.007439573761075735,
0.0050434693694114685,
0.03620580956339836,
0.02159564383327961,
0.013576989993453026,
0.031874485313892365,
-0.0040656570345163345,
0.002747288206592202,
-0.01683824323117733,
-0.010165189392864704,
0.013159306719899178,
-0.08618345111608505,
-0.008906911127269268,
-0.012132629752159119,
0.04387269914150238,
-0.016279609873890877,
0.12700466811656952,
0.009083525277674198,
0.029532596468925476,
0.03314085677266121,
0.0029560194816440344,
-0.08491586148738861,
0.023456040769815445,
-0.03734641522169113,
-0.04303592070937157,
-0.03596166893839836,
-0.01671658456325531,
-0.041971635073423386,
-0.018116982653737068,
-0.030688486993312836,
-0.018732134252786636,
-0.03821518272161484,
-0.060913294553756714,
0.046987295150756836,
-0.04078834876418114,
-0.031791456043720245,
-0.003137953346595168,
0.041669491678476334,
0.0052855717949569225,
0.02497411146759987,
0.045898113399744034,
0.020763741806149483,
-0.025251924991607666,
0.01911860518157482,
-0.029292277991771698,
0.0001975302438950166,
0.028690410777926445,
0.06902601569890976,
-0.029952112585306168,
-0.0023474697954952717,
0.012790080159902573,
0.020551064983010292,
0.012336191721260548,
0.021380968391895294,
0.007840963080525398,
0.018150724470615387,
-0.08249086886644363,
-0.05428445711731911,
0.006606384180486202,
-0.008506323210895061,
0.035174015909433365,
-0.01549337338656187,
-0.00645518209785223,
0.0309466402977705,
-0.008918761275708675,
0.0021890404168516397,
0.02265857718884945,
0.04306618869304657,
0.0019939178600907326,
0.008671609684824944,
-0.05308998003602028,
-0.004949522670358419,
-0.010491213761270046,
-0.026544837281107903,
-0.010118930600583553,
0.016604144126176834,
-0.011214833706617355,
0.01953890547156334,
0.05126618966460228,
-0.01670999638736248,
-0.021010152995586395,
0.028754938393831253,
-0.0031573039013892412,
0.005818009842187166,
-0.004220105707645416,
0.0032989492174237967,
0.049827903509140015,
0.02512127161026001,
0.039356354624032974,
0.01298347394913435,
-0.023452382534742355,
-0.05133521556854248,
-0.01390113029628992,
0.044205863028764725,
0.02221798337996006,
-0.05082247406244278,
-0.0064646112732589245,
-0.034945905208587646,
-0.028055867180228233,
0.03143980726599693,
0.008909906260669231,
0.017093824222683907,
0.00026368984254077077,
-0.0069543360732495785,
-0.031924642622470856,
-0.035401735454797745,
-0.040880076587200165,
0.01949390396475792,
0.011796590872108936,
-0.015411809086799622,
-0.035883110016584396,
0.01014800276607275,
-0.02346828766167164,
0.03084852360188961,
0.03945544734597206,
0.02470468357205391,
-0.0072339666076004505,
-0.006053415592759848,
0.0003894958063028753,
-0.023949170485138893,
0.0032433040905743837,
-0.06063481792807579,
0.015812980011105537,
-0.0071035148575901985,
-0.0051279631443321705,
0.03661326318979263,
-0.021132292225956917,
-0.03588717058300972,
0.040073707699775696,
-0.0003815419040620327,
-0.012543190270662308,
0.020282164216041565,
-0.04352625086903572,
0.030084997415542603,
0.009166141971945763,
-0.03880438953638077,
0.0002793861785903573,
0.033620741218328476,
-0.008517549373209476,
-0.00041678230627439916,
-0.008162115700542927,
0.026257917284965515,
-0.03508007898926735,
0.002285958966240287,
-0.04070012643933296,
0.02970702387392521,
-0.03557803854346275,
0.012949518859386444,
0.029290780425071716,
0.005274748429656029,
-0.0032172389328479767,
-0.040426790714263916,
0.0015264487592503428,
-0.004098528064787388,
0.007095928303897381,
0.027195056900382042,
-0.011335892602801323,
0.023105069994926453,
-0.012313731014728546,
0.00776287168264389,
-0.010499486699700356,
0.047464221715927124,
0.01715848408639431,
0.05225507915019989,
-0.0448179617524147,
-0.02274315617978573,
-0.038051072508096695,
-0.029484113678336143,
0.015136855654418468,
-0.01844888925552368,
0.09636371582746506,
0.011842092499136925,
-0.022922756150364876,
0.019655469805002213,
-0.04515543207526207,
-0.033712439239025116,
0.012738796882331371,
0.01562455203384161,
0.03879595920443535,
-0.06946735084056854,
0.06928935647010803,
-0.013770204037427902,
-0.0042282771319150925,
-0.047085899859666824,
-0.03536045551300049,
0.05009297654032707,
-0.01400180533528328,
-0.024089226499199867,
-0.03207920491695404,
0.033825311809778214,
-0.016573017463088036,
-0.025390353053808212,
0.045238301157951355,
0.06135395169258118,
0.0004142996622249484,
-0.03131109103560448,
0.010809940285980701,
-0.01591501384973526,
0.06104958802461624,
0.022626491263508797,
-0.023938683792948723,
0.01235472597181797,
0.0019144922262057662,
0.01398625411093235,
-0.0021421965211629868,
0.06032901257276535,
-0.008263691328465939,
-0.005328512750566006,
-0.011659407056868076,
-0.008839920163154602,
0.0442739836871624,
-0.038842279464006424,
0.037016600370407104,
0.015536925755441189,
0.028755739331245422,
-0.019054308533668518,
-0.013482991605997086,
0.023949934169650078,
0.0016070370329543948,
0.026363568380475044,
-0.021099034696817398,
0.01869148388504982,
-0.03907109797000885,
-0.044166162610054016,
0.016223624348640442,
0.017970073968172073,
0.0310590248554945,
-0.015099127776920795,
0.04372566193342209,
-0.006240552756935358,
-0.0024012501817196608,
0.026640096679329872,
-0.00633968273177743,
0.051200054585933685,
-0.00794578343629837,
-0.023788439109921455,
0.001690973062068224,
-0.0006644026725552976,
-0.0006961506442166865,
-0.021301111206412315,
-0.006734867580235004,
-0.01517200656235218,
0.01557182427495718,
-0.04588887840509415,
0.03903770446777344,
0.004388923291116953,
0.006348132621496916,
0.009000575169920921,
-0.017796238884329796,
0.00801861472427845,
-0.016009053215384483,
-0.012565006501972675,
0.012217194773256779,
-0.004948394373059273,
0.008729398250579834,
0.032402124255895615,
0.05297685042023659,
-0.0268748477101326,
-0.03948836028575897,
0.02876075729727745,
-0.024622155353426933,
0.006741681601852179,
-0.040180884301662445,
-0.04094933718442917,
0.021549103781580925,
-0.040079329162836075,
0.03834161534905434,
0.00040390671347267926,
0.009204407222568989,
0.05110126733779907,
0.008162611164152622,
-0.010417628102004528,
-0.03799665719270706,
0.012938565574586391,
-0.03382836654782295,
-0.024331143125891685,
0.008459703996777534,
0.004401843529194593,
-0.0006979833706282079,
-0.014859075658023357,
0.047278039157390594,
-0.01150950975716114,
0.01410475093871355,
-0.025325648486614227,
-0.05035918951034546,
-0.009426218457520008,
-0.02279309183359146,
-0.053117264062166214,
0.02326231263577938,
-0.04299400374293327,
-0.01586645096540451,
0.032660044729709625,
-0.013458874076604843,
0.023583166301250458,
-0.008066886104643345,
0.04899212718009949,
-0.010917357169091702,
0.11688556522130966,
0.015394746325910091,
-0.023311521857976913,
-0.00013636317453347147,
0.044266387820243835,
0.11520083248615265,
0.014269083738327026,
0.0210482906550169,
-0.029681971296668053,
-0.016200829297304153,
-0.01127916481345892,
0.023543989285826683,
0.012562473304569721,
0.0036974630784243345,
0.011367487721145153,
0.018017277121543884,
0.020260648801922798,
0.0582919679582119,
-0.03371574729681015,
0.002689685206860304,
0.029660381376743317,
-0.0351940281689167,
-0.022791896015405655,
0.011162623763084412,
0.022217612713575363,
-0.0041018384508788586,
0.02309628389775753,
0.012809053994715214,
0.009436541236937046,
-0.009147063829004765,
-0.01616550050675869,
-0.02204650454223156,
-0.06957463920116425,
0.024062782526016235,
-0.016111809760332108,
-0.056921858340501785,
-0.024780021980404854,
0.009018424898386002,
-0.03080124594271183,
-0.04393578693270683,
0.03219201788306236,
0.038133639842271805,
-0.0158557016402483,
-0.019973760470747948,
0.011572146788239479,
0.042859770357608795,
0.0068008736707270145,
0.009074820205569267,
0.005855229217559099,
-0.06305515766143799,
0.016407059505581856,
-0.013372025452554226,
0.0012320067035034299,
-0.02366456389427185,
0.0019071357091888785,
-0.0021458708215504885,
0.013767036609351635,
0.03753591328859329,
-0.0630192756652832,
-0.042755771428346634,
0.03071230836212635,
0.043765049427747726,
0.0037788143381476402,
-0.025931574404239655,
-0.06363751739263535,
0.010198800824582577,
-0.03246143087744713,
0.0001118053260142915,
-0.001590445637702942,
0.019876085221767426,
-0.008998562581837177,
-0.006249557249248028,
0.038045838475227356,
-0.03663962706923485,
-0.026075713336467743,
0.0055823372676968575,
0.011786195449531078,
-0.046262964606285095,
0.01485402137041092,
0.013859760947525501,
0.04160972684621811,
0.013330906629562378,
0.0069237663410604,
0.0023803687654435635,
-0.02313537523150444,
-0.10034503787755966,
0.05260086432099342,
-0.003338292008265853,
0.011456561274826527,
-0.05608723312616348,
-0.007509205956012011,
0.04337319731712341,
0.03616912290453911,
-0.023305319249629974,
0.024654868990182877,
-0.024548502638936043,
0.05390186980366707,
0.05243690311908722,
-0.06474638730287552,
0.00400713924318552,
0.057225532829761505,
-0.014097140170633793,
0.033470429480075836,
-0.017085615545511246,
0.012351476587355137,
0.015028194524347782,
0.0025842085015028715,
0.01977096125483513,
-0.007130781188607216,
-0.005009778775274754,
0.02579714171588421,
0.013419601134955883,
-0.010273519903421402,
-0.03909970819950104,
0.03615834563970566,
0.010180814191699028,
0.008878731168806553,
-0.02267928421497345,
-0.05708816647529602,
-0.005328490864485502,
-0.014817669987678528,
0.003812953596934676,
0.015130664221942425,
0.01837823912501335,
-0.042217157781124115,
-0.0016325131291523576,
-0.03922976553440094,
0.012039369903504848,
-0.012946897186338902,
-0.018258750438690186,
0.027480145916342735,
-0.015171105973422527,
-0.03825214132666588,
0.024672312662005424,
-0.050011247396469116,
-0.016540346667170525,
0.004839743487536907,
-0.010688796639442444,
0.01541415136307478,
-0.01210777647793293,
-0.010606527328491211,
-0.005248486530035734,
0.057583581656217575,
0.004730032756924629,
-0.02273854799568653,
0.02094395086169243,
-0.01845516636967659,
-0.049682632088661194,
0.01782592572271824,
-0.011289483867585659,
0.029434913769364357,
-0.008906505070626736,
-0.01831001602113247,
0.009081246331334114,
0.10120624303817749,
-0.011856411583721638,
-0.01623280718922615,
0.0013823916669934988,
-0.027280619367957115,
0.03846694156527519,
0.0016151821473613381,
-0.0039552198722958565,
-0.023526614531874657,
0.002368489047512412,
0.04195784777402878,
-0.011082065291702747,
-0.022559866309165955,
0.01556838396936655,
0.03464122861623764,
-0.04003448039293289,
0.018870841711759567,
0.013603518716990948,
0.0147865554317832,
0.06266362965106964,
0.0349433496594429,
0.010078013874590397,
0.025395529344677925,
0.004950086120516062,
-0.03690547123551369,
-0.09419924765825272,
-0.005008187144994736,
-0.01766807772219181,
0.016662390902638435,
0.025094041600823402,
-0.04617957025766373,
0.01964464969933033,
0.04161876440048218,
-0.07082334905862808,
-0.03769867122173309,
-0.04023626819252968,
-0.013519113883376122,
-0.05728166177868843,
-0.030792856588959694,
-0.0018003885634243488,
0.025603992864489555,
0.03107624500989914,
0.031245632097125053,
0.03780593350529671,
0.02863464504480362,
-0.029256286099553108,
0.007477176375687122,
0.009530487470328808,
0.006071658805012703,
0.02709324099123478,
0.010568340308964252,
0.05714945122599602,
-0.04327022284269333,
0.007960803806781769,
0.006886829622089863,
-0.0034081798512488604,
0.035329535603523254,
0.0022099309135228395,
0.005891995504498482,
0.034282803535461426,
0.029493559151887894,
0.01355879195034504,
0.012475799769163132,
-0.002342849737033248,
0.056966956704854965,
0.00615899171680212,
0.01773938722908497,
-0.04856684058904648,
0.0121050626039505,
0.005980490241199732,
-0.01966235041618347,
-0.013190265744924545,
0.02446027845144272,
-0.02825429104268551,
-0.029982883483171463,
0.019405251368880272,
-0.016429686918854713,
0.018302876502275467,
0.004062080290168524,
-0.0007093641324900091,
0.004151537548750639,
-0.02053018845617771,
0.026965999975800514,
0.023543886840343475,
-0.01936730369925499,
0.03460932523012161,
-0.038319773972034454,
-0.02848619408905506,
-0.014698119834065437,
0.006574590224772692,
-0.02257450297474861,
-0.021724816411733627,
0.01474406011402607,
0.046199824661016464,
0.0019843080081045628,
0.0004650930059142411,
-0.014289634302258492,
-0.01223176158964634,
0.051231496036052704,
0.02686495892703533,
0.01777537167072296,
-0.013141400180757046,
-0.021885734051465988,
-0.031642552465200424,
-0.0436328686773777,
0.02579696662724018,
0.007612379267811775,
-0.012218513526022434,
-0.04177895560860634,
-0.06720933318138123,
0.01592511497437954,
0.015636170282959938,
0.08141372352838516,
-0.04613277688622475,
-0.050210125744342804,
0.02726156637072563,
-0.025620799511671066,
0.006578098051249981,
-0.05682530254125595,
-0.004436987452208996,
-0.017525052651762962,
-0.008847459219396114,
-0.050792593508958817,
-0.0015270393341779709,
-0.047988492995500565,
0.04236364737153053,
0.02280307188630104,
0.00586771871894598,
-0.04438246786594391,
-0.03605383262038231,
-0.022032812237739563,
0.045806437730789185,
0.044999491423368454,
-0.02685227431356907,
0.06583858281373978,
-0.016957752406597137,
-0.009912123903632164,
0.0288010835647583,
-0.0004753984685521573,
-0.05456256866455078,
0.007537064608186483,
0.002220979193225503,
-0.005713712424039841,
0.014912089332938194,
-0.044644277542829514,
0.0064226677641272545,
-0.061582453548908234,
-0.0025654251221567392,
0.0201491080224514,
-0.02327563613653183,
-0.00826650857925415,
0.01867513172328472,
0.04654698818922043,
0.04658928140997887,
-0.044862132519483566,
0.039275117218494415,
0.02601999044418335,
-0.008280397392809391,
-0.03787248581647873,
0.011809214018285275,
0.010636357590556145,
-0.021478042006492615,
-0.010891907848417759,
0.015204147435724735,
-0.008504596538841724,
0.002527964999899268,
0.035331182181835175,
0.017882220447063446,
-0.03743433952331543,
-0.03564918041229248,
0.014310363680124283,
-0.04985973238945007,
0.026813840493559837,
0.02152092009782791,
-0.05562020093202591,
0.048043444752693176,
-0.006632429547607899,
-0.0001662490685703233,
-0.01670934073626995,
0.04634831100702286,
-0.03373724967241287,
-0.003942633513361216,
-0.0007623896235600114,
-0.015395166352391243,
0.00962537806481123,
-0.013433882035315037,
0.009500234387814999,
0.01583978161215782,
0.0322364903986454,
-0.022549839690327644,
0.011660092510282993,
-0.012967261485755444,
-0.036705635488033295,
-0.05764824151992798,
0.004335201345384121,
-0.034249525517225266,
0.005654467269778252,
0.0610334575176239,
0.03814942389726639,
-0.024515915662050247,
0.005755096208304167,
-0.008210130967199802,
-0.02994382195174694,
0.01532351691275835,
-0.040658533573150635,
0.009716497734189034,
-0.054323308169841766,
0.01616874895989895,
-0.025667812675237656,
-0.018487025052309036
] |
<p>Consider a parallel-plate capacitor. Charge is stored physically on electrodes ("plates") which are flat and parallel to one another. If one electrode has charge $+Q$ and the other electrode has charge $-Q$, and $V$ is the potential difference between the electrodes, then the capacitance $C$ is $$C = \frac{Q}{V}$$</p>
<p>(This definition of $C$ is given in, for example, <em>Introduction to Electrodynamics</em> by David J. Griffiths.)</p>
<p>But, now, let's think about the energy stored in the electric field between the electrodes of this parallel-plate capacitor. As stated in Griffiths on page 105, "How much work $W$ does it take to charge the capacitor up to a final amount $Q$?" It turns out that $W$ is $$W = \frac{1}{2} CV^2$$</p>
<p>So:</p>
<p>(i) the capacitor's capacitance $C$ goes like $\frac{1}{V}$; and </p>
<p>(ii) the energy $W$ stored in the electric field goes like $V^2$. </p>
<p><strong>Are statements (i) and (ii) at odds with one another?</strong> I am sure that they <em>cannot</em> be. But conceptually I am having difficulty.</p>
<p>We desire high capacitance -- we want to put as much charge on the electrodes as possible, because if we accomplish this, then I think that will increase the energy density of the system. But is what I just said true?</p>
<p>If we manage to increase $Q$, then by $V = \frac{Q}{C}$, the potential difference $V$ between the plates will also increase. This, I think, is why capacitor electrodes are separated by a material (such as a polarizable dielectric material like a slab of plastic); otherwise $V$ will become too large and the breakdown voltage will be reached, generating a spark.</p>
<p>But, now, the equation $W = \frac{1}{2} CV^2$ (where I think that $W$ can be conceptualized as the energy stored in the electric field between the electrodes) seems to say that as $V$ increases, so does the energy $W$, quadratically.</p>
<p>So, my question is, <strong>do we want a capacitor to have a <em>large</em> potential difference $V$ or a <em>small</em> potential difference $V$?</strong> If $V$ is large, then $W$ is large (which we want), but $C$ is small (which we do <strong><em>not</em></strong> want).</p>
<p>Am I somehow thinking of two different potential differences $V$ and confusing them?</p>
| 10,786 |
[
-0.03757542744278908,
-0.01948375068604946,
0.04655931517481804,
-0.02407344989478588,
0.030833717435598373,
-0.02156968228518963,
-0.010226408019661903,
-0.021854693070054054,
0.0243076104670763,
-0.02050359733402729,
-0.002729295752942562,
0.031608495861291885,
0.043482374399900436,
0.011657064780592918,
0.0072659715078771114,
0.001732564764097333,
0.026023661717772484,
-0.03414011001586914,
0.013205279596149921,
-0.010993625037372112,
-0.022688554599881172,
0.02794840931892395,
-0.019123166799545288,
0.023763589560985565,
-0.004217938054352999,
0.036772921681404114,
0.007845678366720676,
-0.00755581259727478,
-0.023855319246649742,
0.04116011783480644,
-0.006386290770024061,
-0.030834969133138657,
0.02177342399954796,
-0.00733555294573307,
0.02544431760907173,
0.012195473536849022,
-0.03266650065779686,
-0.046948038041591644,
0.009723140858113766,
0.035427600145339966,
-0.0060554854571819305,
0.016860753297805786,
-0.008688878268003464,
0.04101736471056938,
-0.017193524166941643,
0.000265237846178934,
0.02340906299650669,
-0.027836676687002182,
0.015274811536073685,
-0.06159093230962753,
0.03754635527729988,
-0.0068116155453026295,
0.054533060640096664,
0.05409742891788483,
-0.016805900260806084,
-0.016823995858430862,
0.07480166107416153,
0.06456691771745682,
0.013346812687814236,
-0.039419542998075485,
-0.011543026193976402,
0.01552107185125351,
-0.026685701683163643,
-0.030151616781949997,
-0.00520989578217268,
0.04091278091073036,
0.005152715370059013,
-0.005003781523555517,
0.0022549692075699568,
-0.036287762224674225,
0.02128607966005802,
0.040495045483112335,
-0.013411197811365128,
-0.043073609471321106,
0.007890586741268635,
0.017517177388072014,
-0.002754180459305644,
0.020994853228330612,
0.022557087242603302,
0.028718050569295883,
0.014143696054816246,
0.004855230450630188,
0.051604680716991425,
0.07924656569957733,
-0.011087056249380112,
-0.0045738741755485535,
0.06364589184522629,
0.013941704295575619,
0.027699988335371017,
0.02787979133427143,
0.029217040166258812,
0.0045164888724684715,
0.007715299725532532,
-0.005020273383706808,
-0.006599262822419405,
0.020395465195178986,
-0.018444517627358437,
0.037039726972579956,
0.000763660587836057,
-0.0067856875248253345,
-0.010530147701501846,
0.015730079263448715,
0.027246903628110886,
0.05929841846227646,
0.028890883550047874,
-0.07265432924032211,
-0.006099661812186241,
0.022661365568637848,
0.03290144354104996,
-0.0077972207218408585,
-0.056346483528614044,
0.019338998943567276,
0.026179954409599304,
0.00678159249946475,
-0.003124365583062172,
-0.022206686437129974,
0.023948801681399345,
-0.022198811173439026,
0.05328328162431717,
0.023994704708456993,
0.008519324474036694,
-0.03894690051674843,
0.02078472077846527,
-0.060020387172698975,
-0.07651937007904053,
0.01834445260465145,
-0.0020867965649813414,
-0.001726440037600696,
-0.020996615290641785,
-0.0026224555913358927,
0.011347050778567791,
0.026566417887806892,
-0.017418136820197105,
0.007194643374532461,
0.008093859069049358,
0.0012748570879921317,
-0.09686559438705444,
-0.021213600412011147,
0.05074544996023178,
-0.022082701325416565,
0.0022764168679714203,
-0.0627790242433548,
-0.008641690947115421,
0.034212302416563034,
0.06709527224302292,
-0.02139340527355671,
-0.013879254460334778,
-0.015571417286992073,
0.026064898818731308,
-0.0007864297367632389,
-0.008618396706879139,
-0.03493715450167656,
0.016871334984898567,
-0.008785713464021683,
0.004620311316102743,
-0.053891610354185104,
0.015020380727946758,
0.026032526046037674,
0.012687988579273224,
0.01627339795231819,
0.06999341398477554,
-0.044129591435194016,
-0.003923114854842424,
-0.012704976834356785,
-0.037883516401052475,
0.014045787043869495,
0.06880944967269897,
0.021595416590571404,
0.025864562019705772,
0.06331738829612732,
0.009676894173026085,
0.01748036779463291,
0.0073137846775352955,
0.003353912616148591,
0.060367852449417114,
-0.060501497238874435,
-0.0290517657995224,
-0.052559103816747665,
0.008223512209951878,
0.003806777996942401,
-0.052116114646196365,
-0.04223977401852608,
0.0024513653479516506,
0.008498837240040302,
0.027680763974785805,
0.06343777477741241,
0.011407507583498955,
0.005636448506265879,
-0.03851523622870445,
-0.009397967718541622,
-0.04632486775517464,
-0.05492379143834114,
0.0638863816857338,
0.012971865944564342,
-0.021329417824745178,
0.016632968559861183,
-0.02411569282412529,
-0.010243629105389118,
-0.029506875202059746,
-0.01282430998980999,
0.01131359115242958,
0.05825767666101456,
-0.03330421447753906,
0.014600401744246483,
0.03512093797326088,
0.04914132133126259,
0.021646086126565933,
0.047091446816921234,
0.01711832359433174,
0.0028302017599344254,
-0.014703531749546528,
0.030629346147179604,
-0.055669452995061874,
0.04424535855650902,
0.008371759206056595,
0.0002588114293757826,
0.03214571997523308,
0.0009978717425838113,
-0.019289784133434296,
0.01974106952548027,
0.01824617013335228,
0.0491495206952095,
0.04038608446717262,
0.0008986141765490174,
-0.003890017047524452,
0.049801167100667953,
-0.026252631098031998,
0.03378551825881004,
-0.02270735427737236,
-0.022819343954324722,
-0.05221543833613396,
0.010327647440135479,
0.04794551804661751,
0.04132631793618202,
-0.042336683720350266,
0.04469418153166771,
0.007229516748338938,
0.015828294679522514,
0.038871198892593384,
-0.04395092651247978,
-0.03069588914513588,
-0.0377814918756485,
0.046260371804237366,
-0.002987660001963377,
0.01599496603012085,
-0.012810626067221165,
-0.01217960100620985,
-0.0017923458945006132,
-0.026577549055218697,
0.012740666046738625,
0.003257601987570524,
0.010958547703921795,
0.013241749256849289,
0.029769958928227425,
0.04042275249958038,
-0.05029493197798729,
0.02572825737297535,
-0.0368470624089241,
0.032045066356658936,
0.02302885428071022,
-0.010221298784017563,
0.009225275367498398,
-0.04713406786322594,
-0.0054799881763756275,
0.008417566306889057,
0.01884843036532402,
-0.01451495848596096,
0.008832558989524841,
-0.0014583331067115068,
-0.05085119605064392,
0.0030422143172472715,
-0.006014460232108831,
-0.03156200423836708,
0.004345308989286423,
-0.025519227609038353,
0.030021991580724716,
-0.0005885576247237623,
0.05019325390458107,
-0.04988691210746765,
0.01613006368279457,
-0.004078262019902468,
-0.060560110956430435,
-0.013033791445195675,
-0.015303471125662327,
-0.051379840821027756,
-0.011574598960578442,
-0.06368234008550644,
-0.0311263520270586,
0.05294373631477356,
0.019920077174901962,
-0.003451783675700426,
0.04427700117230415,
-0.01287609152495861,
-0.04602242633700371,
0.0077375308610498905,
-0.0225323885679245,
0.004762794356793165,
-0.050979796797037125,
-0.030854711309075356,
0.05573294311761856,
0.019555263221263885,
-0.06547782570123672,
-0.0008795676403678954,
-0.018011393025517464,
-0.043472014367580414,
0.006216567941009998,
0.01624438539147377,
0.028954174369573593,
-0.02920735813677311,
0.033188384026288986,
0.012118926271796227,
-0.021385636180639267,
-0.015060866251587868,
-0.04671946167945862,
-0.037435609847307205,
0.005042229313403368,
-0.0355222150683403,
0.0671694204211235,
-0.026472488418221474,
-0.059068117290735245,
0.056145697832107544,
-0.0064476290717720985,
-0.01710081845521927,
-0.0041952552273869514,
-0.02366269752383232,
0.005916888825595379,
0.0022919049952179193,
-0.03626091778278351,
0.028271250426769257,
-0.014532474800944328,
0.001970244338735938,
0.015546844340860844,
0.01316071581095457,
0.009285315871238708,
0.003020168747752905,
-0.023426968604326248,
0.009149461053311825,
0.020503589883446693,
0.002281055087223649,
0.009609411470592022,
-0.004455191548913717,
-0.029662951827049255,
0.009386522695422173,
0.0010294831590726972,
0.02275344729423523,
0.03400110825896263,
-0.024554798379540443,
0.05360152944922447,
-0.0016516236355528235,
0.0031556705944240093,
-0.04597603902220726,
0.05155450105667114,
0.021029047667980194,
-0.028211286291480064,
0.016494140028953552,
0.011236170306801796,
0.053713954985141754,
-0.04408055916428566,
0.00018051550432574004,
0.020866811275482178,
0.06874630600214005,
-0.027705902233719826,
-0.04860851913690567,
-0.012479615397751331,
-0.006662380415946245,
0.03208323195576668,
-0.024438681080937386,
0.011435674503445625,
0.06336236745119095,
0.01775841973721981,
0.03212961181998253,
0.005915422458201647,
-0.010381867177784443,
-0.004121317062526941,
-0.06809035688638687,
0.004935941193252802,
-0.0006753457710146904,
0.04513801261782646,
0.017344331368803978,
0.06774686276912689,
0.029876472428441048,
-0.011457172222435474,
0.040481261909008026,
0.0037583918310701847,
-0.07228928804397583,
-0.01345402654260397,
-0.0007022338104434311,
0.005604179110378027,
0.010532541200518608,
-0.012026607990264893,
-0.011598045937716961,
0.005370352417230606,
-0.027728652581572533,
-0.04783603549003601,
-0.0016106727998703718,
-0.06477223336696625,
0.04861251637339592,
-0.039545319974422455,
-0.04720299690961838,
-0.01260281726717949,
0.029845697805285454,
0.030801448971033096,
-0.087067611515522,
-0.01425452996045351,
0.021743809804320335,
-0.05013531818985939,
0.024020861834287643,
0.012352359481155872,
0.004611234646290541,
0.04972220957279205,
0.00815058033913374,
-0.007566855289041996,
0.019922912120819092,
0.037625424563884735,
-0.023320535197854042,
0.018507737666368484,
0.04860764369368553,
0.04987996444106102,
-0.026053713634610176,
-0.058222681283950806,
-0.030441109091043472,
-0.01736781932413578,
-0.04057405889034271,
0.0870547965168953,
-0.00865956675261259,
-0.012992353178560734,
0.0022798103746026754,
0.019665276631712914,
0.007903026416897774,
0.0611504428088665,
0.03728187084197998,
0.02336697280406952,
-0.01621026173233986,
-0.0653904601931572,
-0.009256022982299328,
-0.02194417454302311,
-0.01776827871799469,
0.011624734848737717,
-0.017454657703638077,
-0.033549558371305466,
0.01319505088031292,
0.007900435477495193,
0.004591668024659157,
-0.04343840107321739,
0.023294376209378242,
0.021077364683151245,
-0.02097383141517639,
-0.001579792471602559,
-0.02548913285136223,
-0.027180418372154236,
-0.004255779553204775,
0.05404431000351906,
0.005253706593066454,
0.001087941462174058,
-0.08494380116462708,
-0.022958558052778244,
0.02765565738081932,
0.055961549282073975,
-0.007068678271025419,
-0.009726280346512794,
-0.04313932731747627,
-0.020644934847950935,
0.021734651178121567,
-0.056796882301568985,
0.025990158319473267,
-0.026173671707510948,
0.030183646827936172,
-0.04277491569519043,
-0.0564747080206871,
-0.03692414611577988,
0.019478484988212585,
-0.0005362830706872046,
0.04029986634850502,
-0.023723874241113663,
0.0011704725911840796,
-0.003581412835046649,
0.012970129027962685,
0.027695517987012863,
0.08511538058519363,
-0.024984391406178474,
-0.005048865918070078,
-0.004804939031600952,
-0.004218029323965311,
-0.003189368639141321,
-0.07556070387363434,
-0.009709201753139496,
-0.0060594468377530575,
0.004521300550550222,
0.022434528917074203,
-0.032654475420713425,
-0.05221540480852127,
0.0414067767560482,
-0.008897707797586918,
-0.000968827516771853,
0.020337209105491638,
-0.017775243148207664,
0.09479036927223206,
0.026020757853984833,
-0.015915244817733765,
0.0561571940779686,
0.015136750414967537,
-0.08006761968135834,
0.01095059234648943,
-0.025900823995471,
0.008648866787552834,
-0.01290159672498703,
-0.019882163032889366,
-0.028349049389362335,
0.019457247108221054,
-0.05501645430922508,
0.025784924626350403,
-0.02965753711760044,
0.019049132242798805,
-0.03523790463805199,
-0.03372235596179962,
0.020474372431635857,
0.008758116513490677,
0.03745703026652336,
0.0011674610432237387,
-0.047106653451919556,
0.026227759197354317,
0.027481941506266594,
-0.004822829272598028,
0.004000573884695768,
0.025322536006569862,
0.023051610216498375,
0.022182485088706017,
0.006358720827847719,
-0.018538927659392357,
-0.053355950862169266,
0.010493484325706959,
-0.005066512618213892,
-0.012312549166381359,
0.05592888593673706,
0.009687045589089394,
0.0046985698863863945,
0.012511316686868668,
-0.04412529617547989,
-0.07034006714820862,
0.033355385065078735,
-0.015759006142616272,
0.009788994677364826,
-0.0411607064306736,
-0.009965138509869576,
0.032444678246974945,
0.012187667191028595,
-0.03927764669060707,
-0.02492315135896206,
0.031072551384568214,
0.017284436151385307,
0.0006656911573372781,
0.013257701881229877,
-0.00903414562344551,
0.010458191856741905,
-0.03501836210489273,
-0.005569790489971638,
0.006831663195043802,
-0.04221431910991669,
-0.003823664737865329,
0.008235717192292213,
0.011722895316779613,
0.02849874459207058,
0.0009750811150297523,
0.004411941394209862,
-0.012161915190517902,
-0.025027785450220108,
-0.016878720372915268,
-0.005304092075675726,
0.01347998809069395,
-0.019674692302942276,
-0.04350610077381134,
-0.01374153420329094,
-0.009646722115576267,
0.03965755179524422,
-0.051235612481832504,
-0.056278690695762634,
0.04782673344016075,
-0.000056347675126744434,
-0.0415215864777565,
-0.0005828026914969087,
0.028431465849280357,
0.022381355985999107,
0.027834678068757057,
0.011530992574989796,
-0.014306031167507172,
-0.060721609741449356,
-0.030005261301994324,
-0.0019532109145075083,
-0.009131929837167263,
-0.0008382161031477153,
-0.02938411384820938,
0.051675379276275635,
-0.04556363448500633,
-0.0004363342886790633,
0.02064630761742592,
-0.015663063153624535,
0.021099476143717766,
0.02566787786781788,
-0.016324790194630623,
0.01190627459436655,
-0.007357265334576368,
-0.035426557064056396,
0.0031108269467949867,
-0.047502078115940094,
0.0032732593826949596,
0.05460888892412186,
0.038351528346538544,
0.05083909630775452,
0.010286214761435986,
-0.03676115348935127,
0.007185053080320358,
-0.011945035308599472,
-0.01870911754667759,
0.021584711968898773,
-0.0007188717718236148,
0.010936325415968895,
-0.029536494985222816,
-0.018035640940070152,
0.036443330347537994,
0.03681749477982521,
-0.027963746339082718,
-0.018421396613121033,
0.026337554678320885,
0.03983055800199509,
-0.001022371812723577,
-0.05428437888622284,
-0.05035969987511635,
0.05205578729510307,
-0.031001215800642967,
-0.019174724817276,
0.004800031427294016,
-0.021148456260561943,
0.03171379864215851,
0.019495416432619095,
0.005836030002683401,
-0.0550086535513401,
-0.024934450164437294,
-0.02443300187587738,
0.016356628388166428,
-0.009094558656215668,
0.011144442483782768,
0.006102931220084429,
0.000019140679796691984,
0.009566026739776134,
0.006150151137262583,
0.03288307040929794,
-0.03095235489308834,
-0.054799847304821014,
-0.01761576160788536,
-0.003366046817973256,
-0.023161692544817924,
0.02151426114141941,
-0.01039003487676382,
-0.04663003236055374,
0.01294588204473257,
-0.04097506403923035,
0.06042703986167908,
0.03570843115448952,
0.025209948420524597,
0.007798099424690008,
0.02975461632013321,
-0.03432783484458923,
0.013840931467711926,
-0.04747890308499336,
-0.023559683933854103,
0.12331077456474304,
0.07022152841091156,
0.008838584646582603,
-0.02176908403635025,
0.01456084381788969,
-0.02960684895515442,
0.005888695362955332,
-0.03580596670508385,
0.01006295345723629,
-0.038509801030159,
-0.015079381875693798,
-0.01148730143904686,
0.052509259432554245,
0.0034980163909494877,
0.04511469602584839,
0.035177212208509445,
-0.030092235654592514,
-0.022161521017551422,
0.005490508861839771,
0.048249416053295135,
-0.038310810923576355,
0.049937982112169266,
-0.012534202076494694,
0.011036471463739872,
-0.031010901555418968,
-0.005115934181958437,
-0.025213394314050674,
0.0022636710200458765,
0.0614323690533638,
-0.004562802612781525,
-0.02277606539428234,
0.0011720879701897502,
-0.00032359291799366474,
-0.015150493942201138,
-0.03972463682293892,
0.018483705818653107,
0.024778103455901146,
0.025409020483493805,
-0.010163604281842709,
0.013837739825248718,
-0.008328763768076897,
-0.00008293953578686342,
0.026922333985567093,
0.03027452901005745,
-0.03599272668361664,
0.009185313247144222,
-0.055607881397008896,
0.05598610267043114,
-0.0035370802506804466,
0.013775589875876904,
0.04350191354751587,
0.018084367737174034,
0.00943793449550867,
-0.0019299748819321394,
-0.02014567330479622,
0.014846397563815117,
0.007919099181890488,
-0.004612488206475973,
0.009409124962985516,
-0.04306121543049812,
0.04348325729370117,
0.014274097979068756,
-0.01647857390344143,
-0.04029233381152153,
-0.04899037256836891,
-0.012812687084078789,
-0.008274722844362259,
0.006511682644486427,
-0.006802546791732311,
0.009805606678128242,
-0.014732228592038155,
-0.023180881515145302,
-0.02672710455954075,
-0.038262736052274704,
-0.026799406856298447,
0.03312082961201668,
0.016555368900299072,
-0.010665942914783955,
0.013026993721723557,
-0.006304842419922352,
-0.05379866436123848,
0.050032973289489746,
0.005567542277276516,
-0.009872056543827057,
-0.0234749224036932,
0.033605094999074936,
-0.013445585034787655,
0.06763393431901932,
-0.0033007245510816574,
0.008893964812159538,
0.012373929843306541,
0.0384589321911335,
0.02185611054301262,
-0.014920484274625778,
-0.035434093326330185,
-0.019669262692332268,
-0.04919477924704552,
0.015106420032680035,
-0.005862004589289427,
-0.019692236557602882,
0.011373603716492653,
0.013096376322209835,
0.004587670788168907,
0.02762814238667488,
-0.02771890163421631,
-0.022134296596050262,
0.03223349526524544,
-0.017722811549901962,
0.0019569406285881996,
0.010242789052426815,
0.017612861469388008,
-0.01011131051927805,
-0.031079227104783058,
0.0027668867260217667,
0.0005999261047691107,
-0.049739520996809006,
0.02453858219087124,
-0.006565049756318331,
0.014979347586631775,
-0.0391274057328701,
0.03683408722281456,
-0.05345570296049118,
-0.04512619599699974,
-0.008626393973827362,
0.0338960736989975,
0.017024239525198936,
0.024706289172172546,
-0.022875091060996056,
0.05374143645167351,
-0.004722967743873596,
0.009691281244158745,
0.011206192895770073,
0.011129436083137989,
-0.012519681826233864,
-0.02060127817094326,
0.015040135011076927,
0.02645890787243843,
0.005529783666133881,
-0.009433966130018234,
-0.02980789914727211,
0.03654245659708977,
0.0005240209284238517,
-0.07571499794721603,
-0.011502758599817753,
-0.017732571810483932,
0.020548220723867416,
0.04725438356399536,
-0.004977148491889238,
-0.02334844321012497,
0.048203662037849426,
-0.005329866893589497,
0.006114291958510876,
-0.011694543063640594,
-0.0468948669731617,
-0.006529961712658405,
-0.007943594828248024,
0.025711843743920326,
0.0012843153672292829,
0.020484140142798424,
0.03489070013165474,
-0.00978932622820139,
-0.008757092989981174,
-0.024869095534086227,
0.028697146102786064,
-0.022387512028217316,
-0.004625679459422827,
0.02572338841855526,
0.012600112706422806,
0.024654490873217583,
0.0359022319316864,
-0.022259604185819626,
-0.0015212526777759194,
0.017028862610459328,
0.001837235176935792,
-0.08534152805805206,
-0.02428259141743183,
-0.009046237915754318,
0.014656538143754005,
0.0446607805788517,
-0.022960739210247993,
0.040777429938316345,
0.015315387398004532,
-0.0900871679186821,
0.004053689539432526,
-0.037510160356760025,
0.013433746993541718,
-0.004948718473315239,
-0.004394405987113714,
-0.04804541543126106,
0.026605335995554924,
0.010789682157337666,
0.05205182731151581,
0.01826232299208641,
0.026851002126932144,
0.016549918800592422,
-0.0292547307908535,
-0.023269351571798325,
0.04545793682336807,
-0.00983394030481577,
-0.0014634276740252972,
0.09453167766332626,
-0.03015402890741825,
-0.01139785535633564,
0.013077429495751858,
-0.006964206229895353,
-0.013328426517546177,
0.0033812541514635086,
0.017340360209345818,
-0.021244894713163376,
0.0479147806763649,
-0.01764356903731823,
0.000003234095629522926,
-0.018156614154577255,
-0.03595160320401192,
0.023579323664307594,
-0.005113239865750074,
-0.0029164839070290327,
-0.010968046262860298,
0.052445366978645325,
-0.0009948379592970014,
-0.017473360523581505,
0.029783589765429497,
-0.03745727986097336,
-0.03268091753125191,
0.04785139113664627,
0.06566692143678665,
0.009846491739153862,
-0.005365284625440836,
-0.0021397145465016365,
-0.0456731952726841,
-0.038959767669439316,
-0.005984141957014799,
0.009762648493051529,
0.03837957605719566,
0.024385901167988777,
0.011366290971636772,
-0.0017714818241074681,
0.02827889658510685,
0.040214650332927704,
-0.025698009878396988,
-0.07291781157255173,
-0.008601313456892967,
-0.0005696660955436528,
0.015280652791261673,
0.016108600422739983,
-0.04307292029261589,
-0.038912735879421234,
0.018219590187072754,
0.014818660914897919,
0.013604649342596531,
-0.02768455632030964,
-0.032321035861968994,
-0.029803453013300896,
-0.08076637238264084,
0.02751411311328411,
0.0023550193291157484,
-0.040042661130428314,
-0.01754792407155037,
-0.05083984136581421,
-0.01578887365758419,
0.03286893665790558,
0.07956670969724655,
-0.014320436865091324,
-0.05451514199376106,
0.025204099714756012,
-0.01991346664726734,
0.04216329753398895,
-0.06083594262599945,
-0.0038773524574935436,
0.04289302974939346,
0.010625622235238552,
0.02188163250684738,
0.020373603329062462,
0.006099835503846407,
0.024174891412258148,
0.05515206605195999,
-0.0031155727338045835,
-0.023088965564966202,
0.009442253969609737,
-0.011194330640137196,
0.03921719267964363,
-0.00987229123711586,
-0.02723802626132965,
0.09142596274614334,
-0.015492886304855347,
0.019733507186174393,
0.003182071726769209,
-0.04976809769868851,
-0.009835016913712025,
-0.009378699585795403,
-0.029171552509069443,
0.027130546048283577,
-0.05671481043100357,
0.01481549721211195,
0.0664500966668129,
-0.02790714055299759,
-0.022526899352669716,
0.048642151057720184,
-0.027923651039600372,
-0.012213634327054024,
0.07987722009420395,
0.008205280639231205,
0.00476286793127656,
0.02880934067070484,
0.03701141104102135,
-0.011638310737907887,
0.012143081054091454,
0.012061364948749542,
0.03566150739789009,
0.05216103792190552,
0.0025564762763679028,
0.030365105718374252,
0.08254490792751312,
0.0038967805448919535,
0.004523740615695715,
0.010177187621593475,
-0.018726035952568054,
-0.04408089071512222,
-0.01856069825589657,
0.000674358569085598,
0.003687510499730706,
-0.0357232466340065,
0.021211890503764153,
-0.029435785487294197,
0.10119883716106415,
-0.001632584142498672,
-0.026249347254633904,
0.008493942208588123,
0.024776704609394073,
-0.0012589114485308528,
0.0024905360769480467,
-0.009161479771137238,
0.007236482109874487,
-0.0158422589302063,
0.014482359401881695,
-0.034309323877096176,
0.009570775553584099,
0.010836508125066757,
-0.02327912487089634,
0.012348593212664127,
0.02859724499285221,
-0.0004355748533271253,
-0.010830381885170937,
0.015072607435286045,
-0.025239329785108566,
0.008091984316706657,
0.028062131255865097,
0.03572700172662735,
0.01846233941614628,
0.02121558226644993,
-0.013376421295106411,
0.002413741545751691,
0.04243748262524605,
-0.02687712386250496,
-0.0012089041993021965,
0.007957365363836288,
0.0060902731493115425,
0.028824497014284134,
-0.007651968393474817
] |
<p>I would like to know how to take the functional derivative of the holonomy, or Wilson line. I have tried it and I will show what I have done below, but before I wanted to say that I also have seen and done this with the characteristic deifferential equation for the holonomy
$$
\frac{\partial U}{\partial s}+\dot{\gamma}^a A_{a} U=0
$$
with $\dot{\gamma}$ a tangent vector to the curve and $A$ the connection. By varying this equation I can find what $\frac{\delta U}{\delta A}$ is, but I would like to know how to do it from the expression for $U$
$$
U=\mathcal{P}\exp \left[ -\int_{\gamma} \dot{\gamma}^a(s) A_a(\gamma(s)) ds \right]
$$
with $\dot{\gamma}^a=\frac{dx^a}{ds}$ as before. Now I have tried to directly vary this with respect to $A_b$
$$
\frac{\delta U}{\delta A_b(x)}=\mathcal{P} \exp \left[ -\int_{\gamma} \dot{\gamma}^a A_a ds \right] \cdot \frac{\delta}{\delta A_b}\left[ -\int_{\gamma} \dot{\gamma}^a A_a ds \right]
$$
Now if $A_a=A_{a}^{i}\tau^i$ then
$$
\frac{\delta}{\delta A_{b}^i }\left[ -\int_{\gamma} \dot{\gamma}^a A_{a}^j \tau^j ds \right]=-\int_{\gamma} \dot{\gamma}^a \delta _{ab}\delta_{ij} \delta^3(\gamma(s)-x) \tau^j ds=-\int_{\gamma}\dot{\gamma}^b \delta^3(\gamma(s)-x) \tau^j ds
$$
So I end with
$$
\frac{\delta U}{\delta A_{b}^j}=U(\gamma)\left[ -\int_{\gamma}\dot{\gamma}^b \delta^3(\gamma(s)-x) \tau^j ds \right]
$$
Which isn't right.. Can someone point me in a better direction, Thanks.</p>
| 10,787 |
[
0.05781501531600952,
-0.002261531539261341,
0.028169959783554077,
-0.03476111218333244,
0.014416242949664593,
0.014829067513346672,
-0.07209406793117523,
-0.03013070859014988,
0.00902028288692236,
-0.023254791274666786,
0.025045322254300117,
0.023808414116501808,
0.05903523787856102,
0.03345274180173874,
0.02767745964229107,
-0.006220221519470215,
0.0130100566893816,
-0.018373936414718628,
-0.005024921149015427,
-0.0217225831001997,
0.037514735013246536,
0.003383216680958867,
-0.018197594210505486,
-0.025283824652433395,
0.0022981984075158834,
0.038906991481781006,
-0.018001407384872437,
-0.007444270420819521,
-0.05976375937461853,
0.06114131957292557,
-0.005055480170994997,
-0.06633497029542923,
-0.004981511738151312,
0.015950655564665794,
0.015371259301900864,
0.0266891997307539,
-0.0195461455732584,
-0.01548174861818552,
-0.006910314783453941,
0.01836264505982399,
-0.03714293986558914,
-0.02997559867799282,
-0.009177361615002155,
0.07770618051290512,
-0.0038007854018360376,
0.006329992786049843,
-0.009073822759091854,
-0.03218067064881325,
0.02122182957828045,
-0.005854881834238768,
0.08476334065198898,
0.03174044191837311,
0.02320847474038601,
0.05135999247431755,
-0.018568353727459908,
-0.06315597891807556,
0.035478588193655014,
0.024426523596048355,
0.008996359072625637,
-0.06459203362464905,
-0.0245516337454319,
-0.0013962136581540108,
-0.013651628978550434,
-0.05372793227434158,
-0.036208752542734146,
0.008004551753401756,
0.016016967594623566,
-0.03676306828856468,
0.014776158146560192,
-0.06201711297035217,
0.009210297837853432,
-0.017665322870016098,
-0.0023889506701380014,
-0.015617486089468002,
-0.004608020186424255,
0.015460864640772343,
-0.02600831165909767,
0.015171026811003685,
0.01692317984998226,
0.025456948205828667,
0.0006365601439028978,
0.045594505965709686,
0.021410632878541946,
0.03439173847436905,
0.02672548033297062,
0.011032517068088055,
0.0737273246049881,
-0.03171338886022568,
-0.012215574271976948,
0.027549823746085167,
-0.015215749852359295,
0.01748640649020672,
0.012920658104121685,
-0.0601329579949379,
0.02205953374505043,
0.026487234979867935,
0.030271170660853386,
0.013510947115719318,
-0.017236512154340744,
-0.04402203857898712,
-0.0016602284740656614,
-0.02671658620238304,
0.010667044669389725,
0.047411542385816574,
0.046980585902929306,
0.010092790238559246,
-0.0213533453643322,
-0.0011498651001602411,
-0.037169910967350006,
-0.04837047681212425,
-0.055319223552942276,
0.04612103849649429,
-0.04401303455233574,
0.002457510447129607,
-0.005123921204358339,
-0.02000485733151436,
-0.004547546152025461,
-0.015072169713675976,
0.012990028597414494,
0.0176751296967268,
0.0582522489130497,
-0.00982440635561943,
0.007855414412915707,
-0.01563180796802044,
-0.035574428737163544,
0.02207917720079422,
0.026011578738689423,
0.03932802751660347,
-0.03198270499706268,
-0.029278423637151718,
-0.0024802829138934612,
-0.020251885056495667,
0.0039005884900689125,
0.036027055233716965,
-0.0034765966702252626,
-0.0026627208571881056,
-0.07983503490686417,
-0.04315905272960663,
0.03587280586361885,
0.02033247798681259,
0.029611792415380478,
-0.058768197894096375,
0.004203761927783489,
0.05159807205200195,
0.04881050065159798,
0.025569507852196693,
-0.017168208956718445,
0.029579633846879005,
0.008732970803976059,
-0.015485372394323349,
-0.033006638288497925,
-0.03200725466012955,
-0.03885521739721298,
-0.015239961445331573,
0.011791831813752651,
-0.03888193145394325,
0.03642388433218002,
0.02610078826546669,
0.014919474720954895,
0.00852268747985363,
0.08326826989650726,
-0.010233180597424507,
0.03378937020897865,
0.03707476332783699,
-0.019221674650907516,
-0.04117152839899063,
0.06307166814804077,
0.007093833293765783,
-0.02514117956161499,
0.006121567916125059,
-0.006823577918112278,
0.0017251065000891685,
-0.05500701814889908,
0.03919548913836479,
0.03656826913356781,
-0.06917022168636322,
-0.024967461824417114,
0.01627371460199356,
-0.01633348874747753,
0.012453441508114338,
-0.01943463459610939,
-0.04539614915847778,
-0.02297530695796013,
0.0036542117595672607,
0.01901835761964321,
0.017350967973470688,
0.015615667216479778,
0.009694665670394897,
0.012485146522521973,
-0.0485868938267231,
-0.007541084662079811,
-0.03522443771362305,
0.024294981732964516,
-0.014451912604272366,
-0.05108080431818962,
0.03895633667707443,
-0.016923002898693085,
-0.02525356039404869,
-0.017824819311499596,
-0.015535470098257065,
0.051929719746112823,
0.047306451946496964,
0.03184588998556137,
-0.014940641820430756,
0.02313971519470215,
0.0031557921320199966,
0.06653916835784912,
-0.0027520402800291777,
0.0460815392434597,
-0.019207080826163292,
0.03278663754463196,
0.006931339390575886,
-0.03966109827160835,
0.018063511699438095,
-0.04346275329589844,
-0.0006196783506311476,
-0.014025744050741196,
-0.03420662879943848,
-0.01646021567285061,
0.014555425383150578,
-0.028897957876324654,
0.04950311779975891,
0.0711783766746521,
0.02417246624827385,
0.013003204017877579,
0.030256595462560654,
-0.029342837631702423,
0.06716826558113098,
-0.002472563413903117,
-0.04698432981967926,
-0.04430443421006203,
0.03234076872467995,
0.009886125102639198,
0.03228486701846123,
-0.03555365651845932,
-0.03541804850101471,
0.03191101551055908,
0.007794618606567383,
0.02351156435906887,
0.008817394264042377,
-0.002402858342975378,
-0.04797309637069702,
0.037124376744031906,
-0.0040016938000917435,
-0.018298709765076637,
0.006256193853914738,
0.020742325112223625,
-0.016886992380023003,
0.04999462887644768,
-0.013145376928150654,
0.008767643943428993,
-0.01882677525281906,
-0.021366247907280922,
0.002216135151684284,
0.043979108333587646,
0.005490477196872234,
0.06913464516401291,
-0.017112838104367256,
0.017063425853848457,
0.06964825093746185,
-0.016380412504076958,
-0.007700644433498383,
0.016054891049861908,
-0.047004107385873795,
0.051605284214019775,
-0.005900606978684664,
-0.000682378129567951,
-0.015221955254673958,
0.00023842095106374472,
0.025235842913389206,
0.0013800327433273196,
-0.01349432859569788,
-0.01022888533771038,
-0.009668168611824512,
0.00008068900206126273,
0.008222117088735104,
0.0528346449136734,
0.01803295686841011,
-0.012353322468698025,
-0.037721604108810425,
0.03934817761182785,
0.032293278723955154,
0.01386822760105133,
0.04055490717291832,
-0.0442277155816555,
-0.00798056460916996,
-0.025264643132686615,
0.014815025962889194,
0.02984381839632988,
0.020751219242811203,
-0.0028449080418795347,
0.02327265404164791,
-0.015360835939645767,
-0.04664379358291626,
-0.011771980673074722,
0.04762385040521622,
0.014105736277997494,
-0.029376866295933723,
-0.034692250192165375,
0.023639502003788948,
0.03266608342528343,
-0.0326538123190403,
0.015369459986686707,
-0.020837143063545227,
-0.06620678305625916,
0.024085721001029015,
0.020176025107502937,
0.013135072775185108,
-0.028469623997807503,
0.05364622175693512,
0.039251383394002914,
-0.004782788455486298,
0.00734932953491807,
-0.05629633739590645,
-0.006410318426787853,
0.022872142493724823,
0.03572894632816315,
-0.0051909396424889565,
-0.007696983404457569,
-0.07143979519605637,
0.10085485875606537,
0.00811353325843811,
-0.02602970600128174,
0.015908133238554,
0.00920130591839552,
-0.01729397289454937,
-0.04414995387196541,
0.01436321996152401,
-0.0006854576640762389,
-0.016844378784298897,
0.011031687259674072,
0.001630467944778502,
0.08230441808700562,
0.03823670744895935,
0.01077080424875021,
-0.015518778935074806,
0.05089513212442398,
0.00024159350141417235,
0.03143209591507912,
0.04129151999950409,
-0.015509098768234253,
0.020578185096383095,
-0.008837265893816948,
0.007236815057694912,
0.03483644872903824,
-0.019731562584638596,
-0.03098330646753311,
0.03228871524333954,
0.052954528480768204,
-0.016394808888435364,
0.022601816803216934,
0.01091006863862276,
0.00515673216432333,
-0.0537298321723938,
-0.002849109936505556,
0.024451544508337975,
0.03169532120227814,
-0.016998155042529106,
-0.0038116993382573128,
0.039980579167604446,
0.014427520334720612,
-0.013309474103152752,
-0.027404585853219032,
-0.0377676784992218,
-0.026766356080770493,
0.017415642738342285,
-0.04612017422914505,
0.0060392338782548904,
0.027528654783964157,
0.043146077543497086,
0.0014502033591270447,
-0.03300507366657257,
-0.023931492120027542,
0.002410524059087038,
-0.045785002410411835,
-0.008157731033861637,
-0.00802957359701395,
0.0545407235622406,
0.025821702554821968,
0.024070478975772858,
0.0373847521841526,
0.03121626004576683,
-0.010777601040899754,
-0.02742166258394718,
-0.0631602481007576,
0.05506217107176781,
-0.043278250843286514,
-0.0006709504523314536,
-0.027230175212025642,
-0.053118761628866196,
0.03798038884997368,
-0.03396109864115715,
-0.007578013464808464,
-0.01984444633126259,
0.009997459128499031,
-0.055702704936265945,
0.02798233926296234,
-0.043940648436546326,
-0.019838426262140274,
-0.044197600334882736,
0.043439172208309174,
0.03402909263968468,
-0.004152954556047916,
-0.016207512468099594,
-0.016467761248350143,
-0.017727645114064217,
0.019095463678240776,
-0.01689252443611622,
0.01329571008682251,
0.010085909627377987,
0.01189333200454712,
0.008460077457129955,
0.0036913142539560795,
-0.0020608764607459307,
-0.03425987809896469,
0.013701092451810837,
0.021758947521448135,
0.0350094735622406,
-0.03154556453227997,
0.007980666123330593,
-0.08383163809776306,
-0.00201733922585845,
-0.005603823810815811,
0.10031688958406448,
-0.0075954776257276535,
0.015680363401770592,
0.03332369402050972,
0.014573232270777225,
-0.002788795158267021,
0.013700471259653568,
0.022805674001574516,
-0.027668599039316177,
-0.000013447604032990057,
-0.05752435326576233,
-0.009006023406982422,
-0.03315746784210205,
-0.031219085678458214,
0.01567971333861351,
-0.011866789311170578,
-0.07237112522125244,
-0.016103994101285934,
-0.021194377914071083,
0.006273539736866951,
-0.006238116417080164,
-0.0075487713329494,
0.009323001839220524,
-0.016405431553721428,
0.007232521194964647,
-0.022170456126332283,
0.021820535883307457,
0.07066179811954498,
0.0180456954985857,
-0.024195274338126183,
0.015783051028847694,
-0.06698717921972275,
-0.04775480553507805,
0.03658454120159149,
0.04933637008070946,
0.009469127282500267,
-0.012440341524779797,
-0.07299517095088959,
-0.003955459222197533,
0.05019185692071915,
0.0032053780741989613,
0.005987063050270081,
0.012294508516788483,
0.003970849793404341,
-0.02008969895541668,
-0.03329934924840927,
-0.04400496184825897,
0.0603318028151989,
0.001994561171159148,
-0.04534337297081947,
-0.05743052810430527,
0.009918903931975365,
-0.02084113098680973,
0.037651654332876205,
-0.015060639940202236,
0.04214383661746979,
0.03263787552714348,
-0.01904863677918911,
-0.0042300778441131115,
0.04171021282672882,
-0.0365433394908905,
-0.07273513078689575,
-0.0008441321551799774,
0.014462258666753769,
-0.0216347835958004,
0.03617159649729729,
-0.00039171657408587635,
-0.024047531187534332,
0.03723348304629326,
-0.002347503090277314,
0.01941382698714733,
0.04655720666050911,
-0.03139030188322067,
0.051671385765075684,
0.010265910997986794,
-0.01873849518597126,
0.04197118431329727,
0.025040099397301674,
-0.03287442773580551,
-0.011527344584465027,
-0.02839810587465763,
0.02764265239238739,
-0.02669454924762249,
-0.043861426413059235,
-0.02916830964386463,
-0.0017351777059957385,
-0.005324822384864092,
0.03773222491145134,
-0.039927802979946136,
-0.027173738926649094,
-0.0063320426270365715,
-0.049480702728033066,
0.0025687331799417734,
0.0057923379354178905,
0.000348907255101949,
0.01355659868568182,
0.020893290638923645,
0.0013905091909691691,
0.0252902302891016,
0.01422817911952734,
0.0073713865131139755,
-0.05044366419315338,
-0.00030540351872332394,
0.02982994168996811,
-0.0195748433470726,
-0.016215531155467033,
0.00852729007601738,
-0.021728739142417908,
-0.0025351191870868206,
-0.03401249274611473,
0.02000102959573269,
0.0394117534160614,
-0.009870077483355999,
0.0012741775717586279,
-0.02398795261979103,
0.003973356448113918,
-0.017107434570789337,
-0.028949014842510223,
-0.004557810723781586,
-0.0444200225174427,
-0.008773453533649445,
0.002577692735940218,
0.002477402100339532,
-0.08290715515613556,
0.0025065746158361435,
0.025138063356280327,
0.0007770293159410357,
-0.037948127835989,
-0.022202681750059128,
0.02203056402504444,
0.012469043955206871,
-0.00939890369772911,
0.020407095551490784,
0.05421294644474983,
-0.03535318747162819,
0.013059365563094616,
0.012020054273307323,
0.03418824076652527,
0.025285035371780396,
-0.03639617934823036,
-0.009504145942628384,
0.00796838104724884,
-0.00634935824200511,
-0.0008124513551592827,
0.024302195757627487,
0.02398645505309105,
-0.01688295416533947,
0.006142748985439539,
0.028455162420868874,
-0.014901777729392052,
0.012528969906270504,
-0.0019154759356752038,
-0.048989515751600266,
-0.01806323230266571,
0.04355141147971153,
-0.004896874073892832,
-0.027391735464334488,
-0.030609536916017532,
0.015087058767676353,
0.013956173323094845,
-0.006647288333624601,
0.014341157861053944,
-0.0394178070127964,
-0.000021287907657097094,
0.0170025322586298,
-0.010094351135194302,
-0.018137963488698006,
-0.005670520011335611,
0.02905888669192791,
-0.00494016706943512,
-0.02025802806019783,
0.01582907699048519,
0.004200623836368322,
0.05335667356848717,
-0.033476412296295166,
0.021528849378228188,
0.023890327662229538,
-0.057156920433044434,
-0.017417853698134422,
0.004228850360959768,
-0.08822040259838104,
0.006375750992447138,
0.04047388955950737,
0.006444250699132681,
0.03670734912157059,
0.030629396438598633,
0.029475094750523567,
-0.023244144394993782,
-0.031517595052719116,
-0.0682128518819809,
0.009609523229300976,
-0.04344949871301651,
0.02501913160085678,
-0.03482573479413986,
-0.026552267372608185,
0.039110761135816574,
0.01967453584074974,
-0.08726154267787933,
0.03348791226744652,
-0.022468773648142815,
0.042773738503456116,
0.0036516906693577766,
0.016562875360250473,
-0.054374612867832184,
0.05744190514087677,
-0.0024651980493217707,
0.0524173229932785,
0.03349686786532402,
-0.005340013653039932,
0.04294696822762489,
0.047516874969005585,
0.021253494545817375,
-0.00458407960832119,
-0.02343544363975525,
-0.05042063817381859,
0.044191695749759674,
0.06811888515949249,
0.02187034673988819,
0.019418565556406975,
0.009385062381625175,
0.04377216845750809,
-0.050543490797281265,
0.014846920035779476,
-0.025559404864907265,
-0.014961461536586285,
0.0365733802318573,
-0.0552917942404747,
-0.05357450246810913,
0.062112778425216675,
-0.02426227554678917,
0.010727672837674618,
-0.008974445052444935,
0.014337404631078243,
0.020852331072092056,
0.0134510463103652,
0.009519071318209171,
-0.0027153496630489826,
0.0620586983859539,
-0.024248585104942322,
0.0012117361184209585,
-0.00858128909021616,
-0.006849322468042374,
0.12001034617424011,
0.0331229604780674,
-0.009744630195200443,
-0.062022410333156586,
0.016172118484973907,
-0.013041195459663868,
0.009287852793931961,
-0.04572928696870804,
0.01875285804271698,
0.015879373997449875,
-0.07442107796669006,
-0.0192004032433033,
0.052388399839401245,
-0.03806419298052788,
0.011103253811597824,
0.05883170664310455,
-0.014880589209496975,
-0.011598394252359867,
0.040716610848903656,
-0.0072601065039634705,
-0.02719234861433506,
0.016905957832932472,
-0.018764592707157135,
0.004301363602280617,
-0.016851019114255905,
0.009801005013287067,
-0.06477771699428558,
-0.004452352877706289,
-0.0059810359962284565,
-0.02490699104964733,
-0.009992657229304314,
0.005556884687393904,
0.03574158251285553,
0.0023173673544079065,
0.01693512126803398,
-0.0075782956555485725,
0.023995282128453255,
-0.028393011540174484,
0.040440142154693604,
0.003899127710610628,
-0.002369822934269905,
0.021153755486011505,
0.021703198552131653,
0.05324164032936096,
-0.021970098838210106,
-0.010202775709331036,
0.0035499250516295433,
0.050782617181539536,
-0.0026610379572957754,
0.03561294451355934,
-0.020935991778969765,
0.003706702496856451,
-0.0022872367408126593,
-0.022734006866812706,
-0.0295406561344862,
-0.04613761603832245,
-0.022664479911327362,
-0.026928037405014038,
-0.02714739553630352,
-0.012914552353322506,
0.014559613540768623,
0.05042591318488121,
0.051291823387145996,
-0.0007536271587014198,
-0.007239044643938541,
0.023367060348391533,
0.007217950653284788,
0.0258371252566576,
-0.01453312672674656,
-0.00961391068994999,
-0.025687813758850098,
0.0044040558859705925,
-0.01843423582613468,
-0.04098732769489288,
-0.016817806288599968,
-0.0156695656478405,
-0.00006831288919784129,
0.03963909670710564,
-0.022096266970038414,
-0.024151939898729324,
-0.060232896357774734,
-0.002149721374735236,
-0.014174757525324821,
0.00895708054304123,
-0.02061411365866661,
0.024925174191594124,
0.037946559488773346,
0.04401477426290512,
0.03328893706202507,
-0.033343084156513214,
0.016462476924061775,
0.06879372149705887,
0.030767623335123062,
-0.004697396419942379,
-0.0011419951915740967,
0.010579992085695267,
-0.03083587810397148,
-0.004380282945930958,
-0.00011014386109309271,
0.002240568632259965,
0.0013268974144011736,
0.013363402336835861,
-0.05584864318370819,
0.0004892596043646336,
-0.031330715864896774,
-0.008147369138896465,
0.028940260410308838,
0.029109932482242584,
0.004752165172249079,
0.06567011773586273,
-0.022186437621712685,
-0.026669180020689964,
-0.009145542047917843,
0.003594871610403061,
0.020252784714102745,
-0.022733980789780617,
0.018096519634127617,
-0.01285960990935564,
-0.03513987362384796,
0.011770733632147312,
-0.020832465961575508,
-0.017461318522691727,
0.005562493111938238,
-0.04508139193058014,
0.012775734066963196,
0.0012402718421071768,
0.04062768071889877,
-0.002681588288396597,
0.02191607467830181,
0.022122537717223167,
-0.011155890300869942,
0.024481184780597687,
0.055076271295547485,
0.04523104056715965,
-0.02230621874332428,
0.010861305519938469,
0.011590692214667797,
0.05282086506485939,
0.04954005032777786,
-0.04733012244105339,
-0.012065200135111809,
-0.02945128083229065,
-0.01719728298485279,
0.027207037433981895,
0.022095536813139915,
0.01745019108057022,
0.0308146420866251,
-0.045660484582185745,
0.000760829309001565,
0.020809482783079147,
0.008370030671358109,
-0.039623454213142395,
-0.06343439221382141,
-0.04308347404003143,
-0.012894181534647942,
-0.038625266402959824,
0.03996198624372482,
0.0026686303317546844,
0.040638066828250885,
0.003531333990395069,
-0.008863153867423534,
-0.03309964761137962,
-0.013944970443844795,
-0.00469539500772953,
0.002422996796667576,
-0.011661325581371784,
0.00033249883563257754,
0.00036215822910889983,
0.02669604867696762,
0.048232290893793106,
-0.0007907814579084516,
-0.010721733793616295,
0.005145138129591942,
0.027321048080921173,
-0.0663338154554367,
-0.0024766442365944386,
0.008533223532140255,
-0.0013728198828175664,
0.04647856578230858,
-0.05378407984972,
-0.01358818169683218,
0.008055880665779114,
0.0029726203065365553,
0.019696509465575218,
-0.02367352321743965,
0.009980360046029091,
-0.020320307463407516,
-0.04583849012851715,
-0.032207462936639786,
0.07285387814044952,
0.04579056426882744,
0.010142582468688488,
-0.024126211181282997,
0.01802874356508255,
-0.031467895954847336,
-0.023242764174938202,
-0.00865846686065197,
0.058847542852163315,
0.034559216350317,
-0.056192547082901,
0.03688566014170647,
-0.027149440720677376,
-0.030986705794930458,
0.07157972455024719,
0.007491514552384615,
-0.03743372857570648,
-0.029506826773285866,
0.02369438111782074,
0.01919863373041153,
-0.006402844563126564,
0.05144462361931801,
0.03150920569896698,
-0.00720294751226902,
-0.03721965476870537,
0.007366087753325701,
0.014375370927155018,
-0.044986527413129807,
0.011004626750946045,
0.0333554744720459,
-0.008044260554015636,
-0.047523383051157,
0.019493674859404564,
-0.03148535266518593,
-0.007496570236980915,
-0.04331590607762337,
-0.013925159350037575,
0.00661492720246315,
-0.05397650599479675,
-0.015127312391996384,
-0.02198147214949131,
0.03612147271633148,
0.03504014387726784,
-0.011547158472239971,
-0.024584606289863586,
-0.0023965078871697187,
-0.02267679013311863,
-0.05843978747725487,
0.04221811518073082,
0.0015010354109108448,
-0.018896957859396935,
-0.016052739694714546,
-0.01428933721035719,
-0.026105917990207672,
0.005501714535057545,
-0.003696480533108115,
-0.028443561866879463,
-0.017219848930835724,
0.011194601655006409,
0.006718898192048073,
0.0038096255157142878,
-0.046997711062431335,
-0.026152433827519417,
0.05227256566286087,
-0.055142391473054886,
0.013991746120154858,
0.008652913384139538,
-0.0509585440158844,
-0.034153975546360016,
0.018391676247119904,
0.006138014607131481,
0.04038324952125549,
0.03748684749007225,
-0.02321317233145237,
0.012411840260028839,
0.03730794042348862,
0.02937769517302513,
0.047515854239463806,
0.0037521235644817352,
-0.004537226166576147,
-0.005691838450729847,
0.0058095199055969715,
0.004883008077740669,
0.03668737784028053,
-0.018231745809316635,
0.07889742404222488,
0.022372223436832428,
0.007592012174427509,
0.018347645178437233,
0.03347868472337723,
-0.03888051211833954,
0.016524147242307663,
-0.02203439176082611,
-0.0395246297121048,
0.04866762086749077,
0.004422840662300587,
-0.0012318347580730915,
0.022671982645988464,
-0.015491207130253315,
-0.01887408085167408,
-0.01966329663991928,
-0.0020709848031401634,
0.002081116894260049,
0.017612719908356667,
-0.017482832074165344,
0.022628260776400566,
-0.020626286044716835,
0.028189104050397873,
0.02248390018939972,
-0.053835585713386536,
-0.008681793697178364,
0.02909628488123417,
-0.02782650850713253,
0.0005715209408663213,
0.0188688263297081,
0.01894156076014042,
0.005453955847769976,
-0.02152032032608986,
0.03515377640724182,
-0.002298560459166765,
0.027884628623723984,
0.0015401117270812392,
-0.01371296588331461,
0.018863024190068245,
-0.04585478827357292,
-0.012867016717791557,
-0.057951148599386215,
0.01467357948422432,
-0.013240301981568336,
0.017471211031079292,
0.03970889747142792,
0.020777326077222824,
0.015441011637449265,
0.05016021803021431,
-0.020891454070806503,
0.07674392312765121,
-0.0202092994004488,
0.04711829125881195,
0.0020403931848704815,
-0.00027184069040231407,
0.005097744055092335,
0.028187284246087074,
0.048950355499982834,
0.031691983342170715,
-0.015094578266143799,
-0.01316793356090784,
-0.002943497383967042,
-0.03654923290014267,
-0.007810521405190229,
-0.008060302585363388,
0.02035413309931755,
0.04758157208561897,
-0.01866304688155651,
0.0010919396299868822,
-0.047516901046037674,
-0.053869251161813736,
-0.049406010657548904,
0.02977645769715309,
0.04081038385629654,
0.03418140485882759,
0.040807269513607025,
-0.01860680803656578,
-0.02084255777299404,
0.0883975550532341,
-0.042112499475479126,
-0.038699451833963394,
0.006052161566913128,
0.0011202797759324312,
-0.0016131110023707151,
0.011766324751079082
] |
<p>I always get a little uneasy that all the theories I can think of (at least since Newton) are constructed in a way such that they would be true in heaven and on earth ... but we can never go everywhere and test it out. </p>
<p>So here is the question:</p>
<blockquote>
<p>Is there some good justification to implement something like the principle of relativity in scientific theories other than it turned out to work good so far? </p>
</blockquote>
<p>Some more motivation:</p>
<p>We have an understanding of different places in space (and time) and what different velocities are. Like imagine me and my droogs cruising our skateboards down the neighborhood and there is a truck driving in the other direction. I see a cactus on the roadside and I wonder how the trucker in his ride sees it. </p>
<p><img src="http://i.imgur.com/7qhvM.png" alt=""></p>
<p>Now in the maths, space $\vec x$ and spacetime $t$ represent physical space and physical time. And if I know my coordinates, the form of the plant and its location and orientation in space, I can find out what I see and also what the trucker from his position sees. A <em>coordinate transformation</em> (replacing some letter on a piece of paper with some other letters in a systematic way) is conventually interpreted as taking the data from one "perspective" and transforming it into "another perspecitive".</p>
<p>It's supposed to be a fruitful approach to physics to consider only the observable quantities. Maybe I interpret the principle of relativity the wrong way, but I find it funny that a theory tells me there are spacetime events where I can never get to (outside the light cone). And simultaneously I'm guaranteed that if I'm there I would also be able to physics and come to the right conclusions. At the very least, I feel this is somewhat redundant - why not drop it?</p>
| 10,788 |
[
-0.02122604288160801,
-0.02903822995722294,
0.00995031651109457,
-0.042221564799547195,
0.03346048668026924,
-0.008591877296566963,
-0.0371382050216198,
0.038310326635837555,
-0.01594190113246441,
0.003029567888006568,
0.010632310062646866,
0.04067150503396988,
0.02383747696876526,
0.017715662717819214,
0.035238396376371384,
0.00649716891348362,
0.0020778037142008543,
0.019397947937250137,
-0.04467024281620979,
-0.048870932310819626,
0.013673449866473675,
0.015777595341205597,
0.0034081062767654657,
0.0025660532992333174,
-0.009248251095414162,
0.014102679677307606,
-0.014861902222037315,
-0.01275493111461401,
0.003370885271579027,
0.04962369054555893,
0.01555714476853609,
-0.016055837273597717,
-0.016873611137270927,
0.020506618544459343,
0.038906268775463104,
-0.005826457403600216,
-0.007591828238219023,
-0.01967255026102066,
0.054131168872117996,
0.010244127362966537,
-0.03441966697573662,
0.015539763495326042,
-0.02674790844321251,
0.06110791862010956,
-0.010041537694633007,
0.06451472640037537,
0.010692683048546314,
0.024057505652308464,
0.0695456862449646,
-0.021339189261198044,
0.052486881613731384,
0.000902796455193311,
-0.05596579983830452,
0.028689680621027946,
-0.05021880567073822,
-0.006357476115226746,
0.09197688847780228,
0.043956004083156586,
-0.04338519647717476,
-0.054279033094644547,
-0.028848150745034218,
-0.020811282098293304,
0.0032322234474122524,
0.011152542196214199,
-0.014187089167535305,
-0.00039736597682349384,
-0.030730219557881355,
-0.02357957512140274,
0.032981473952531815,
-0.018588710576295853,
-0.01376674696803093,
0.01176801323890686,
0.027853485196828842,
0.027159977704286575,
-0.02352464199066162,
-0.020203743129968643,
0.03564305230975151,
-0.0009134283754974604,
0.04065673425793648,
0.026781154796481133,
0.0007995936903171241,
-0.00419317651540041,
0.012560168281197548,
0.027330299839377403,
0.01366363000124693,
0.0236657727509737,
0.048595111817121506,
-0.011660696007311344,
0.017106886953115463,
0.05298999696969986,
0.006873332429677248,
0.010620001703500748,
0.03055817261338234,
-0.01916278712451458,
-0.006275605875998735,
0.04716898500919342,
0.0002915581571869552,
-0.0034553927835077047,
0.011172774247825146,
-0.013346284627914429,
-0.02344238944351673,
-0.022688381373882294,
0.003132518380880356,
0.045235298573970795,
-0.015932857990264893,
-0.024426506832242012,
-0.010013188235461712,
0.020226679742336273,
0.002051218179985881,
0.01309063658118248,
-0.04788043722510338,
0.01023080199956894,
0.02468229830265045,
0.06489084661006927,
0.016278279945254326,
-0.031294796615839005,
0.009921921417117119,
-0.0146144675090909,
0.09026395529508591,
0.055466797202825546,
0.06360859423875809,
-0.028535202145576477,
0.019315361976623535,
-0.00947393849492073,
-0.06462576985359192,
0.012491695582866669,
0.016375860199332237,
0.013924571685492992,
0.010370101779699326,
-0.029051432386040688,
0.008218272589147091,
0.020492421463131905,
0.032912954688072205,
0.0174880288541317,
0.04184475913643837,
0.005134920123964548,
-0.10974577069282532,
-0.05548250302672386,
0.027872849255800247,
0.05397676303982735,
-0.041833728551864624,
-0.07306884229183197,
-0.005500259343534708,
0.027667300775647163,
0.07502885907888412,
-0.020417090505361557,
-0.00037999419146217406,
0.019790684804320335,
0.040535781532526016,
-0.0015507802600041032,
0.005668606609106064,
-0.01882842369377613,
-0.013849815353751183,
-0.07609642297029495,
-0.0034306866582483053,
-0.03230016678571701,
0.0025196215137839317,
0.059386301785707474,
-0.01647152751684189,
-0.02509508654475212,
0.06373963505029678,
-0.02332763746380806,
-0.019494235515594482,
0.001680224435403943,
-0.021980898454785347,
-0.016256002709269524,
0.059970129281282425,
0.021894004195928574,
0.02344883792102337,
0.012400412000715733,
0.035713523626327515,
0.046485815197229385,
-0.012116960249841213,
-0.01361793465912342,
0.04548962414264679,
-0.050186339765787125,
-0.0012773099588230252,
0.05977188050746918,
-0.0057018171064555645,
-0.014291667379438877,
-0.028687788173556328,
-0.042405836284160614,
-0.016761695966124535,
-0.005650701466947794,
0.025805868208408356,
0.02290024794638157,
-0.01703142374753952,
0.013638188131153584,
0.030465418472886086,
-0.06189568713307381,
-0.017847007140517235,
-0.060891248285770416,
-0.011125276796519756,
-0.03683307766914368,
-0.015742359682917595,
0.022437792271375656,
0.01781405322253704,
0.00018225905660074204,
-0.05415920168161392,
-0.00981931947171688,
0.012474286369979382,
0.051287610083818436,
0.018340975046157837,
0.006108423694968224,
-0.009547930210828781,
0.05773811787366867,
0.028627905994653702,
0.012274697422981262,
-0.018065297976136208,
0.010283688083291054,
-0.045931681990623474,
0.023333555087447166,
-0.02423159033060074,
0.0009838500991463661,
0.0062409513629972935,
0.031534671783447266,
0.006297660060226917,
0.003094334155321121,
-0.030596725642681122,
0.03203588351607323,
-0.0456278957426548,
0.08804310113191605,
0.06170458346605301,
-0.026378536596894264,
0.00307239918038249,
0.03910939767956734,
0.006380626931786537,
0.03513253480195999,
0.025849822908639908,
-0.03842218965291977,
-0.05660911276936531,
-0.016920404508709908,
0.034382984042167664,
0.030281225219368935,
-0.0061158910393714905,
-0.0047698053531348705,
0.028251899406313896,
0.053900301456451416,
0.014003152959048748,
0.025408916175365448,
-0.013570861890912056,
-0.03186805546283722,
-0.014160461723804474,
-0.014432139694690704,
0.019409481436014175,
0.0033696594182401896,
0.03319702669978142,
-0.01003436278551817,
0.007319296710193157,
-0.03357795625925064,
0.009479891508817673,
0.0042433300986886024,
-0.0018961646128445864,
0.025627214461565018,
0.0648636668920517,
0.009822936728596687,
0.019597630947828293,
0.004896862432360649,
-0.0074034202843904495,
0.03398919850587845,
0.007551109883934259,
0.01179526187479496,
-0.047175195068120956,
0.01318974420428276,
0.00646965904161334,
0.043708737939596176,
-0.04214195907115936,
-0.02012396790087223,
0.027768006548285484,
-0.04558252543210983,
0.00957542471587658,
-0.023950496688485146,
-0.03335033729672432,
0.03340322896838188,
0.010182473808526993,
0.002133509609848261,
0.02599429525434971,
0.016321351751685143,
-0.049460507929325104,
-0.027324210852384567,
0.0028364635072648525,
0.008236495777964592,
-0.0009868297493085265,
0.03832000494003296,
-0.03818697854876518,
0.039814747869968414,
-0.04949362948536873,
-0.03384680300951004,
0.03211766481399536,
-0.00836867280304432,
0.007227766793221235,
-0.008961533196270466,
-0.000294925004709512,
-0.06608384102582932,
-0.04082489013671875,
-0.03402070328593254,
0.012619450688362122,
-0.05388087406754494,
-0.01934358850121498,
0.05782104656100273,
-0.007087685167789459,
-0.07992985099554062,
0.0031984103843569756,
-0.04128429293632507,
-0.04605168104171753,
0.009999874047935009,
-0.007852884940803051,
-0.009355010464787483,
-0.03777093067765236,
0.01618470624089241,
0.0046586752869188786,
-0.03422476723790169,
-0.01790790632367134,
-0.028789840638637543,
-0.056339602917432785,
0.030003584921360016,
0.033294886350631714,
0.0696791559457779,
-0.011886832304298878,
0.011346732266247272,
0.04642795771360397,
0.04062991216778755,
-0.050901852548122406,
-0.04637131839990616,
0.02717801369726658,
-0.025415686890482903,
0.008897306397557259,
0.0027931665536016226,
0.022819435223937035,
0.01564343087375164,
0.03563852235674858,
0.023458300158381462,
0.044717494398355484,
0.0002497556561138481,
0.030016355216503143,
-0.012968217022716999,
-0.016936829313635826,
0.02179541625082493,
0.019854217767715454,
0.015416130423545837,
0.04466787353157997,
-0.0376376248896122,
0.0025535598397254944,
-0.0008815727196633816,
-0.006634053308516741,
0.04245540499687195,
-0.08076469600200653,
0.04626702889800072,
0.03448048606514931,
0.004558663349598646,
0.015625327825546265,
0.02068287879228592,
0.0059350342489778996,
0.017682116478681564,
-0.025314494967460632,
0.007449431344866753,
0.04965256154537201,
0.02172302082180977,
-0.003917937632650137,
0.020017456263303757,
0.030269987881183624,
-0.03437471762299538,
-0.05516860634088516,
-0.014025543816387653,
0.024774620309472084,
0.007713550701737404,
-0.008837515488266945,
-0.0013672910863533616,
0.0689871534705162,
0.03836605325341225,
-0.001973717240616679,
0.04316658899188042,
-0.03317728266119957,
0.01936941035091877,
-0.026960810646414757,
-0.024846578016877174,
0.028534986078739166,
0.021424874663352966,
0.01777650974690914,
0.036793965846300125,
0.006779853720217943,
0.008408168330788612,
0.01779266633093357,
0.02248712070286274,
-0.09117419272661209,
-0.004745191894471645,
-0.008540316484868526,
-0.016841145232319832,
-0.0370868518948555,
-0.010591529309749603,
0.02547561377286911,
-0.042364589869976044,
-0.009544461034238338,
-0.008507464081048965,
0.015447321347892284,
-0.08356267958879471,
0.014008955098688602,
-0.02042919397354126,
-0.0485125407576561,
-0.022217832505702972,
0.061201874166727066,
0.05410180985927582,
-0.017916157841682434,
-0.024660160765051842,
0.04299936071038246,
-0.014531160704791546,
-0.030896158888936043,
-0.02432367391884327,
-0.015384604223072529,
0.05069460719823837,
0.028096435591578484,
0.017427265644073486,
-0.027508486062288284,
-0.012790360487997532,
0.025435281917452812,
0.017855549231171608,
0.045820336788892746,
-0.023287557065486908,
-0.029357003048062325,
-0.020064327865839005,
-0.0068697198294103146,
-0.026572374626994133,
0.004338023252785206,
0.040935058146715164,
-0.03473998233675957,
-0.02422710321843624,
0.042949359863996506,
0.014006994664669037,
-0.0039143869653344154,
0.018757585436105728,
-0.00477550458163023,
-0.021843384951353073,
-0.02196410857141018,
-0.022371431812644005,
-0.026042912155389786,
-0.013137709349393845,
0.007822629064321518,
0.025594187900424004,
-0.006598943844437599,
-0.002043328480795026,
-0.01951322704553604,
0.006170951295644045,
0.0070573086850345135,
-0.02228502556681633,
0.03168649971485138,
-0.028053291141986847,
-0.0019646864384412766,
0.017750917002558708,
0.018562138080596924,
-0.005897198338061571,
0.024481449276208878,
0.043796148151159286,
0.008254843764007092,
-0.020398752763867378,
-0.07905495166778564,
-0.035650789737701416,
0.022976204752922058,
0.0000016610936199867865,
0.0021933307871222496,
-0.006619162857532501,
-0.04468587413430214,
-0.00528867868706584,
0.04564768075942993,
-0.042494673281908035,
0.0073116617277264595,
0.0019335902761667967,
-0.003723739180713892,
-0.04520372673869133,
-0.03997557610273361,
-0.02564844861626625,
-0.004108672961592674,
-0.016872834414243698,
0.012091362848877907,
-0.021541422232985497,
0.001426979317329824,
-0.008807236328721046,
0.04138787090778351,
0.03946525231003761,
0.034410614520311356,
0.043805334717035294,
-0.011778177693486214,
-0.03472299873828888,
-0.0029101676773279905,
-0.05118314176797867,
-0.08160457015037537,
0.004758406896144152,
0.060039859265089035,
-0.019949641078710556,
0.03568233922123909,
-0.025220854207873344,
-0.05201926827430725,
0.06317277252674103,
-0.018812181428074837,
-0.017623411491513252,
0.006967798341065645,
-0.06281508505344391,
0.008689837530255318,
0.009529064409434795,
0.04666481539607048,
0.006779732648283243,
0.016856800764799118,
-0.011784304864704609,
0.01062801480293274,
0.0032108905725181103,
0.036541715264320374,
0.014685017056763172,
0.015028160065412521,
-0.0310591422021389,
-0.008769582957029343,
-0.04083307087421417,
0.03217349201440811,
-0.006067743990570307,
-0.009098462760448456,
-0.022606302052736282,
-0.05147145688533783,
-0.021023308858275414,
0.021642275154590607,
0.022221675142645836,
0.02749801054596901,
-0.01356723252683878,
0.009679623879492283,
-0.01966121233999729,
-0.025778748095035553,
0.013671224936842918,
-0.013473276048898697,
0.014924954622983932,
0.03597329184412956,
0.011569448746740818,
-0.011805950663983822,
-0.02261037938296795,
0.00977026205509901,
0.03237413242459297,
-0.022395258769392967,
0.02496793307363987,
0.002798372181132436,
0.039974842220544815,
0.06261343508958817,
-0.02214488573372364,
-0.044410236179828644,
0.03359013795852661,
-0.01735767163336277,
-0.003755698911845684,
-0.028710288926959038,
-0.06271987408399582,
-0.010572806932032108,
0.029895499348640442,
-0.034564439207315445,
-0.04730262607336044,
0.0022468219976872206,
0.011157848872244358,
-0.04019775614142418,
-0.04363095015287399,
0.015515522100031376,
-0.021792715415358543,
-0.0530223548412323,
-0.006525059696286917,
0.04072403907775879,
-0.0239072535187006,
-0.015525730326771736,
-0.007464439142495394,
0.011468464508652687,
0.06968338042497635,
-0.06528403609991074,
0.00870348047465086,
0.027830393984913826,
0.008900661021471024,
0.026265056803822517,
0.008922477252781391,
0.02873794175684452,
-0.011474769562482834,
-0.044428251683712006,
-0.03821507468819618,
0.032216597348451614,
0.011635356582701206,
-0.01897578313946724,
0.0073719630017876625,
0.046929240226745605,
0.000481984403450042,
-0.016383778303861618,
-0.045167215168476105,
0.015553025528788567,
0.009933358989655972,
-0.012358436360955238,
-0.004870555829256773,
0.012476637959480286,
0.017380785197019577,
-0.015341420657932758,
-0.00827957782894373,
0.01396319828927517,
-0.03254285827279091,
0.0035169445909559727,
0.031903576105833054,
-0.029401933774352074,
0.013629426248371601,
0.02696932479739189,
0.005871276371181011,
0.04286171495914459,
-0.010524976067245007,
0.00792476162314415,
0.009189260192215443,
-0.01020868681371212,
-0.05021894350647926,
-0.00201084790751338,
-0.03699834272265434,
0.000291394186206162,
0.06728561222553253,
-0.001693157129921019,
0.058056846261024475,
0.04971126839518547,
0.015350453555583954,
-0.02231976017355919,
-0.00856839306652546,
0.005048937629908323,
-0.014555244706571102,
-0.006591520272195339,
0.033448610454797745,
-0.008537504822015762,
-0.02145545929670334,
0.04500546306371689,
0.04364725202322006,
-0.025929100811481476,
0.010444894433021545,
0.029018841683864594,
0.026366742327809334,
0.03098682127892971,
-0.030858702957630157,
-0.036196544766426086,
0.0036215197760611773,
-0.030676323920488358,
0.01945340819656849,
0.0026204888708889484,
-0.0044053709134459496,
0.0538383312523365,
0.017162857577204704,
0.011138195171952248,
-0.011827158741652966,
0.004203991033136845,
-0.07243426144123077,
-0.021532731130719185,
0.007838580757379532,
0.03660251945257187,
0.006319340784102678,
-0.02575649507343769,
0.0676765888929367,
-0.036392875015735626,
0.01612156257033348,
-0.01147751696407795,
-0.07950808852910995,
-0.04297381639480591,
-0.02983788400888443,
-0.01771695353090763,
0.057287998497486115,
0.033472802489995956,
-0.014682156965136528,
-0.014712906442582607,
-0.05682173743844032,
0.040026843547821045,
0.029510965570807457,
0.07141643017530441,
-0.01912393607199192,
0.0536808967590332,
-0.005078385584056377,
0.0042650592513382435,
-0.021295608952641487,
-0.0017394341994076967,
0.13145609200000763,
0.02163304202258587,
0.00753319077193737,
-0.0197865329682827,
0.024815816432237625,
-0.034077633172273636,
0.01904323697090149,
-0.029699379578232765,
0.03871767967939377,
-0.012040212750434875,
0.0327080637216568,
-0.014768516644835472,
0.033730294555425644,
0.018692921847105026,
-0.03952748328447342,
0.05375877395272255,
-0.049373749643564224,
-0.033156026154756546,
0.0020627626217901707,
0.023451142013072968,
-0.003806408029049635,
0.00118345208466053,
-0.027746358886361122,
0.00253944075666368,
-0.028040263801813126,
0.0017327216919511557,
-0.008988436311483383,
-0.03521445393562317,
0.030095195397734642,
0.0021221276838332415,
-0.017105404287576675,
0.0429999902844429,
0.032123368233442307,
-0.047344304621219635,
-0.06352422386407852,
-0.00978020578622818,
0.004190624225884676,
-0.0073797376826405525,
0.025366798043251038,
0.019032908603549004,
0.007469861768186092,
0.011973820626735687,
0.02095836214721203,
0.0013500233180820942,
-0.030178071931004524,
-0.038800548762083054,
-0.041946087032556534,
0.07220609486103058,
-0.012303256429731846,
-0.009725592099130154,
-0.005363895557820797,
-0.017539866268634796,
0.0137102659791708,
-0.11652590334415436,
-0.013818508945405483,
0.004157898481935263,
0.058127082884311676,
0.031288158148527145,
0.002443180186673999,
0.015760475769639015,
0.024792321026325226,
-0.0067191896960139275,
-0.002288620686158538,
-0.0029740016907453537,
-0.015830177813768387,
-0.013176991604268551,
0.0013378830626606941,
0.03723575174808502,
0.024566907435655594,
-0.0348629504442215,
-0.05905488133430481,
0.002556777326390147,
-0.047737784683704376,
-0.0005067470483481884,
0.015180916525423527,
0.035536497831344604,
0.006494816392660141,
-0.017918966710567474,
0.015345199033617973,
-0.01745482161641121,
-0.03279275447130203,
0.0033977741841226816,
-0.007097567897289991,
-0.00956285186111927,
-0.025720182806253433,
0.046328477561473846,
-0.0011667382204905152,
0.06745144724845886,
0.0039990684017539024,
-0.014565634541213512,
-0.019736969843506813,
0.06172574311494827,
-0.009599815122783184,
0.008696237578988075,
-0.025998970493674278,
0.01433104369789362,
-0.0004547464777715504,
-0.01814412511885166,
-0.013754668645560741,
0.04281949624419212,
0.032419849187135696,
-0.017536673694849014,
0.012324321083724499,
0.03224741667509079,
-0.0012008720077574253,
-0.0223709549754858,
0.03618425503373146,
-0.024973992258310318,
-0.006892298348248005,
0.042285267263650894,
0.032906290143728256,
-0.0496346578001976,
-0.010312075726687908,
-0.025780554860830307,
-0.0072942678816616535,
-0.0484568253159523,
-0.014450709335505962,
-0.009322741068899632,
0.011476891115307808,
-0.02128005400300026,
0.0256796944886446,
-0.013728712685406208,
0.028332538902759552,
-0.02587977796792984,
-0.007531790994107723,
-0.037929680198431015,
-0.03140055388212204,
-0.03229869529604912,
0.03425613418221474,
-0.05074227601289749,
-0.012602582573890686,
0.03259483724832535,
0.015926020219922066,
-0.016745027154684067,
-0.01539338193833828,
0.018953220918774605,
0.018091687932610512,
0.03711453080177307,
-0.0065157124772667885,
-0.0062850783579051495,
0.006516868714243174,
-0.015542383305728436,
-0.021977711468935013,
0.04145776852965355,
-0.02423127181828022,
0.019792959094047546,
-0.0011295105796307325,
-0.024998195469379425,
0.0021077177952975035,
0.03745342791080475,
-0.026221176609396935,
0.012262503616511822,
0.0034125512465834618,
-0.04098278656601906,
-0.000852039607707411,
-0.00249850912950933,
0.07363122701644897,
-0.02161899395287037,
-0.013229016214609146,
0.020827556028962135,
0.005174967925995588,
0.014135307632386684,
0.024036196991801262,
0.009642457589507103,
-0.0359196737408638,
-0.04280625283718109,
0.004268444608896971,
-0.029861414805054665,
0.02644256129860878,
0.04800320789217949,
-0.062407657504081726,
0.04731844365596771,
0.04741990193724632,
0.025881625711917877,
-0.07122770696878433,
0.007218838203698397,
0.05086248740553856,
0.03566373884677887,
0.06156960874795914,
-0.026142558082938194,
-0.002700490178540349,
0.011174303479492664,
-0.08461359143257141,
0.015768887475132942,
-0.011670928448438644,
-0.022021058946847916,
-0.03860615938901901,
0.004062833730131388,
-0.0283108688890934,
0.07473818212747574,
0.04563438147306442,
0.052312806248664856,
0.006815975997596979,
0.04047362506389618,
-0.011593786999583244,
-0.049953412264585495,
-0.004422813653945923,
0.04556642100214958,
-0.015378451906144619,
0.014461572282016277,
0.041114047169685364,
-0.012572611682116985,
-0.025476081296801567,
0.010572029277682304,
-0.0023548551835119724,
0.03126237541437149,
-0.010219112038612366,
0.009440720081329346,
0.02349342219531536,
0.05437936633825302,
0.026747068390250206,
-0.019169313833117485,
-0.02394520863890648,
-0.009053338319063187,
-0.013162890449166298,
0.006631310097873211,
0.008927219547331333,
-0.013056661002337933,
0.01129613071680069,
-0.06450355798006058,
-0.017706437036395073,
-0.0006072399555705488,
-0.009865960106253624,
-0.023586370050907135,
0.006788510829210281,
0.049999311566352844,
-0.006152038462460041,
0.0006001838482916355,
-0.025438137352466583,
-0.041257668286561966,
0.006658461876213551,
0.05610448867082596,
0.019167298451066017,
-0.010471450164914131,
-0.012287259101867676,
-0.02188348025083542,
-0.04045905917882919,
-0.016494955867528915,
0.012791506946086884,
0.003159782150760293,
-0.0487484335899353,
-0.0283642765134573,
-0.015110688284039497,
-0.013587700203061104,
0.007225251290947199,
-0.001453008851967752,
-0.008861254900693893,
0.039910007268190384,
0.019242210313677788,
0.028166022151708603,
0.018026744946837425,
-0.013304285705089569,
-0.003769973525777459,
-0.08131485432386398,
0.020736778154969215,
-0.002078998601064086,
-0.009058550000190735,
-0.04567963629961014,
-0.024948278442025185,
-0.03530357405543327,
0.01859784498810768,
0.018691210076212883,
-0.002310274401679635,
0.011011381633579731,
0.022719454020261765,
-0.0005028644227422774,
0.019369641318917274,
-0.05403755605220795,
0.02196282520890236,
0.010959874838590622,
-0.042367756366729736,
0.026874147355556488,
-0.019457416608929634,
-0.02510003373026848,
0.005271453410387039,
0.04797705262899399,
-0.019376298412680626,
0.05250563845038414,
0.008090510033071041,
-0.026706760749220848,
0.03224320709705353,
0.007501968182623386,
0.0025677867233753204,
0.011873754672706127,
0.019800469279289246,
0.015166545286774635,
0.016310716047883034,
-0.04783835634589195,
-0.044279132038354874,
0.0030943213496357203,
-0.04937997832894325,
-0.048095736652612686,
-0.008844684809446335,
-0.032532185316085815,
0.03137828782200813,
-0.019811181351542473,
0.00035290326923131943,
0.04621180146932602,
-0.05672287568449974,
-0.027294300496578217,
0.02693798951804638,
-0.001615996239706874,
0.029696354642510414,
0.02189246378839016,
0.028773844242095947,
0.025399211794137955,
-0.04110659286379814,
-0.009184329770505428,
-0.0022384861949831247,
0.013279921375215054,
-0.006841737311333418,
0.04056613892316818,
0.03519123047590256,
0.0022077448666095734,
0.011873391456902027,
0.016900161281228065,
0.06056798994541168,
-0.04972583055496216,
0.038458406925201416,
-0.0015976382419466972,
-0.015335765667259693,
0.010709411464631557,
-0.0009808692848309875,
0.004124983213841915,
0.08223025500774384,
-0.00830321479588747,
-0.026003623381257057,
-0.0554034523665905,
-0.009244722314178944,
-0.011659489013254642,
0.021613912656903267,
0.002008480252698064,
0.02120823971927166,
-0.014021718874573708,
0.03803711012005806,
-0.025022851303219795,
-0.006030777469277382,
0.036509305238723755,
-0.02282083034515381,
-0.026274558156728745,
-0.02711034007370472,
-0.023862091824412346,
0.03292364254593849,
-0.024765174835920334,
-0.04412224516272545,
-0.04755464568734169,
0.02126876823604107,
0.014232179149985313,
0.030217686668038368,
-0.008793591521680355,
-0.013434692285954952,
-0.03629900515079498,
0.053674086928367615,
-0.07666990906000137,
-0.018555788323283195,
-0.004733760375529528,
0.007665784098207951,
-0.002607082249596715,
0.0044133770279586315
] |
<p>I was reviewing the paper-<a href="http://www.sciencedirect.com/science/article/pii/S0370269304010032" rel="nofollow">Coupling of a vector gauge field to a massive tensor field</a></p>
<p>In the calculation I found the term $ 2\mu^2 \varepsilon^{ijk} \dfrac{\partial_j}{\partial^2}B_k\dot{B}$ which needed to be integrated by parts. How can I do this? Please help me.</p>
<p><em>Note</em>: Here $B_k$ is the space component of an antisymmetric tensor field and $\dot{B}$ is the time derivative of $B_k$.</p>
<p>(<em>Edit: corrected the index</em>)</p>
| 10,789 |
[
0.02267693728208542,
-0.004082218278199434,
-0.002336349105462432,
-0.007848587818443775,
0.034463126212358475,
0.013974834233522415,
-0.0124046066775918,
-0.0019874388817697763,
0.02176622860133648,
-0.0561196431517601,
0.03991677612066269,
0.05616089701652527,
0.08719103038311005,
0.030080748721957207,
0.020286960527300835,
0.0009435283136554062,
-0.04870301112532616,
0.007257554680109024,
0.01741635613143444,
-0.04068811237812042,
0.00009367519669467583,
0.049209754914045334,
-0.013367285951972008,
-0.017668617889285088,
-0.009486798197031021,
0.058436594903469086,
0.025428298860788345,
-0.00481412373483181,
-0.017269816249608994,
0.03221634775400162,
-0.04286234453320503,
-0.047138698399066925,
0.03726033493876457,
-0.025942884385585785,
0.010855116881430149,
0.006851830054074526,
-0.017040183767676353,
-0.05955186113715172,
0.023310018703341484,
0.0025319375563412905,
-0.017139965668320656,
0.003796875709667802,
-0.03528771176934242,
0.05001106485724449,
-0.019704824313521385,
0.03243258595466614,
-0.021456433460116386,
0.012431650422513485,
0.04374159872531891,
-0.01577794924378395,
0.056076958775520325,
0.03028504177927971,
0.046778690069913864,
0.009090828709304333,
-0.04948629066348076,
-0.008978300727903843,
0.03235208988189697,
0.0632326528429985,
0.03263583406805992,
-0.045995086431503296,
0.004135816358029842,
-0.025721287354826927,
-0.01801796816289425,
-0.023027176037430763,
-0.01229797676205635,
0.01434449665248394,
-0.0005649137892760336,
-0.025971313938498497,
0.040733449161052704,
-0.009693451225757599,
0.0074144150130450726,
-0.03140295296907425,
0.007268291898071766,
-0.0695909634232521,
-0.0026043332181870937,
0.001461690291762352,
0.012922227382659912,
0.035733360797166824,
-0.00845245085656643,
-0.004212092142552137,
-0.026293961331248283,
0.005895774345844984,
0.014082768931984901,
0.04561838135123253,
0.02640410326421261,
0.018213292583823204,
0.045373495668172836,
0.021606644615530968,
-0.013466333039104939,
0.032885871827602386,
-0.008999072946608067,
0.05363596975803375,
0.06072857975959778,
-0.004208028316497803,
-0.023493634536862373,
-0.0007152165635488927,
0.02330402098596096,
0.06577402353286743,
-0.004467225633561611,
-0.012029984034597874,
-0.01061681192368269,
-0.006549641955643892,
0.007558723911643028,
0.05787017568945885,
0.036631029099226,
0.004055360797792673,
-0.0018985646311193705,
-0.02999940887093544,
0.0027500649448484182,
-0.012192381545901299,
-0.051167719066143036,
0.009201650507748127,
-0.007900813594460487,
-0.046075426042079926,
-0.011553088203072548,
-0.015535389073193073,
-0.019613509997725487,
-0.014648004435002804,
0.027241049334406853,
0.045217376202344894,
0.05153810977935791,
-0.015552444383502007,
0.01927931420505047,
-0.04002861678600311,
-0.07775527238845825,
0.004767731763422489,
0.053252365440130234,
-0.004773792345076799,
-0.06860276311635971,
0.007880765944719315,
0.04613814502954483,
-0.011882226914167404,
0.03392115607857704,
-0.020649047568440437,
0.029420532286167145,
-0.03224445879459381,
-0.06783577799797058,
-0.09105730056762695,
0.014737395569682121,
-0.003247926477342844,
0.005451638251543045,
-0.08732673525810242,
-0.00010273075895383954,
0.06991197168827057,
0.10625341534614563,
0.01126989908516407,
0.004743498750030994,
0.018072452396154404,
0.01358600053936243,
0.010373064316809177,
-0.018116198480129242,
-0.03449542820453644,
0.006571067031472921,
-0.013961728662252426,
-0.00033543992321938276,
-0.037028245627880096,
-0.0060830796137452126,
0.019075682386755943,
-0.011572732590138912,
0.007755146827548742,
0.09432712197303772,
0.017636949196457863,
-0.0025016271974891424,
0.024212772026658058,
-0.02269946038722992,
-0.01632845774292946,
0.04585173726081848,
0.011235237121582031,
0.018917426466941833,
-0.002134207636117935,
0.016605228185653687,
0.02082955837249756,
0.007474266458302736,
0.04877696931362152,
0.044580020010471344,
-0.03508588299155235,
0.01649579219520092,
-0.005650059320032597,
-0.006006116513162851,
-0.013272484764456749,
-0.014307478442788124,
-0.07397773116827011,
-0.02158522605895996,
0.03108181618154049,
-0.011108866892755032,
0.02209794893860817,
0.0028701340779662132,
0.025362836197018623,
0.02331319823861122,
-0.058186277747154236,
-0.03679128736257553,
-0.06786078959703445,
-0.002478180453181267,
0.011122094467282295,
-0.03841587156057358,
0.014622454531490803,
-0.011525292880833149,
0.013597212731838226,
-0.043020278215408325,
-0.022544056177139282,
-0.0018683592788875103,
0.009743358008563519,
0.023611323907971382,
0.014935789629817009,
0.01573621667921543,
-0.004426354076713324,
0.028543932363390923,
0.03280111402273178,
0.013806940987706184,
-0.006611393764615059,
-0.006843417417258024,
0.02067086473107338,
-0.028868166729807854,
0.018230976536870003,
0.003205212764441967,
-0.02496039681136608,
0.015282751992344856,
0.028806256130337715,
0.00780095811933279,
0.04298241809010506,
-0.04064217954874039,
0.0516887865960598,
0.0733451396226883,
0.022038348019123077,
0.005005124025046825,
0.013153991661965847,
0.04184078052639961,
0.033307600766420364,
0.0010696555254980922,
-0.027796950191259384,
-0.02868478000164032,
0.015329013578593731,
0.02647692896425724,
0.005747437011450529,
-0.02383824996650219,
0.001271730405278504,
0.019537946209311485,
0.010230472311377525,
0.017968131229281425,
0.034136150032281876,
-0.017556557431817055,
-0.04745024815201759,
0.03280912712216377,
-0.014905136078596115,
-0.01761128567159176,
-0.01664934866130352,
0.023040076717734337,
-0.0019142950186505914,
0.02746005356311798,
-0.0014214343391358852,
-0.0008648691582493484,
0.01485768985003233,
-0.028517842292785645,
0.008563708513975143,
0.011300456710159779,
-0.01975748874247074,
0.06176503375172615,
-0.031052419915795326,
0.03345286101102829,
0.06571381539106369,
-0.0038060955703258514,
0.0033841996919363737,
-0.022491807118058205,
-0.02621682919561863,
0.01982438936829567,
-0.019065557047724724,
-0.03659089654684067,
-0.02913106419146061,
0.01367180049419403,
-0.041349682956933975,
-0.011601514182984829,
0.02242131344974041,
0.00561770424246788,
-0.020101172849535942,
0.014869527891278267,
0.025493867695331573,
0.04323927313089371,
0.03888709843158722,
0.010456462390720844,
-0.014622348360717297,
0.034361980855464935,
-0.009406340308487415,
0.04137284308671951,
0.028000762686133385,
-0.03016861155629158,
0.004773723892867565,
-0.0571562722325325,
-0.007958715781569481,
0.051840025931596756,
0.002406493993476033,
-0.02721824124455452,
0.04195980727672577,
0.0033036847598850727,
-0.04543657600879669,
-0.03684449940919876,
-0.005104809068143368,
0.019097723066806793,
-0.04510083049535751,
0.014538822695612907,
0.0184449702501297,
0.043387025594711304,
-0.011843821965157986,
-0.008350612595677376,
-0.005036532878875732,
-0.04971592128276825,
0.01639988273382187,
-0.013233260251581669,
0.003435443853959441,
-0.018569039180874825,
0.04041554778814316,
0.014202406629920006,
-0.0020941589027643204,
0.013386654667556286,
-0.04431517422199249,
-0.053301289677619934,
0.015077781863510609,
0.036406662315130234,
0.030662963166832924,
0.0019201872637495399,
-0.0554036982357502,
0.09978281706571579,
0.012366501614451408,
-0.01436465885490179,
-0.0163589920848608,
-0.0019873983692377806,
-0.0038563867565244436,
-0.04658278822898865,
-0.009235726669430733,
0.007646768819540739,
0.013476643711328506,
-0.00463629886507988,
0.0202481709420681,
0.03490384668111801,
0.07188486307859421,
0.00889545027166605,
-0.051009874790906906,
-0.01484632771462202,
-0.009539765305817127,
0.016552044078707695,
0.06742198765277863,
0.006914726924151182,
-0.027019931003451347,
0.017304060980677605,
-0.0071174330078065395,
0.00233194581232965,
0.007581527344882488,
-0.040940191596746445,
0.046095360070466995,
0.01718135178089142,
0.0032600536942481995,
-0.02976602129638195,
0.037895143032073975,
-0.008309360593557358,
-0.024646028876304626,
0.029625725001096725,
0.025727448984980583,
0.009960735216736794,
-0.011882809922099113,
-0.0017152178334072232,
0.02280467189848423,
0.02159125544130802,
-0.012636594474315643,
-0.0123286759480834,
-0.004934848286211491,
-0.005926291923969984,
0.018479757010936737,
-0.053600337356328964,
-0.018075531348586082,
0.011227643117308617,
0.024557875469326973,
0.012541192583739758,
-0.009353002533316612,
-0.014788694679737091,
0.006174874491989613,
-0.04561256989836693,
0.0032332544215023518,
-0.03071318194270134,
0.046587735414505005,
0.0003637623449321836,
-0.015578542836010456,
0.004708488006144762,
-0.0009593833237886429,
0.0675954520702362,
-0.008351977914571762,
-0.06473585218191147,
0.05809132754802704,
-0.024617817252874374,
-0.04209540784358978,
0.015227106399834156,
-0.06201915442943573,
-0.016023291274905205,
-0.02298882231116295,
-0.007295411080121994,
-0.006949177011847496,
-0.00005879156742594205,
-0.0630083829164505,
0.04574155434966087,
-0.05166449397802353,
0.006082233972847462,
-0.016367802396416664,
0.009992108680307865,
0.05540747568011284,
-0.03954750671982765,
-0.014599394053220749,
0.030117010697722435,
-0.009743502363562584,
-0.019759686663746834,
-0.03954365849494934,
0.007784966379404068,
0.03192916512489319,
0.0329209603369236,
0.023105543106794357,
0.021425724029541016,
-0.05975600332021713,
-0.0011435634223744273,
-0.0063792383298277855,
0.05594751238822937,
0.023061873391270638,
-0.0064741456881165504,
-0.009328923188149929,
-0.026169098913669586,
-0.0029316223226487637,
-0.005012315697968006,
0.08578253537416458,
0.002564522437751293,
-0.006661873776465654,
0.04823543131351471,
0.03555518761277199,
-0.020917590707540512,
0.030310818925499916,
0.05065351352095604,
-0.0029670491348952055,
-0.0006900675361976027,
-0.0749221220612526,
-0.006031819619238377,
0.018330741673707962,
0.0005330224521458149,
0.0071081905625760555,
-0.01982278749346733,
-0.03300655633211136,
-0.008135480806231499,
0.025408346205949783,
0.006965549197047949,
0.003558964468538761,
0.020896583795547485,
-0.006241501774638891,
-0.01182054728269577,
0.025131884962320328,
-0.010321836918592453,
0.0007620143005624413,
0.07910200208425522,
0.032410066574811935,
0.008106271736323833,
-0.0028599570505321026,
-0.08465356379747391,
-0.03568340465426445,
0.028073657304048538,
0.03477909788489342,
0.0029017040506005287,
-0.03696523606777191,
-0.07808937877416611,
0.011834687553346157,
0.063412606716156,
0.0029494089540094137,
0.012816750444471836,
-0.002138765761628747,
-0.0008276594453491271,
0.00653789471834898,
0.015602990053594112,
-0.022064000368118286,
0.051707688719034195,
-0.015186462551355362,
0.010243946686387062,
-0.04354483261704445,
-0.010772938840091228,
-0.009277921169996262,
0.023821638897061348,
0.0013916228199377656,
0.03373560309410095,
0.010252686217427254,
-0.006431101355701685,
0.005293389782309532,
0.025558635592460632,
-0.05488463118672371,
-0.07428110390901566,
0.023745840415358543,
0.006051318254321814,
-0.04998951405286789,
0.020564567297697067,
-0.051765695214271545,
-0.026179814711213112,
0.08008527010679245,
0.021516481414437294,
0.0017641960876062512,
-0.013298091478645802,
-0.04880371317267418,
0.02372029982507229,
0.02964547649025917,
-0.014878571033477783,
0.04937645047903061,
0.007063135504722595,
0.029994798824191093,
0.009680178947746754,
-0.028731007128953934,
0.015485254116356373,
-0.028212226927280426,
0.022289283573627472,
-0.018278909847140312,
0.002112150192260742,
-0.06503836065530777,
0.05955100059509277,
-0.016615362837910652,
0.020156878978013992,
0.0026274402625858784,
-0.015886973589658737,
-0.007746069226413965,
0.009544990956783295,
-0.003387668402865529,
-0.01582656241953373,
0.03370517119765282,
0.018258046358823776,
-0.001885731820948422,
-0.003154079895466566,
0.03639715909957886,
-0.03236811235547066,
-0.01664947345852852,
0.02325592376291752,
0.0012237796327099204,
0.029414525255560875,
-0.021796593442559242,
-0.01688777469098568,
0.009286392480134964,
-0.04599101468920708,
0.02665279060602188,
-0.011774682439863682,
-0.029648922383785248,
0.008891803212463856,
-0.027493121102452278,
-0.04103383794426918,
0.0071375565603375435,
0.029208527877926826,
0.026485033333301544,
-0.03488917276263237,
0.0038140127435326576,
0.04519045725464821,
0.03418820723891258,
-0.06779464334249496,
-0.04505982995033264,
0.038532424718141556,
-0.012660923413932323,
-0.02235771343111992,
-0.03898725286126137,
0.018167350441217422,
-0.03247341513633728,
-0.027669496834278107,
0.050169944763183594,
0.04871983826160431,
-0.02821802906692028,
-0.04072603955864906,
-0.03175685927271843,
0.02397477813065052,
-0.005651838146150112,
0.005179367959499359,
-0.00579471280798316,
0.03227878734469414,
-0.00524908397346735,
-0.014144808985292912,
0.019532425329089165,
0.08115049451589584,
-0.031475793570280075,
-0.006297912448644638,
-0.01005251333117485,
0.013270653784275055,
0.027612395584583282,
0.005173010285943747,
0.0050679356791079044,
0.019524384289979935,
0.025587165728211403,
-0.014013612642884254,
-0.04124990105628967,
0.011792026460170746,
-0.0024044981691986322,
0.04718957841396332,
-0.03757253661751747,
0.0024614317808300257,
-0.023101933300495148,
-0.02855386957526207,
0.025248343124985695,
-0.016538720577955246,
0.0067138466984033585,
-0.04238588735461235,
0.0578477717936039,
-0.012285144999623299,
0.01194476056843996,
0.03730584308505058,
-0.006148281041532755,
0.01658337190747261,
-0.023833468556404114,
-0.039061445742845535,
0.03279046714305878,
-0.004572216887027025,
-0.05862707272171974,
0.006835615262389183,
-0.014448365196585655,
-0.010314896702766418,
0.07815108448266983,
-0.04031621292233467,
0.048591677099466324,
0.012065757997334003,
0.015517393127083778,
0.007900699973106384,
-0.015198538079857826,
-0.012481315061450005,
-0.004078784491866827,
0.016501300036907196,
0.025318367406725883,
-0.05709795281291008,
0.005748098716139793,
0.03262283280491829,
0.0284536425024271,
-0.03044445812702179,
0.05381917580962181,
0.018403993919491768,
0.03667651116847992,
0.004819488152861595,
0.0010927291586995125,
-0.0576191172003746,
0.029632342979311943,
-0.001875721151009202,
0.03242748975753784,
-0.04204881191253662,
-0.005598344374448061,
0.0781967043876648,
0.043078791350126266,
0.01581386663019657,
0.04623264819383621,
-0.022005857899785042,
-0.027419231832027435,
0.006431750021874905,
0.03732641041278839,
0.0026598451659083366,
0.00537221459671855,
0.035477206110954285,
0.06864813715219498,
-0.013204773887991905,
-0.007323571015149355,
-0.005668706726282835,
-0.03406146913766861,
0.010050637647509575,
-0.03209291771054268,
-0.0613880380988121,
0.04398396611213684,
-0.019548581913113594,
-0.00906162429600954,
0.04412706196308136,
0.0002305676753167063,
0.02364877611398697,
-0.0109641058370471,
0.031029323115944862,
-0.007136612199246883,
0.07282201200723648,
0.002588778967037797,
-0.00514353159815073,
-0.008535679429769516,
0.009239524602890015,
0.11302553117275238,
0.049563195556402206,
0.0036552161909639835,
-0.05157767981290817,
0.025775641202926636,
-0.0287260003387928,
-0.005014490801841021,
-0.0746656060218811,
0.046811994165182114,
-0.04156799986958504,
-0.030593624338507652,
-0.005087711848318577,
0.0445113368332386,
-0.01819293387234211,
-0.01712869107723236,
0.012061732821166515,
-0.02057798206806183,
-0.05002377927303314,
-0.010640292428433895,
0.009287236258387566,
-0.01474958285689354,
-0.03444341942667961,
-0.05571752414107323,
0.04758089780807495,
-0.03264265134930611,
0.006069266702979803,
-0.06259064376354218,
-0.0071619534865021706,
-0.00313368602655828,
0.011276664212346077,
-0.04865560308098793,
0.01586304046213627,
0.006161761004477739,
0.017604634165763855,
-0.013260080479085445,
0.027813050895929337,
0.058356113731861115,
0.009998015128076077,
0.048211656510829926,
0.00480993464589119,
-0.01880728267133236,
-0.010754279792308807,
0.03381072357296944,
0.01814868673682213,
-0.03136593475937843,
0.015923017635941505,
-0.027118811383843422,
0.08075428754091263,
0.039463117718696594,
-0.01820002868771553,
0.011758485808968544,
-0.01574774645268917,
0.020686309784650803,
-0.07497242093086243,
-0.007770783267915249,
0.02075321599841118,
-0.005150157026946545,
-0.03515986353158951,
0.011155779473483562,
0.0027417694218456745,
0.014865295961499214,
0.02364782616496086,
-0.005019987467676401,
-0.009398246183991432,
-0.0005408234428614378,
0.0037472774274647236,
0.013752027414739132,
0.01251106709241867,
-0.012557760812342167,
-0.01035073772072792,
-0.04170650988817215,
0.005912601947784424,
-0.019583774730563164,
-0.01814374327659607,
-0.00011407664715079591,
0.02781054563820362,
0.019740421324968338,
-0.013955540955066681,
-0.038115669041872025,
-0.025811558589339256,
-0.050521597266197205,
0.017516396939754486,
0.025272531434893608,
-0.018473120406270027,
0.0050948611460626125,
0.0009183342335745692,
0.0168925654143095,
0.030226366594433784,
-0.015066983178257942,
0.001351608894765377,
-0.008807835169136524,
0.010329672135412693,
0.03162993863224983,
-0.005058866925537586,
-0.005344444885849953,
0.005159297492355108,
-0.006110163405537605,
0.026351137086749077,
0.0021901989821344614,
-0.0031093545258045197,
0.003510936163365841,
0.02737945318222046,
0.011988786980509758,
0.02834068052470684,
0.0042398907244205475,
-0.01195135060697794,
0.0229913629591465,
-0.006052564363926649,
0.02391541190445423,
0.0174541138112545,
0.012122134678065777,
-0.045176997780799866,
-0.025068551301956177,
-0.0011767498217523098,
-0.0006799062248319387,
0.004758914466947317,
0.011738305911421776,
-0.029098568484187126,
-0.002901796717196703,
-0.04255282133817673,
-0.0014375647297129035,
-0.034970156848430634,
0.009446908719837666,
-0.03349938616156578,
-0.008586030453443527,
-0.007483501918613911,
0.007528890389949083,
-0.017570506781339645,
0.006912426557391882,
-0.03659863770008087,
0.0178994033485651,
0.042985349893569946,
0.00010993040632456541,
-0.03269677236676216,
0.0008799000643193722,
0.00528302974998951,
0.00941661186516285,
0.039582688361406326,
0.00868139136582613,
-0.05236922204494476,
0.0014728556852787733,
-0.0034926014486700296,
-0.0050116549246013165,
0.015928922221064568,
0.011501663364470005,
0.02663511410355568,
0.027803562581539154,
-0.043943826109170914,
-0.04827182739973068,
0.07261749356985092,
-0.04528672993183136,
-0.01635388471186161,
0.00898045301437378,
-0.06384723633527756,
-0.033189211040735245,
-0.038122065365314484,
0.012969855219125748,
0.012365968897938728,
-0.011958329007029533,
-0.01759491302073002,
-0.0224616639316082,
-0.019714925438165665,
-0.014191939495503902,
-0.002823340008035302,
0.015254205092787743,
0.020608149468898773,
-0.02885122038424015,
-0.013443996198475361,
0.023440489545464516,
0.05731355771422386,
-0.029225720092654228,
-0.01874244585633278,
-0.014422995038330555,
0.01291837077587843,
-0.08296442031860352,
-0.017103027552366257,
-0.012633131816983223,
0.028549226000905037,
0.03352881222963333,
-0.0927051454782486,
0.030300453305244446,
0.01712982729077339,
-0.029538830742239952,
0.006867289077490568,
-0.027600541710853577,
-0.02435387670993805,
-0.044792916625738144,
-0.024569261819124222,
-0.0211245846003294,
0.0142877958714962,
0.05797881633043289,
0.017820486798882484,
-0.031921952962875366,
0.013667413033545017,
-0.050273023545742035,
-0.0359983816742897,
-0.018788568675518036,
0.029705515131354332,
0.0013382559409365058,
-0.06118006631731987,
0.051505427807569504,
-0.006350441835820675,
-0.043235231190919876,
0.026798054575920105,
-0.008852117694914341,
-0.023525739088654518,
-0.0004011435084976256,
-0.005194251425564289,
0.010773289948701859,
0.014449307695031166,
0.038565754890441895,
-0.00013460569607559592,
0.03844461590051651,
-0.007062472403049469,
0.03460920974612236,
-0.004315313417464495,
-0.046418447047472,
0.04737774655222893,
0.014492389746010303,
-0.010489346459507942,
-0.014654447324573994,
0.050818413496017456,
-0.03218725696206093,
-0.032102104276418686,
-0.04569534957408905,
-0.008810770697891712,
0.03616098314523697,
-0.04322947934269905,
0.009129823185503483,
-0.032406337559223175,
0.02068968489766121,
0.07537191361188889,
-0.016341254115104675,
-0.04796149209141731,
0.013949178159236908,
-0.030097119510173798,
-0.02722204476594925,
0.004983163438737392,
0.011430606245994568,
-0.00784843135625124,
-0.044826194643974304,
-0.045667361468076706,
0.003269878914579749,
0.022646555677056313,
0.0007936912006698549,
-0.05794738605618477,
-0.03125433996319771,
0.005463156849145889,
0.004124140832573175,
0.00785533431917429,
-0.01128537766635418,
0.0010444140061736107,
0.02747468091547489,
-0.05347570404410362,
0.025977561250329018,
0.019478607922792435,
-0.06124589592218399,
-0.01557640265673399,
-0.03157603368163109,
-0.010003650560975075,
0.00966393481940031,
0.06705667078495026,
0.01417221687734127,
-0.003982397262006998,
0.022200915962457657,
0.016530347988009453,
0.023483823984861374,
-0.047801289707422256,
-0.0020007079001516104,
-0.009912773966789246,
-0.01133634615689516,
-0.0025294923689216375,
0.006632281467318535,
-0.028731683269143105,
0.030111847445368767,
0.014051401987671852,
0.016004452481865883,
0.020181285217404366,
-0.0009631800348870456,
-0.04374253749847412,
0.021769439801573753,
-0.024626174941658974,
0.012251604348421097,
0.06961933523416519,
0.03806520625948906,
0.0006888338248245418,
0.052705395966768265,
-0.006071549374610186,
-0.06798536330461502,
0.0005016316426917911,
-0.06067292019724846,
-0.0027584852650761604,
-0.05015011504292488,
-0.022835686802864075,
0.01573524810373783,
-0.062385525554418564,
0.0251493938267231,
0.051596470177173615,
-0.03650685399770737,
0.020390084013342857,
0.0772443637251854,
0.02370717003941536,
0.015482275746762753,
0.04094579070806503,
0.04163263365626335,
0.016716673970222473,
-0.004100262187421322,
0.021872352808713913,
0.022698285058140755,
0.018710654228925705,
0.018900148570537567,
0.011638987809419632,
0.03802569955587387,
-0.042200494557619095,
-0.03237754479050636,
-0.0075537716038525105,
0.0157376229763031,
-0.06352152675390244,
-0.0172308050096035,
0.02892444282770157,
-0.009105290286242962,
0.05758752301335335,
0.004099952522665262,
-0.022845599800348282,
0.05408383905887604,
-0.01896878518164158,
0.014141742140054703,
-0.03406256064772606,
-0.014381862245500088,
-0.01619630493223667,
0.04956800863146782,
0.0034246521536260843,
0.04343310371041298,
-0.02174392156302929,
-0.007670435588806868,
-0.02981291152536869,
-0.0507320873439312,
-0.0015280742663890123,
-0.06201179698109627,
0.03116312436759472,
0.011578429490327835,
-0.016943102702498436,
0.01414590422064066,
-0.048420898616313934,
-0.02669490873813629,
-0.007678263820707798,
0.026838364079594612,
0.011433965526521206,
-0.007418382912874222,
-0.033554885536432266,
0.005414866842329502,
-0.016177957877516747,
0.057925812900066376,
-0.05485812947154045,
-0.0009236849145963788,
-0.02310182712972164,
0.032650675624608994,
-0.0199729073792696,
-0.0219765342772007
] |
<p>are bubbles of spacetime pinching-off allowed solutions to general relativity? With "pinch-off bubble" i really mean a finite 3D volume of space whose 2D boundary decreases until it reaches zero and it disconnects from the mother spacetime, becoming a compact "child" spacetime</p>
<p>I've read this as a way in eternal cosmologies to produce new universes, but i don't know if that is something something allowed in general relativity or is something from a more advanced theory (i.e: string theory) </p>
<p>In particular, unlike unitary black holes, this does not seem to conserve information, unless someone believes that complementarity can do strange things as clone the information (including the quantum one). Does that automatically make this an unphysical solution?</p>
| 10,790 |
[
-0.013018852099776268,
-0.002722847042605281,
0.002399078104645014,
-0.045262329280376434,
0.0025397285353392363,
0.001650285325013101,
-0.046681422740221024,
-0.03558589518070221,
0.015308923088014126,
-0.03267849236726761,
0.01018146239221096,
0.006219648756086826,
0.009945059195160866,
-0.004492688924074173,
0.006371476221829653,
0.02154449000954628,
-0.00559339951723814,
-0.027643579989671707,
-0.00008790603169472888,
-0.03629845380783081,
0.01285242848098278,
0.02365078590810299,
0.006053336430341005,
-0.013848706148564816,
-0.02043604478240013,
0.007921609096229076,
-0.04059306159615517,
0.008140264078974724,
0.017315849661827087,
0.064242422580719,
-0.005865284241735935,
-0.03302210569381714,
-0.011190015822649002,
0.04531702771782875,
0.019356954842805862,
-0.022777890786528587,
-0.02165570855140686,
-0.028371794149279594,
0.0009800308616831899,
-0.03298977017402649,
-0.030340509489178658,
-0.02379779890179634,
-0.023206496611237526,
0.07200384885072708,
-0.004286666866391897,
-0.005285792518407106,
-0.0021891603246331215,
-0.03175511956214905,
0.028741778805851936,
-0.05054028332233429,
0.048849452286958694,
0.0023390138521790504,
0.029361708089709282,
0.024767903611063957,
-0.01562952809035778,
0.03295300155878067,
0.09537067264318466,
0.08180433511734009,
-0.001951393554918468,
-0.0037882747128605843,
-0.0419047586619854,
0.02406494878232479,
-0.0007202404667623341,
-0.0035719217266887426,
-0.026590444147586823,
0.041636742651462555,
-0.0038894801400601864,
-0.002263006055727601,
-0.010682553984224796,
-0.03382856398820877,
0.020869381725788116,
0.0035687140189111233,
0.025205310434103012,
0.013513143174350262,
0.03446316719055176,
0.0022000025492161512,
-0.004723846446722746,
-0.036758244037628174,
0.036303337663412094,
0.0478244312107563,
-0.014871104620397091,
-0.0017590021016076207,
0.026684250682592392,
0.041710179299116135,
0.003940674476325512,
0.015329459682106972,
0.08018451184034348,
-0.03514697402715683,
0.0175741259008646,
0.07200437039136887,
-0.016378073021769524,
-0.034936875104904175,
0.04023255035281181,
-0.021889938041567802,
-0.03236205503344536,
0.05918044596910477,
0.04223988577723503,
0.03383707255125046,
-0.02015862613916397,
-0.026480840519070625,
0.0009015322430059314,
-0.014681000262498856,
0.022273121401667595,
0.08119789510965347,
0.03147421032190323,
-0.035026635974645615,
-0.07449810206890106,
0.02817147597670555,
-0.006470709573477507,
0.00923250149935484,
-0.03823688253760338,
0.011059953831136227,
-0.048650555312633514,
0.0012270885054022074,
0.0495767705142498,
-0.027126392349600792,
0.0064475866965949535,
-0.034263625741004944,
0.03310919553041458,
0.0556548647582531,
0.04625007510185242,
-0.004139259923249483,
0.03172183409333229,
-0.0009537130245007575,
-0.07867928594350815,
0.011845054104924202,
0.05083684250712395,
-0.0066836318001151085,
-0.05889440327882767,
0.0395461730659008,
0.018066320568323135,
-0.025229334831237793,
0.004587959963828325,
0.0025282665155828,
0.06741263717412949,
-0.05438549071550369,
-0.07987194508314133,
-0.05878817290067673,
0.0329781137406826,
-0.000995074980892241,
-0.02997937984764576,
-0.06107911467552185,
0.01566762663424015,
0.02004794031381607,
0.08389104902744293,
-0.02128959447145462,
-0.005185989663004875,
0.030330143868923187,
0.07604164630174637,
-0.0037158112972974777,
-0.03189847990870476,
-0.010017603635787964,
-0.013250877149403095,
-0.058680109679698944,
-0.013091789558529854,
-0.056495122611522675,
-0.0046360185369849205,
0.04625963792204857,
0.006333217956125736,
-0.03233439102768898,
0.08256891369819641,
-0.015535113401710987,
0.041902728378772736,
0.02530316449701786,
-0.03353588283061981,
-0.024766400456428528,
0.08266206085681915,
0.021254174411296844,
-0.00729562621563673,
0.06188756600022316,
-0.0014677768340334296,
0.0203813798725605,
0.01494557224214077,
0.01244005374610424,
-0.009657581336796284,
-0.03935612738132477,
-0.02071676217019558,
-0.012847328558564186,
0.024200044572353363,
-0.007737248204648495,
-0.0013324592728167772,
0.003087391145527363,
-0.036676034331321716,
-0.02351324073970318,
-0.0170309878885746,
0.008977468125522137,
-0.026760350912809372,
-0.009343666024506092,
-0.008257771842181683,
-0.06325558573007584,
0.014408684335649014,
-0.05784651264548302,
0.029950350522994995,
0.021440688520669937,
0.021071551367640495,
0.031049668788909912,
-0.005003133323043585,
0.04017041251063347,
-0.0773886889219284,
-0.04496890679001808,
-0.0107822734862566,
0.06424406915903091,
-0.04447308927774429,
-0.00490266177803278,
-0.011740188114345074,
0.02775556407868862,
0.009746016934514046,
-0.01109260693192482,
0.015918251127004623,
0.023320313543081284,
-0.005574604496359825,
-0.01225157082080841,
0.03042491525411606,
0.03075355477631092,
-0.059710387140512466,
0.02308746799826622,
0.017744440585374832,
0.0001648736943025142,
0.03637195751070976,
0.024504024535417557,
-0.06548483669757843,
0.03086574748158455,
0.011422546580433846,
0.042557913810014725,
-0.022255564108490944,
0.04779820144176483,
-0.006299569737166166,
0.028744716197252274,
0.004609308205544949,
-0.0415022149682045,
-0.04679632931947708,
-0.008786091580986977,
0.027657000347971916,
0.04415685683488846,
-0.028530368581414223,
0.02097160927951336,
0.03934933617711067,
0.012062321417033672,
0.0008094084332697093,
0.014123741537332535,
-0.018783820793032646,
-0.030948834493756294,
0.021169796586036682,
-0.014493592083454132,
0.000041717426938703284,
0.03873930126428604,
0.04571231082081795,
0.01736551709473133,
-0.01670636609196663,
-0.04289565980434418,
-0.024355068802833557,
0.011621505953371525,
0.01109269168227911,
-0.02639923058450222,
-0.009916132315993309,
-0.029228178784251213,
0.003349588019773364,
-0.016337495297193527,
0.06432166695594788,
0.03328985720872879,
0.024775994941592216,
-0.01986847072839737,
-0.04294333606958389,
-0.01467527449131012,
-0.007235299330204725,
0.025523418560624123,
0.00010065890091937035,
-0.011225832626223564,
0.007770150434225798,
-0.03671479597687721,
0.004387800116091967,
0.02755173109471798,
0.004149469081312418,
-0.008101806975901127,
0.006366955116391182,
0.0322953499853611,
-0.015117726288735867,
0.010960264131426811,
-0.039135292172431946,
-0.05356724560260773,
0.016555842012166977,
-0.0016023780917748809,
0.014971314929425716,
0.01275468897074461,
-0.05043290555477142,
0.044245634227991104,
-0.02740577608346939,
-0.019255926832556725,
0.0405743271112442,
-0.013237148523330688,
0.05018691346049309,
0.001227933564223349,
0.0007770282099954784,
-0.02802812121808529,
0.0000818103872006759,
-0.04912726953625679,
0.019240926951169968,
-0.007870697416365147,
0.03684472665190697,
0.06248089298605919,
0.005500044208019972,
-0.062117934226989746,
-0.008642408065497875,
-0.012559434399008751,
-0.03969024494290352,
-0.012262048199772835,
-0.0024243814405053854,
0.04074421525001526,
-0.027512332424521446,
0.04833068326115608,
0.01947520487010479,
-0.05940401926636696,
0.01348823681473732,
-0.04814617708325386,
-0.051706742495298386,
0.04092404618859291,
-0.027515238150954247,
0.05115076154470444,
0.00804087519645691,
-0.029603585600852966,
0.06938986480236053,
0.006014646962285042,
-0.008829399943351746,
0.010189862921833992,
0.011107299476861954,
0.03305201232433319,
-0.00678224628791213,
-0.013570601120591164,
0.012438863515853882,
-0.00732280733063817,
-0.0006567857344634831,
0.04131161421537399,
0.059305209666490555,
0.010797079652547836,
-0.007870313711464405,
-0.05596313998103142,
-0.0020023530814796686,
-0.01643158495426178,
0.025141283869743347,
0.013562974520027637,
0.004343464970588684,
-0.03247995674610138,
0.005175797268748283,
-0.004822022281587124,
0.012186069041490555,
-0.0117828119546175,
-0.026709748432040215,
0.0339406356215477,
0.026899326592683792,
0.020505178719758987,
0.014734597876667976,
0.021869532763957977,
-0.02189802937209606,
-0.026945803314447403,
0.000609660055488348,
0.010794058442115784,
0.03278042748570442,
-0.010382315143942833,
0.019489355385303497,
0.018592339009046555,
0.012440278194844723,
-0.020124461501836777,
-0.0051328628323972225,
0.028574809432029724,
-0.015496042557060719,
0.0366683267056942,
0.00020573742222040892,
-0.01243678666651249,
0.04100155085325241,
0.01794835552573204,
0.0020184784661978483,
0.002515796571969986,
-0.03702753037214279,
0.0034952322021126747,
-0.033916451036930084,
-0.0284979697316885,
-0.008806058205664158,
0.022376658394932747,
0.0068933297879993916,
0.008639110252261162,
0.0297256987541914,
0.023463666439056396,
0.022658804431557655,
-0.019773442298173904,
-0.0805405005812645,
-0.008174940012395382,
-0.05738157778978348,
0.006936334539204836,
0.003618307877331972,
0.0257014948874712,
-0.01918502151966095,
0.019861582666635513,
-0.03201412037014961,
-0.02070198394358158,
0.009832898154854774,
-0.0951719880104065,
-0.00104760960675776,
-0.033149123191833496,
-0.03342437744140625,
0.011579209938645363,
0.01672675646841526,
0.03596477955579758,
0.0019238691311329603,
0.024597126990556717,
0.009403771720826626,
-0.02141568809747696,
0.015333554707467556,
0.025037826970219612,
0.02341236174106598,
-0.00047587885637767613,
0.009772546589374542,
0.02265424095094204,
0.04267457127571106,
-0.007093723863363266,
-0.0020698991138488054,
0.0486779548227787,
0.006069079507142305,
-0.042089857161045074,
-0.02546785958111286,
-0.034719858318567276,
-0.0550801157951355,
-0.04220716282725334,
0.0035696998238563538,
0.048804882913827896,
0.021507292985916138,
0.014807797968387604,
0.01286382507532835,
0.036565013229846954,
0.02147797867655754,
0.017884770408272743,
0.0670040175318718,
0.011312153190374374,
-0.010191009379923344,
-0.00007435063162120059,
-0.04483712464570999,
-0.03736872225999832,
0.0028485495131462812,
0.025468479841947556,
-0.016825230792164803,
-0.08652366697788239,
0.017592428252100945,
-0.008590531535446644,
0.02901698276400566,
-0.005967350676655769,
-0.023114098235964775,
0.0082427728921175,
0.003140731481835246,
-0.03934049233794212,
0.020808644592761993,
0.009436821565032005,
0.026934389024972916,
0.029457097873091698,
0.03797561302781105,
-0.018741417676210403,
-0.07272899895906448,
0.0019036968005821109,
0.012536498717963696,
0.0031795783434063196,
0.0571012981235981,
-0.0461917407810688,
-0.07334944605827332,
-0.028019806370139122,
0.03348640725016594,
-0.051125407218933105,
0.010145123116672039,
0.0019956305623054504,
-0.011426305398344994,
0.0240451879799366,
0.0035525825805962086,
0.039327096194028854,
0.006486356258392334,
-0.028675885871052742,
0.002067848574370146,
-0.000806138152256608,
0.0164942666888237,
0.0005498362588696182,
0.010761000216007233,
-0.05164139345288277,
0.028036069124937057,
0.00707049947232008,
0.001150177326053381,
0.011621183715760708,
0.03370058164000511,
-0.047224558889865875,
-0.08604328334331512,
0.01157770399004221,
0.02002456597983837,
-0.054315581917762756,
0.037347663193941116,
-0.026132484897971153,
-0.012622958980500698,
-0.000265990209300071,
0.016535241156816483,
-0.01821032725274563,
0.026187144219875336,
-0.023920750245451927,
0.03840000554919243,
-0.004452473949640989,
0.017834441736340523,
0.03569771721959114,
0.052786316722631454,
0.0036397050134837627,
-0.014169723726809025,
-0.03297162055969238,
0.02610754780471325,
-0.06890775263309479,
0.01371045969426632,
-0.021090541034936905,
0.005044580437242985,
-0.019174374639987946,
0.031766992062330246,
-0.025156492367386818,
0.0019812306854873896,
0.017104197293519974,
-0.016989609226584435,
-0.009918411262333393,
0.02274082414805889,
-0.021862009540200233,
-0.0017410203581675887,
-0.006086584646254778,
-0.0009946622885763645,
0.020278003066778183,
-0.03495901823043823,
0.027924925088882446,
-0.0005908283637836576,
-0.00043310713954269886,
0.03315635770559311,
-0.028428297489881516,
0.027395082637667656,
0.015573129989206791,
-0.003040093695744872,
0.019935747608542442,
-0.039491359144449234,
0.029664719477295876,
-0.0038787417579442263,
0.005659416783601046,
0.0392833948135376,
-0.026031654328107834,
0.007683834992349148,
-0.02359721250832081,
-0.010685466229915619,
0.03824259340763092,
-0.06088735908269882,
-0.008663707412779331,
0.03429248556494713,
0.03303804248571396,
-0.09373446553945541,
-0.027004331350326538,
0.04119628667831421,
0.03460731729865074,
-0.017522616311907768,
-0.03512231633067131,
0.030770372599363327,
-0.03868863731622696,
-0.022130774334073067,
-0.04044510796666145,
0.032078567892313004,
-0.042529501020908356,
-0.019140202552080154,
0.027925588190555573,
0.043192554265260696,
0.023972343653440475,
-0.009539284743368626,
0.0171140655875206,
0.0027998427394777536,
0.011115888133645058,
-0.003323084209114313,
-0.008750474080443382,
0.047720395028591156,
-0.02682729996740818,
-0.0356924943625927,
-0.011554411612451077,
-0.019154053181409836,
-0.0027477985713630915,
-0.02315261773765087,
-0.011537319049239159,
0.047278888523578644,
0.0002608334762044251,
0.02516157180070877,
-0.0073369876481592655,
0.011629447340965271,
-0.04498674347996712,
0.004048543516546488,
-0.04555335268378258,
-0.01029948890209198,
-0.0039564743638038635,
-0.05174294486641884,
0.051363397389650345,
-0.009953305125236511,
0.014119611121714115,
0.012885508127510548,
0.041787561029195786,
0.02247794345021248,
-0.05571473389863968,
-0.0035560033284127712,
-0.04350808635354042,
0.019981147721409798,
0.0031226291321218014,
0.014862721785902977,
0.03142485022544861,
0.023989291861653328,
-0.04333503171801567,
-0.043502941727638245,
-0.025580842047929764,
0.037191856652498245,
0.05618629977107048,
-0.030056895688176155,
0.01790802553296089,
0.050576020032167435,
-0.008808274753391743,
-0.018767954781651497,
-0.023902490735054016,
0.00269352737814188,
0.04000396281480789,
0.0003492014657240361,
0.024410132318735123,
-0.016478264704346657,
-0.026608258485794067,
0.038075000047683716,
0.018174445256590843,
-0.019089695066213608,
0.035144876688718796,
0.014741847291588783,
0.028969615697860718,
0.024652421474456787,
0.017885886132717133,
-0.05494260787963867,
0.044927891343832016,
-0.05068763345479965,
0.010246681049466133,
0.021956272423267365,
-0.018606141209602356,
0.02492019161581993,
-0.0014543684665113688,
0.028860751539468765,
-0.01406005397439003,
-0.052571795880794525,
-0.03012053668498993,
-0.0029585170559585094,
0.020346863195300102,
0.008743048645555973,
0.014003711752593517,
-0.005655277520418167,
0.0026009129360318184,
0.020583711564540863,
0.0023366864770650864,
-0.013636734336614609,
-0.06367246806621552,
-0.043400347232818604,
-0.06718198210000992,
-0.026651591062545776,
0.03201744705438614,
0.02223886176943779,
-0.024142004549503326,
0.03431941196322441,
-0.027337420731782913,
-0.00039844735874794424,
-0.013370665721595287,
0.05548914521932602,
-0.040620844811201096,
0.08024831116199493,
-0.011481136083602905,
0.01929575204849243,
-0.041588008403778076,
0.00563952187076211,
0.11322391033172607,
0.05873560160398483,
-0.014503872022032738,
-0.07655227184295654,
0.02727612853050232,
-0.017738087102770805,
-0.0033315399195998907,
-0.08179261535406113,
0.027357591316103935,
0.003911472391337156,
0.001962528098374605,
0.03666039928793907,
0.06638680398464203,
0.010091671720147133,
-0.03759064897894859,
0.052888162434101105,
-0.024185460060834885,
-0.03609886392951012,
-0.004596417769789696,
0.05576932802796364,
-0.0021603142376989126,
0.006744375452399254,
-0.015427503734827042,
0.03334971144795418,
0.004338573198765516,
0.009773562662303448,
-0.021381814032793045,
0.01956358551979065,
0.04469599947333336,
-0.017879430204629898,
-0.05763817951083183,
0.01959412544965744,
0.015201317146420479,
-0.024045834317803383,
-0.001438915147446096,
-0.018791871145367622,
0.02879742905497551,
0.02676486410200596,
-0.010915112681686878,
0.016970457509160042,
0.011054730974137783,
0.013208743184804916,
0.020061619579792023,
0.028111804276704788,
-0.057047732174396515,
-0.004122646059840918,
0.0068542687222361565,
0.01786702871322632,
-0.0373733751475811,
0.015501027926802635,
-0.0020006559789180756,
0.008428913541138172,
0.041248150169849396,
-0.043002378195524216,
-0.020205527544021606,
0.009924475103616714,
0.011169551871716976,
0.01543294358998537,
-0.04836295545101166,
-0.006071228533983231,
0.0315471813082695,
0.005329216830432415,
0.026453521102666855,
-0.013169019483029842,
-0.006361028179526329,
0.028329117223620415,
-0.025917045772075653,
0.015509132295846939,
-0.0007537277415394783,
-0.03150308504700661,
-0.051174718886613846,
0.02366451360285282,
-0.012720729224383831,
-0.022252127528190613,
0.01278776302933693,
-0.004995869006961584,
0.02445707470178604,
0.021268893033266068,
0.007909937761723995,
0.017621422186493874,
-0.05088858678936958,
0.03837641328573227,
-0.038202401250600815,
-0.007619526702910662,
-0.038098566234111786,
0.01352776400744915,
0.02745860069990158,
0.047959525138139725,
-0.03224889189004898,
-0.001407131552696228,
-0.029482778161764145,
0.01984725520014763,
0.006295271683484316,
0.0035022611264139414,
-0.015169383026659489,
-0.017435161396861076,
-0.0827009528875351,
0.0055158184841275215,
-0.023517046123743057,
-0.0015700885560363531,
0.023791532963514328,
0.04056921973824501,
0.048548419028520584,
0.02633916214108467,
-0.022556349635124207,
0.020114993676543236,
0.027983881533145905,
-0.016073208302259445,
-0.031751424074172974,
0.018045982345938683,
0.022688746452331543,
-0.008747993968427181,
-0.005037210416048765,
0.006776101887226105,
-0.012008029967546463,
-0.02171844244003296,
0.035530660301446915,
-0.010941075161099434,
0.003300708020105958,
-0.008744028396904469,
0.019665896892547607,
-0.0433867909014225,
-0.012271296232938766,
-0.034752439707517624,
-0.009223045781254768,
0.007868674583733082,
-0.03139214962720871,
0.02881433442234993,
0.00830734334886074,
-0.03602515533566475,
-0.013185365125536919,
-0.004316343460232019,
0.039611563086509705,
-0.06296242773532867,
0.025027554482221603,
0.046993985772132874,
0.025530589744448662,
0.03214846923947334,
-0.015776019543409348,
-0.045131538063287735,
0.05279937759041786,
-0.0572141595184803,
-0.06409813463687897,
0.03372201323509216,
-0.027823548763990402,
0.023271501064300537,
0.02246028184890747,
-0.03564753383398056,
-0.05275379493832588,
0.05287032946944237,
0.009988423436880112,
0.0071889678947627544,
0.05539047718048096,
-0.02315070480108261,
-0.0050798743031919,
0.02451438643038273,
0.020173560827970505,
0.004393425304442644,
-0.00916074588894844,
0.01392501499503851,
0.014546201564371586,
0.004730308428406715,
-0.010299324057996273,
-0.029725387692451477,
-0.023080017417669296,
-0.003419753396883607,
-0.00715267239138484,
0.03207574039697647,
0.036645133048295975,
0.05908797308802605,
-0.0315888486802578,
0.02227116748690605,
0.05728776007890701,
-0.011694574728608131,
-0.10849136114120483,
-0.011795833706855774,
0.02037259191274643,
0.016871897503733635,
0.036717236042022705,
-0.019312579184770584,
0.04310963302850723,
-0.002630045637488365,
-0.06323868036270142,
0.04698951914906502,
-0.03255956619977951,
-0.03962700814008713,
-0.022593805566430092,
0.008329263888299465,
-0.03902943804860115,
0.03277788683772087,
0.048298902809619904,
0.04686637595295906,
-0.046633318066596985,
0.009325300343334675,
-0.02933906577527523,
-0.014701391570270061,
-0.01545964926481247,
0.012847088277339935,
-0.05836015194654465,
0.016216615214943886,
0.0610903799533844,
-0.010806925594806671,
-0.020469171926379204,
0.0330718494951725,
-0.017975063994526863,
-0.013605020008981228,
-0.0032100402750074863,
0.01387714222073555,
0.03718111664056778,
-0.010332916863262653,
0.043285176157951355,
0.0043926239013671875,
0.0020120185799896717,
0.0379522405564785,
0.01691773347556591,
-0.009953881613910198,
-0.016851168125867844,
0.009203131310641766,
0.010514242574572563,
-0.05836791917681694,
-0.02507198229432106,
0.004944169893860817,
-0.019796548411250114,
0.01383945345878601,
0.002711976645514369,
0.020635973662137985,
-0.006380022969096899,
-0.002786572789773345,
-0.02672206237912178,
-0.0600128211081028,
-0.010525401681661606,
0.05427783727645874,
0.03662293776869774,
-0.005730884149670601,
0.0197280440479517,
-0.04197476804256439,
-0.029466696083545685,
0.03392815217375755,
-0.01491015125066042,
0.014166883192956448,
-0.007905102334916592,
-0.025572020560503006,
-0.0010861766058951616,
0.006369809620082378,
0.023569947108626366,
-0.05298310145735741,
-0.008036783896386623,
0.06939025223255157,
-0.009882531128823757,
0.007259985897690058,
0.00044738806900568306,
-0.022887587547302246,
-0.0347072072327137,
-0.07442767173051834,
0.006909369956701994,
-0.0038183063734322786,
0.02558375895023346,
-0.033569708466529846,
-0.035266902297735214,
-0.014646402560174465,
0.03515002131462097,
0.03081938624382019,
-0.031286004930734634,
0.014991098083555698,
0.04838939756155014,
0.011124780401587486,
0.011211236007511616,
-0.027402441948652267,
-0.018023952841758728,
0.01338388305157423,
-0.023166827857494354,
-0.014210526831448078,
0.029078617691993713,
-0.00031510848202742636,
-0.028379006311297417,
0.031384147703647614,
0.000018639617337612435,
0.013414336368441582,
0.021977869793772697,
-0.026783941313624382,
0.042025551199913025,
0.03114248625934124,
0.0051173255778849125,
0.058789175003767014,
-0.013546505942940712,
0.019504399970173836,
0.032843541353940964,
-0.03248497471213341,
-0.017563339322805405,
-0.0003971825062762946,
-0.009638247080147266,
0.0012860052520409226,
-0.03489546850323677,
-0.009644703939557076,
0.01850857213139534,
-0.010862639173865318,
-0.015950221568346024,
0.08328669518232346,
-0.018364321440458298,
0.005427757278084755,
0.05339594557881355,
0.0029503649566322565,
0.05559217929840088,
-0.03762085735797882,
-0.03746993467211723,
0.022300684824585915,
0.01555400900542736,
0.005935147404670715,
0.02653813734650612,
0.025827476754784584,
-0.012857388705015182,
-0.004528678022325039,
0.010292612947523594,
-0.014191441237926483,
0.03996310010552406,
0.011828321032226086,
0.044411320239305496,
-0.0042908284813165665,
-0.044681791216135025,
0.02532394789159298,
0.0008445338462479413,
0.01958877220749855,
-0.00415338110178709,
-0.02149416320025921,
0.04662574455142021,
-0.008155211806297302,
0.026870328933000565,
-0.018777215853333473,
-0.0009074483532458544,
-0.020903384312987328,
0.018649272620677948,
-0.0017539821565151215,
0.10639721155166626,
0.022459745407104492,
-0.02126331627368927,
-0.015941349789500237,
0.010082976892590523,
0.018468426540493965,
-0.04074236378073692,
-0.007290685549378395,
-0.024951040744781494,
-0.015385317616164684,
0.018452435731887817,
-0.011421283707022667,
-0.016646858304739,
-0.036431457847356796,
0.026262227445840836,
0.0034690957982093096,
-0.001982915448024869,
-0.020114993676543236,
-0.004822524730116129,
-0.02413231134414673,
0.040303561836481094,
-0.039988402277231216,
-0.014933450147509575,
-0.01789802685379982,
0.004271257668733597,
-0.0019845557399094105,
0.009239524602890015
] |
<p>Internal resistance of inductance (or other devices) are said to be in series. But <a href="http://en.wikipedia.org/wiki/Parasitic_capacitance" rel="nofollow">parasitic capacitance</a> is said to be in parallel (in case of an inductor). Why is that so? What determines whether an internal property is in series or parallel?</p>
| 10,791 |
[
-0.03389236703515053,
-0.029945816844701767,
0.006388474255800247,
-0.017531003803014755,
0.03174527361989021,
0.03337079659104347,
-0.026273084804415703,
0.03590666875243187,
0.0031322736758738756,
-0.0021496894769370556,
0.02636159025132656,
0.04536549746990204,
0.033472940325737,
-0.0050696819089353085,
0.002356843091547489,
0.003002526704221964,
-0.0275650005787611,
-0.003280636388808489,
0.0036645939107984304,
-0.01761634089052677,
0.02058633789420128,
0.02490636520087719,
0.06171005219221115,
0.024800708517432213,
-0.0006614369922317564,
0.005434923805296421,
0.009037667885422707,
-0.023321570828557014,
0.0334310382604599,
0.023531761020421982,
-0.021944284439086914,
-0.02593410760164261,
-0.01605038158595562,
0.01032006461173296,
0.047859322279691696,
-0.01982511766254902,
-0.029283979907631874,
-0.024158461019396782,
-0.016643784940242767,
0.05954159423708916,
-0.017359299585223198,
-0.022074615582823753,
-0.023619648069143295,
0.03343495354056358,
-0.024748289957642555,
0.0010355128906667233,
0.01410295907407999,
-0.0026182078290730715,
-0.0018902611918747425,
-0.07669468224048615,
0.056752122938632965,
-0.02923831157386303,
0.05841632932424545,
0.03380116820335388,
-0.005661577917635441,
0.010705980472266674,
0.07376730442047119,
0.05196138471364975,
-0.018297569826245308,
-0.054510749876499176,
0.024102134630084038,
-0.011881278827786446,
0.0021945491898804903,
-0.014394043944776058,
-0.05541309341788292,
0.033174023032188416,
0.036347247660160065,
-0.032945796847343445,
0.01750141941010952,
-0.012138680554926395,
0.006066608242690563,
0.010184979997575283,
0.0000750961626181379,
-0.06359457224607468,
0.023835765197873116,
-0.024077212437987328,
-0.02273731864988804,
0.013419970870018005,
0.05709129944443703,
0.046199291944503784,
-0.020834246650338173,
0.028936604037880898,
0.022204749286174774,
0.02481059543788433,
0.02387484535574913,
-0.031869418919086456,
0.04589004069566727,
0.018217669799923897,
0.008497507311403751,
0.0007906959508545697,
0.017342818900942802,
0.009066266939043999,
0.05264349654316902,
-0.020608296617865562,
0.009067017585039139,
0.05587392672896385,
0.0006284310366027057,
0.013433391228318214,
0.01093239989131689,
-0.01542748138308525,
0.03149590641260147,
-0.0025925759691745043,
0.03749368339776993,
0.050803739577531815,
0.013247576542198658,
-0.055828481912612915,
-0.017364300787448883,
0.06022264063358307,
0.018983902409672737,
-0.029522843658924103,
-0.04351981356739998,
0.04362289980053902,
0.020428605377674103,
0.03696516156196594,
0.018152287229895592,
0.02296825498342514,
0.030964745208621025,
0.007261259015649557,
0.025668473914265633,
0.053859539330005646,
-0.010957982391119003,
0.010517925955355167,
0.013210420496761799,
-0.0302848182618618,
-0.06042439118027687,
0.016835661605000496,
0.0010878518223762512,
-0.013928139582276344,
-0.011064989492297173,
0.033447571098804474,
-0.012227658182382584,
-0.02625003084540367,
-0.002962007187306881,
-0.014715945348143578,
0.053436655551195145,
0.01585150510072708,
-0.07836540788412094,
-0.059414684772491455,
0.014106587506830692,
-0.025030769407749176,
-0.022921044379472733,
-0.06787002831697464,
0.055710505694150925,
0.015006043016910553,
0.0857921615242958,
-0.04609481617808342,
-0.005308917257934809,
-0.0215331818908453,
0.03116471879184246,
0.02375570870935917,
0.023056047037243843,
-0.06715977936983109,
0.016421152278780937,
0.008890031836926937,
0.007941113784909248,
-0.0673503652215004,
0.027492133900523186,
0.04747007042169571,
0.00945298746228218,
-0.027121247723698616,
0.06623837351799011,
-0.010982239618897438,
-0.0006609677220694721,
0.018882306292653084,
-0.021142026409506798,
-0.04407898709177971,
0.056039657443761826,
-0.007342818658798933,
0.02210443839430809,
0.05729953199625015,
0.018620312213897705,
-0.006449240725487471,
0.0014329482801258564,
0.036150973290205,
0.052798572927713394,
-0.03819781914353371,
-0.045672301203012466,
0.006448173429816961,
0.006780280731618404,
0.003386132186278701,
-0.04775896668434143,
-0.03142727538943291,
0.015359192155301571,
0.03236840292811394,
0.03209947794675827,
0.038423795253038406,
-0.01364070363342762,
-0.05583310127258301,
-0.011135888285934925,
-0.015994027256965637,
-0.021296314895153046,
-0.03540772572159767,
0.02610788866877556,
0.008164784871041775,
-0.04701380431652069,
0.05156916379928589,
0.02135142683982849,
0.0010513141751289368,
-0.024758560582995415,
-0.0165390782058239,
-0.025629781186580658,
-0.006722138728946447,
0.008675807155668736,
-0.01914995349943638,
0.0504293330013752,
0.022109750658273697,
0.022881167009472847,
-0.002011373173445463,
0.043406516313552856,
-0.042762331664562225,
-0.03550932556390762,
0.04023757949471474,
-0.014852669090032578,
0.01888928934931755,
-0.013477400876581669,
0.01945158839225769,
0.01343588437885046,
0.0023731610272079706,
-0.025767002254724503,
0.047820672392845154,
-0.011931488290429115,
0.05843639746308327,
0.07699450850486755,
0.020680733025074005,
-0.0012538140872493386,
0.024485480040311813,
0.001247978419996798,
-0.0004737044801004231,
-0.015217645093798637,
0.01728193275630474,
-0.06884819269180298,
0.005041069351136684,
0.01928308978676796,
0.06033579260110855,
-0.07370497286319733,
0.004786200821399689,
0.04896753653883934,
0.06598871946334839,
0.04510476067662239,
0.027209708467125893,
-0.015475013293325901,
-0.0336223840713501,
0.005449378862977028,
0.023100724443793297,
0.011793104000389576,
0.00676775025203824,
0.005576128140091896,
0.020386740565299988,
0.0323529876768589,
0.0016895992448553443,
-0.013927710242569447,
0.05445408448576927,
0.014237229712307453,
0.03795553743839264,
0.04371865466237068,
-0.022499971091747284,
0.022626644000411034,
-0.04757428169250488,
0.0081980274990201,
-0.013086960650980473,
-0.011576018296182156,
0.03509458154439926,
-0.005304496735334396,
0.013461115770041943,
0.0033504560124129057,
-0.02399427630007267,
-0.03271547704935074,
-0.03716190159320831,
0.013344397768378258,
-0.047559481114149094,
0.03477377071976662,
-0.02858109399676323,
0.004010927863419056,
-0.04199337959289551,
-0.02246972732245922,
0.023352814838290215,
0.009249409660696983,
0.059159450232982635,
-0.01639246568083763,
-0.0012692945310845971,
-0.0015472198138013482,
-0.04434382915496826,
0.02018916979432106,
-0.03179960325360298,
-0.061877213418483734,
0.02327081933617592,
-0.014757106080651283,
-0.028710968792438507,
0.05796762555837631,
-0.0003737466468010098,
0.0065118735656142235,
0.013743896037340164,
-0.01709870621562004,
-0.0719112753868103,
-0.01658470742404461,
-0.001831655390560627,
0.012381025590002537,
-0.03886346146464348,
-0.0023968208115547895,
0.06317277997732162,
-0.029201874509453773,
-0.029944971203804016,
-0.00843769870698452,
-0.027756791561841965,
0.004707867279648781,
0.020432965829968452,
-0.0599437840282917,
0.004820056259632111,
-0.037271033972501755,
-0.021590668708086014,
0.02953803353011608,
-0.0700654536485672,
-0.0203412938863039,
-0.03182951360940933,
-0.04559118673205376,
0.00121410028077662,
-0.022708792239427567,
0.05531356856226921,
-0.0021382360719144344,
-0.034499749541282654,
0.05535005405545235,
0.013741775415837765,
-0.0055409143678843975,
-0.00714025879278779,
-0.02918413281440735,
-0.024927183985710144,
-0.05394982919096947,
0.0009707870776765049,
0.056654226034879684,
-0.04034939780831337,
0.015768904238939285,
0.07247211039066315,
0.016426675021648407,
0.04517603665590286,
0.022630244493484497,
0.006570435129106045,
-0.014053750783205032,
0.017317166551947594,
-0.022108586505055428,
0.04727017879486084,
0.022145569324493408,
-0.0502692274749279,
0.03341483697295189,
-0.004192788619548082,
0.008302439004182816,
0.011902613565325737,
0.01600256934762001,
0.002933117328211665,
-0.031288065016269684,
0.020603392273187637,
-0.07115817070007324,
0.02638535015285015,
0.005704841110855341,
0.028243528679013252,
-0.01998218148946762,
0.03496888652443886,
0.016511419788002968,
-0.030275637283921242,
-0.003728078678250313,
0.031106358394026756,
0.021121220663189888,
-0.030143404379487038,
0.002949504880234599,
0.016919605433940887,
-0.016635453328490257,
0.022173985838890076,
-0.03368128836154938,
-0.026787227019667625,
0.04400019347667694,
0.012302744202315807,
0.025317415595054626,
0.026965536177158356,
-0.050697676837444305,
-0.009229709394276142,
-0.07612724602222443,
-0.008992306888103485,
-0.0016459478065371513,
0.04235808551311493,
0.002204917138442397,
0.045359447598457336,
0.022206734865903854,
-0.0019416501745581627,
-0.009718656539916992,
-0.012373514473438263,
-0.10152066498994827,
-0.020948508754372597,
-0.02118051052093506,
-0.005320678930729628,
-0.018828919157385826,
-0.017052430659532547,
0.008366427384316921,
-0.029771752655506134,
-0.023529300466179848,
-0.0022309680934995413,
0.005651196464896202,
-0.04590591415762901,
0.04554476588964462,
0.012544517405331135,
-0.01842733658850193,
-0.020071381703019142,
0.011946480721235275,
0.022051330655813217,
-0.05784061178565025,
0.012699487619102001,
0.02219671756029129,
-0.04277844727039337,
0.022306544706225395,
-0.0020683100447058678,
-0.0011294721625745296,
0.011235161684453487,
0.004569563549011946,
0.028141573071479797,
-0.014462905935943127,
0.008541765622794628,
-0.008638286031782627,
0.0298027191311121,
0.06190722808241844,
0.05574924126267433,
-0.07851599901914597,
-0.02028564177453518,
-0.0732867419719696,
-0.03347238525748253,
-0.011725357733666897,
0.03668024390935898,
0.01724393665790558,
0.02416262961924076,
0.01725936122238636,
0.04039226844906807,
-0.016150569543242455,
0.04975351691246033,
0.006275189109146595,
0.031923189759254456,
-0.027614502236247063,
-0.04996902495622635,
-0.06947410106658936,
-0.03450677916407585,
0.013053320348262787,
0.04633604362607002,
-0.005122332833707333,
-0.052541933953762054,
0.014764110557734966,
0.0182116087526083,
0.008766114711761475,
0.026042131707072258,
0.02532588317990303,
-0.0029680619481951,
0.039605967700481415,
0.014429839327931404,
0.020987344905734062,
-0.014887840487062931,
0.001868676976300776,
0.07854605466127396,
0.025416437536478043,
-0.04883600398898125,
-0.08913704007863998,
-0.0064199864864349365,
0.01774534396827221,
0.018770523369312286,
-0.032055363059043884,
-0.012067124247550964,
-0.024164428934454918,
-0.018738629296422005,
0.05641535297036171,
-0.039516571909189224,
0.054112449288368225,
0.016299573704600334,
-0.00046393502270802855,
-0.033710602670907974,
-0.04697977378964424,
0.017492232844233513,
0.026389745995402336,
0.021070091053843498,
0.02646036073565483,
-0.040398791432380676,
-0.019041065126657486,
-0.06288139522075653,
-0.04357452318072319,
0.04300016537308693,
0.054906103760004044,
-0.014438693411648273,
0.012294545769691467,
0.023783603683114052,
0.056313708424568176,
0.01061750017106533,
-0.04729318246245384,
0.03148501738905907,
-0.019242065027356148,
0.038845282047986984,
0.025751687586307526,
-0.023528585210442543,
-0.0006863836315460503,
0.012638472020626068,
-0.0016814257251098752,
0.002865959657356143,
0.0005571937654167414,
-0.01993415132164955,
0.03603341802954674,
0.016763776540756226,
-0.0374675989151001,
0.05331176146864891,
0.0019094828749075532,
-0.026402246206998825,
-0.006218715105205774,
-0.028765620663762093,
-0.006074334494769573,
-0.034640051424503326,
-0.014657236635684967,
-0.004492510110139847,
0.029558027163147926,
-0.012674937956035137,
0.06781856715679169,
-0.004683362785726786,
0.021717781201004982,
-0.023875905200839043,
-0.010209054686129093,
0.018635045737028122,
0.006672844756394625,
0.005007355008274317,
-0.011823149397969246,
0.004647665657103062,
0.06404204666614532,
0.014317488297820091,
-0.047133732587099075,
0.018069397658109665,
-0.02092018537223339,
0.030348731204867363,
0.016313491389155388,
0.031329959630966187,
0.0021242331713438034,
-0.047905344516038895,
-0.02091062255203724,
0.004864477552473545,
-0.007691982202231884,
0.008489049039781094,
-0.012838740833103657,
0.00593172013759613,
0.01627473346889019,
-0.02225703001022339,
-0.037957727909088135,
0.014064468443393707,
0.012848139740526676,
0.02463395893573761,
-0.04737737029790878,
0.03266967087984085,
0.002432087203487754,
-0.0037221654783934355,
-0.0537245012819767,
-0.04687696695327759,
0.037902750074863434,
0.01892576552927494,
0.011862199753522873,
0.010936025530099869,
-0.006716167088598013,
0.018336420878767967,
-0.031059516593813896,
0.01195171196013689,
0.0679841935634613,
-0.037910688668489456,
-0.02443808503448963,
-0.013080892153084278,
0.001219285069964826,
0.04978569969534874,
0.020539605990052223,
-0.02766156569123268,
-0.00916515477001667,
-0.053079113364219666,
0.006031726486980915,
-0.02549387328326702,
0.023046569898724556,
-0.03259872645139694,
-0.007718804758042097,
-0.018377989530563354,
-0.016000356525182724,
0.06550133973360062,
-0.02035580947995186,
-0.011572452262043953,
0.04365874081850052,
-0.032052624970674515,
-0.034439098089933395,
-0.01394016295671463,
0.018001286312937737,
0.0000020810930436709896,
0.025439966470003128,
0.006498470436781645,
-0.018316594883799553,
-0.08814514428377151,
-0.03329918161034584,
-0.0008034652564674616,
0.05405237153172493,
0.024422846734523773,
-0.021818410605192184,
0.028185827657580376,
-0.03231751173734665,
-0.008790738880634308,
0.03329027444124222,
0.000570072908885777,
0.009982905350625515,
0.0016923712100833654,
-0.010645481757819653,
0.0003595476446207613,
0.004211881663650274,
-0.04863685742020607,
0.007933920249342918,
-0.03496376425027847,
0.0029519349336624146,
0.04070835933089256,
-0.010264277458190918,
0.07253792881965637,
0.03433231636881828,
-0.03686165064573288,
-0.022934872657060623,
-0.016059378162026405,
0.012268172577023506,
-0.018799131736159325,
0.002122623845934868,
0.03947373479604721,
-0.05384620279073715,
-0.011763744056224823,
0.03643115237355232,
0.04379504173994064,
-0.027709415182471275,
-0.007196018006652594,
0.016080474480986595,
-0.0007555817719548941,
0.004430218134075403,
0.009900926612317562,
-0.037061188369989395,
0.04201182723045349,
-0.01919218711555004,
-0.0017552137142047286,
0.020187096670269966,
-0.007979686371982098,
0.05086958408355713,
0.009347950108349323,
-0.005292398855090141,
-0.05037671700119972,
0.002816589083522558,
-0.03675946220755577,
0.03945979103446007,
0.006778132636100054,
0.02525501139461994,
-0.002124924212694168,
-0.0034717521630227566,
0.03619692102074623,
0.015715310350060463,
0.05367584154009819,
-0.026292450726032257,
-0.03479216620326042,
-0.027509624138474464,
-0.003473747754469514,
-0.02262411266565323,
0.014066803269088268,
-0.016414418816566467,
-0.012943555600941181,
0.00831424631178379,
-0.040667496621608734,
0.03383881226181984,
0.026050427928566933,
0.03690169379115105,
0.0007102485396899283,
0.0630151554942131,
-0.03607942909002304,
0.01498956698924303,
-0.040738027542829514,
-0.018519656732678413,
0.11173238605260849,
0.028483020141720772,
0.024081895127892494,
-0.06999719142913818,
0.029906954616308212,
0.004446629900485277,
0.03433753550052643,
-0.026460375636816025,
0.006245299242436886,
0.0019628640729933977,
0.01722683571279049,
0.05048922449350357,
0.011157045140862465,
0.014765518717467785,
0.014178222976624966,
0.017998913303017616,
-0.02758309431374073,
-0.014492455869913101,
-0.035217419266700745,
0.04667703062295914,
-0.01674065925180912,
0.03781303018331528,
-0.02783934772014618,
0.012211757712066174,
-0.0330028161406517,
-0.004293632227927446,
-0.03824766352772713,
-0.014151699841022491,
0.05388764664530754,
0.0012935614213347435,
-0.03599918633699417,
0.026265952736139297,
0.05390128493309021,
-0.02936604432761669,
-0.04785957559943199,
0.012910178862512112,
0.028595251962542534,
-0.01761653833091259,
-0.023973265662789345,
0.01190097164362669,
0.01043422520160675,
-0.001223294879309833,
0.02430586889386177,
0.012651036493480206,
-0.038459211587905884,
0.01751129887998104,
-0.015225687995553017,
0.01279444806277752,
0.0054645296186208725,
0.004715267103165388,
0.026260336861014366,
0.036047231405973434,
0.024339577183127403,
-0.0683453306555748,
-0.055733900517225266,
-0.01248918380588293,
0.013263538479804993,
-0.037206489592790604,
-0.019546274095773697,
-0.03530203551054001,
0.03448666259646416,
-0.006874519865959883,
0.03001813031733036,
-0.0118601955473423,
-0.005964276846498251,
0.009806118905544281,
-0.013560717925429344,
0.020872822031378746,
-0.04266521707177162,
-0.014484873972833157,
0.014346735551953316,
0.010086344555020332,
-0.020790133625268936,
-0.018280813470482826,
0.004405301064252853,
-0.021983280777931213,
0.01679246500134468,
-0.028342824429273605,
-0.0003973179846070707,
0.004869806580245495,
-0.015911970287561417,
-0.0024897281546145678,
-0.0049151461571455,
0.022660821676254272,
-0.016659682616591454,
-0.01460100058466196,
0.07622740417718887,
0.03132552281022072,
-0.024234246462583542,
0.01818348839879036,
0.018653692677617073,
0.037356141954660416,
-0.003982060123234987,
-0.01168737281113863,
-0.0209626667201519,
0.00012759596575051546,
-0.06060381606221199,
0.008916778489947319,
0.017406992614269257,
0.045014359056949615,
0.038053009659051895,
0.03536751866340637,
-0.029435541480779648,
0.032768186181783676,
-0.03942437842488289,
-0.019963650032877922,
0.010813183151185513,
-0.01866956800222397,
0.010649886913597584,
0.0006895447731949389,
0.0034973209258168936,
-0.005725341383367777,
0.004145936109125614,
-0.023516109213232994,
0.012726929038763046,
0.011271637864410877,
0.016675379127264023,
-0.0380847193300724,
-0.025966810062527657,
-0.007627774961292744,
0.048150621354579926,
-0.026188557967543602,
-0.032929886132478714,
-0.0684107318520546,
-0.029854638502001762,
0.03621204197406769,
0.008391860872507095,
0.019588874652981758,
0.0176230538636446,
-0.046306632459163666,
0.013820722699165344,
0.04192917421460152,
0.02468649484217167,
-0.008860045112669468,
-0.034866414964199066,
0.005833526607602835,
-0.011183492839336395,
0.019446775317192078,
-0.017298519611358643,
-0.03994995728135109,
0.061108026653528214,
-0.005266128573566675,
-0.030715208500623703,
0.005057997535914183,
-0.016091791912913322,
0.010510615073144436,
-0.006756217684596777,
0.010734044015407562,
-0.033799272030591965,
0.02352106384932995,
-0.030811341479420662,
0.016931556165218353,
-0.019041666761040688,
-0.0011486277217045426,
-0.009638676419854164,
-0.005052758846431971,
0.010389880277216434,
-0.03953681141138077,
0.010173976421356201,
0.01791076362133026,
0.029016422107815742,
0.005041780881583691,
-0.025323573499917984,
-0.011675058864057064,
0.003700640983879566,
0.0006346733425743878,
0.030584851279854774,
0.022497355937957764,
0.012575042434036732,
0.0188243817538023,
-0.03578793257474899,
0.006518881767988205,
-0.017753053456544876,
0.01249600574374199,
-0.052948590368032455,
-0.004169550724327564,
-0.001057533430866897,
-0.014614511281251907,
0.0009781110566109419,
-0.0017597588011994958,
-0.04591536894440651,
0.009892180562019348,
-0.07244712859392166,
0.012526242062449455,
-0.02879360131919384,
-0.04625830426812172,
-0.02893052063882351,
-0.008947848342359066,
0.007502308581024408,
0.022688305005431175,
0.006979264318943024,
0.019002260640263557,
0.016580011695623398,
0.00040703569538891315,
-0.0037133051082491875,
-0.03659208491444588,
-0.024658555164933205,
0.01900368183851242,
-0.033336881548166275,
-0.014220166020095348,
0.030011482536792755,
-0.01791602373123169,
0.0073679909110069275,
0.010011513717472553,
-0.016438942402601242,
-0.01750396564602852,
-0.001075591193512082,
0.035573188215494156,
0.021562062203884125,
0.0548010990023613,
-0.000966215506196022,
-0.01653454639017582,
-0.03394761681556702,
-0.007881012745201588,
0.039272356778383255,
0.018589915707707405,
0.007549458649009466,
0.005908580496907234,
0.022485235705971718,
0.0062475004233419895,
0.001487327041104436,
-0.014712527394294739,
-0.04359814524650574,
-0.047632381319999695,
0.025669416412711143,
0.028450187295675278,
0.04244448244571686,
-0.032786544412374496,
0.016576267778873444,
-0.04967880994081497,
-0.02641553431749344,
0.03589913621544838,
-0.006993430200964212,
0.0231135543435812,
-0.027763301506638527,
0.020049232989549637,
-0.03907564654946327,
0.033917032182216644,
0.013383179903030396,
0.029020244255661964,
-0.07054758071899414,
0.00006437092088162899,
0.010366074740886688,
-0.03731846064329147,
-0.00003526318323565647,
-0.06567193567752838,
0.0009672219748608768,
0.021562641486525536,
0.010968860238790512,
-0.004751837812364101,
-0.00458848662674427,
-0.05349956452846527,
-0.0375339537858963,
-0.03942285105586052,
0.04752789065241814,
-0.01234644278883934,
-0.01917775720357895,
-0.05783551186323166,
-0.05449473485350609,
-0.021456439048051834,
0.01737312227487564,
0.07743800431489944,
0.00048524176236242056,
-0.02301437221467495,
-0.02234439179301262,
0.013803240843117237,
0.04085918515920639,
-0.04520852118730545,
-0.0036044507287442684,
0.0310475192964077,
-0.03504303842782974,
0.005806909408420324,
-0.03407368063926697,
-0.010602963156998158,
-0.004503282252699137,
0.015213959850370884,
0.028325051069259644,
0.02023705467581749,
-0.024854324758052826,
-0.004014058504253626,
0.014892926439642906,
0.031299468129873276,
-0.002291716868057847,
0.07274854183197021,
0.009603519923985004,
0.020705169066786766,
0.037082526832818985,
-0.004823281429708004,
-0.05907085910439491,
-0.0046961079351603985,
-0.009054819121956825,
-0.010966540314257145,
-0.02586512453854084,
0.04136002063751221,
0.057558026164770126,
-0.028477314859628677,
-0.011604003608226776,
0.021777721121907234,
-0.03890758752822876,
-0.0269033070653677,
0.07292795181274414,
-0.03759198635816574,
0.01973714493215084,
-0.02143234759569168,
0.019991541281342506,
0.014957331120967865,
-0.009777498431503773,
-0.014030416496098042,
0.047788552939891815,
0.06752478331327438,
-0.010436235927045345,
-0.01612653210759163,
0.062288764864206314,
-0.023269807919859886,
0.012449769303202629,
-0.03099745139479637,
0.02218233421444893,
-0.048588450998067856,
-0.0180961936712265,
-0.011478535830974579,
-0.045682769268751144,
0.011192137375473976,
0.06546539813280106,
-0.02840995229780674,
0.10847855359315872,
-0.03919580578804016,
0.019068146124482155,
0.013117142021656036,
-0.0031165829859673977,
-0.00631439546123147,
-0.0044286297634243965,
0.017135299742221832,
0.023068638518452644,
-0.005136593710631132,
-0.03413306176662445,
-0.020580342039465904,
-0.022131403908133507,
0.07702126353979111,
-0.018195435404777527,
0.01901443488895893,
-0.00452415319159627,
0.019431645050644875,
-0.02421276643872261,
0.02607211470603943,
-0.04197003319859505,
-0.031727198511362076,
0.01810697838664055,
0.03003602661192417,
0.014714904129505157,
0.018759990110993385,
-0.020727721974253654,
-0.01022325549274683,
0.04810163378715515,
-0.07977954298257828,
-0.0005300939665175974,
-0.016923634335398674,
0.03634355589747429,
0.017667505890130997,
-0.008458360098302364
] |
<p>I recently came across <a href="http://link.springer.com/article/10.1140%2Fepja%2Fi2013-13072-1" rel="nofollow">this article</a>, published in the respectable <em>European Physical Journal A</em>. (Apparently, there isn't any corresponding arXiv article for this, so I'm sorry if everyone isn't able to access the article.)</p>
<p>Here's the possibility that the author has suggested:</p>
<blockquote>
<p>While looking for the putative Higgs boson of the Standard Model of particle physics, recently, the CMS and the ATLAS experiments at CERN have found strong signals of a new particle at about 125 GeV. ... </p>
<p>Here we show that what they may have found at 125 GeV is the long sought for and missing ingredient of the strong interaction: the sigma-meson of the Chiral Sigma Model, within the framework of the Skyrme model with a topological interpretation of the baryons. Just like a massless gauge boson is a requirement, and hence a prediction of the local gauge theories, in the the same manner, a very heavy scalar meson is a requirement and hence a prediction of the Skyrme model of the hadrons. The 125 GeV particle discovered by the CMS and the ATLAS groups may be an experimental confirmation of this unique prediction of the topological Skyrme model. However the bottom line is that even if the experimentalists finally confirm that this 125 GeV entity is the expected Higgs boson, then there still remains to discover another heavier scalar particle as the sigma-meson of the chiral sigma model/Skyrme model, which remains its unique prediction, as shown in this paper.</p>
</blockquote>
<p>I appreciate that the physics community in general must be very confident that they have identified Higgs correctly (they wouldn't have awarded a Nobel prize if there was any doubt remaining).</p>
<p>The point is, while hoaxes keep sprouting up all the time, this is a well-sourced and peer-reviewed article. Does this possibility appear irrational for any definite reason? Especially since this $\sigma$ meson is still elusive? </p>
<p>Edit : Found another. This one is in Phys. Rev. D and incidentally carries the same name as my question title ! Here are the links - <a href="http://journals.aps.org/prd/abstract/10.1103/PhysRevD.86.093012" rel="nofollow">PRD Link</a>, <a href="http://arxiv.org/abs/1207.1093" rel="nofollow">arxiv link</a> </p>
| 10,792 |
[
-0.05484261363744736,
0.0003682160750031471,
0.027905039489269257,
-0.05907842144370079,
0.051038481295108795,
0.05833561718463898,
0.006457922980189323,
-0.05046529322862625,
0.01444413885474205,
-0.0706857442855835,
0.07116036862134933,
0.015572719275951385,
0.04721540957689285,
0.03611563518643379,
-0.00972040556371212,
0.038754675537347794,
0.00903674028813839,
-0.00911323819309473,
-0.02656438574194908,
-0.03371162340044975,
0.04142036288976669,
0.036432262510061264,
-0.0225144624710083,
0.0020267460495233536,
-0.01213107444345951,
-0.02224087342619896,
0.01531748566776514,
0.026842445135116577,
-0.014935916289687157,
0.06419569253921509,
-0.038389116525650024,
-0.03442196175456047,
0.03898268938064575,
-0.0006343683344312012,
0.02429254539310932,
0.0011118737747892737,
0.010054542683064938,
-0.030981849879026413,
-0.02673012763261795,
0.01846926100552082,
-0.01715201884508133,
-0.02457660622894764,
-0.019332244992256165,
0.09173557907342911,
-0.044747207313776016,
0.007800288498401642,
-0.04243658110499382,
-0.0016212802147492766,
0.07901366800069809,
-0.0794064998626709,
0.04591291397809982,
0.044903166592121124,
0.01934812217950821,
-0.0072796219028532505,
-0.014943139627575874,
-0.04229310154914856,
0.020267996937036514,
0.07279282808303833,
0.00883377157151699,
-0.045813653618097305,
-0.011139573529362679,
-0.04287745803594589,
-0.0032792137935757637,
-0.025670021772384644,
-0.01089982595294714,
0.02410925179719925,
0.0051612406969070435,
0.0011137771653011441,
0.0020743636414408684,
0.009146974422037601,
0.01933906599879265,
-0.004804532043635845,
0.028606083244085312,
0.00927701499313116,
0.054139938205480576,
-0.01994403451681137,
-0.025853721424937248,
0.02262413129210472,
0.02150317281484604,
0.0324217826128006,
-0.02447834610939026,
-0.00345946685411036,
0.003062067786231637,
0.002636438002809882,
0.034952424466609955,
-0.017724361270666122,
0.04766405373811722,
-0.028285611420869827,
-0.03295701742172241,
0.052190884947776794,
-0.037897441536188126,
-0.006680345628410578,
0.058226000517606735,
-0.020127208903431892,
-0.008442211896181107,
0.03059164620935917,
0.022954359650611877,
0.01875278353691101,
-0.03293418884277344,
-0.001016402617096901,
0.024282004684209824,
-0.0004441120254341513,
-0.0017003649845719337,
0.07727301865816116,
-0.008653251454234123,
0.011075598187744617,
-0.01741369254887104,
-0.0021657533943653107,
-0.054332438856363297,
-0.0051388125866651535,
-0.02855059504508972,
-0.016946960240602493,
-0.023499418050050735,
0.02540021575987339,
-0.036268334835767746,
-0.019651876762509346,
-0.00881371833384037,
-0.040836237370967865,
0.02930191159248352,
0.027701521292328835,
0.011160101741552353,
0.015061081387102604,
-0.010828257538378239,
-0.05750197172164917,
-0.04663768410682678,
0.023658806458115578,
0.05715832859277725,
-0.00477049732580781,
-0.040704146027565,
0.04809251055121422,
0.0005714214057661593,
0.02432495728135109,
0.021687017753720284,
0.020268382504582405,
0.039256609976291656,
-0.015862734988331795,
-0.09579834342002869,
-0.05517440661787987,
0.07701857388019562,
0.014980253763496876,
-0.051037292927503586,
-0.07228219509124756,
-0.012427928857505322,
0.01845746859908104,
0.08017674088478088,
0.026811279356479645,
0.029319563880562782,
-0.03000073879957199,
0.041522447019815445,
0.002380723599344492,
-0.01054930780082941,
-0.017781032249331474,
0.015136667527258396,
-0.00640077143907547,
-0.060724955052137375,
-0.04078102484345436,
0.01525135152041912,
-0.032666727900505066,
0.01284768059849739,
-0.01665974035859108,
0.021632850170135498,
0.015171831473708153,
-0.0008454433991573751,
-0.020436322316527367,
0.0010310213547199965,
-0.006844726856797934,
0.07750529795885086,
-0.004084832035005093,
-0.011752703227102757,
0.04239330068230629,
-0.023559831082820892,
0.014996359124779701,
0.010769959539175034,
0.02597353234887123,
0.03052072413265705,
-0.03906925767660141,
-0.022549493238329887,
-0.030731867998838425,
-0.015384545549750328,
-0.008051558397710323,
-0.03752507269382477,
-0.03269403427839279,
-0.04275289922952652,
0.059171177446842194,
-0.010905370116233826,
0.04784422367811203,
-0.013942514546215534,
-0.02126125805079937,
0.09677756577730179,
-0.060716722160577774,
-0.05297432094812393,
-0.061472684144973755,
-0.07216818630695343,
-0.010466215200722218,
-0.009890217334032059,
0.02493693307042122,
-0.032896772027015686,
0.010795263573527336,
-0.022403163835406303,
-0.017958976328372955,
0.02219943143427372,
0.05094004049897194,
0.04030536115169525,
0.06046503409743309,
-0.0034625809639692307,
0.024184320122003555,
0.026633063331246376,
-0.008151145651936531,
-0.01973237283527851,
-0.002018385101109743,
-0.04390330612659454,
0.010893139988183975,
-0.00448464322835207,
-0.0007548074354417622,
-0.008356252685189247,
0.01083975750952959,
0.02674238197505474,
0.011972788721323013,
0.010949619114398956,
0.03251919522881508,
-0.01768946461379528,
0.04440798982977867,
0.004684101790189743,
0.01036872062832117,
0.002139726420864463,
0.05615225434303284,
0.028763392940163612,
0.016790827736258507,
-0.027170462533831596,
-0.036087438464164734,
-0.06269145011901855,
-0.03964773193001747,
0.04303954914212227,
0.04038703441619873,
-0.01628384180366993,
0.012902257964015007,
0.01036007609218359,
0.03422664478421211,
0.031701263040304184,
0.017161812633275986,
-0.003877882845699787,
-0.043747417628765106,
0.00842242781072855,
-0.0229863952845335,
-0.019627731293439865,
0.030974986031651497,
0.022921519353985786,
-0.02030949667096138,
-0.013962150551378727,
-0.0369730070233345,
-0.017221782356500626,
0.0135604627430439,
-0.013796963728964329,
-0.020580610260367393,
-0.00441788462921977,
-0.03458217903971672,
0.04401444271206856,
-0.03306140750646591,
0.025213435292243958,
0.020534709095954895,
-0.013474168255925179,
0.001578864292241633,
-0.043947868049144745,
-0.03347419947385788,
-0.02442087046802044,
0.02729448862373829,
-0.007747559808194637,
-0.015614948235452175,
0.03451685607433319,
-0.04765966162085533,
0.029026761651039124,
-0.0016851240070536733,
0.008092137984931469,
-0.00008151857036864385,
0.019206298515200615,
0.008434141986072063,
-0.0015548993833363056,
0.008474507369101048,
-0.02160676382482052,
-0.027805805206298828,
0.054415859282016754,
-0.0017346799140796065,
-0.010396699421107769,
0.05272511765360832,
-0.04980539157986641,
-0.002701084828004241,
-0.06169114261865616,
-0.00845655333250761,
-0.004460303112864494,
-0.006678524427115917,
-0.030518945306539536,
0.004105815198272467,
-0.007994968444108963,
-0.016226856037974358,
-0.012274462729692459,
-0.0326240099966526,
0.012814640998840332,
-0.019259121268987656,
0.008399710059165955,
0.0347742885351181,
0.005342307034879923,
-0.03418345749378204,
0.02230864204466343,
-0.005597100127488375,
-0.006867087446153164,
0.007931706495583057,
0.025587547570466995,
-0.022046314552426338,
-0.056665804237127304,
0.05392232537269592,
0.07129476964473724,
-0.01162610575556755,
0.006454066839069128,
-0.07187042385339737,
-0.02891753613948822,
-0.001319441944360733,
-0.005975200794637203,
0.025653116405010223,
-0.008923879824578762,
-0.007537063676863909,
0.1137939915060997,
-0.008982272818684578,
-0.035010989755392075,
-0.002279923064634204,
-0.009629160165786743,
-0.01224171370267868,
-0.0316738598048687,
0.002539238426834345,
-0.006970114540308714,
0.005821716506034136,
0.013597013428807259,
0.009709468111395836,
0.041331324726343155,
0.0037726385053247213,
0.03001396916806698,
-0.028908802196383476,
0.0007478826446458697,
-0.03308652341365814,
-0.00590069405734539,
0.039067428559064865,
0.012381703592836857,
-0.03116241656243801,
-0.01832922361791134,
0.03265106678009033,
0.030746042728424072,
0.02487516775727272,
-0.010556526482105255,
0.06462369114160538,
0.01534118503332138,
0.02163810096681118,
0.016912100836634636,
0.014004150405526161,
-0.002357874531298876,
-0.0525154173374176,
0.0068664271384477615,
-0.018550848588347435,
0.06334611773490906,
0.022264229133725166,
-0.012667974457144737,
0.03999389335513115,
0.039632443338632584,
-0.017320191487669945,
-0.011712661944329739,
-0.020063791424036026,
0.004635773133486509,
0.009871832095086575,
-0.041630495339632034,
0.01575450599193573,
0.005772142671048641,
0.010434143245220184,
0.013615674339234829,
-0.0003065616765525192,
-0.021821819245815277,
-0.021796932443976402,
-0.02957424893975258,
-0.010065880604088306,
-0.02598683536052704,
0.01388587150722742,
0.014298289082944393,
0.03157459571957588,
-0.0309835746884346,
0.0086695346981287,
-0.01831767149269581,
-0.0030015618540346622,
-0.07804115861654282,
-0.019096482545137405,
-0.042296718806028366,
-0.007215762976557016,
0.007599963340908289,
-0.06730949878692627,
-0.02800064906477928,
0.011102413758635521,
-0.011384353041648865,
-0.051033828407526016,
-0.0028876299038529396,
-0.04104301333427429,
0.03446883335709572,
-0.020957475528120995,
-0.03526546061038971,
-0.012572559528052807,
-0.015420726500451565,
0.06119596213102341,
-0.015590940602123737,
0.0018318523652851582,
-0.008283795788884163,
-0.023068657144904137,
-0.0015569335082545877,
-0.04065787419676781,
0.041821446269750595,
-0.003898857394233346,
0.01977166347205639,
-0.007143562659621239,
0.019210947677493095,
-0.06818655878305435,
-0.007775957230478525,
0.05647725239396095,
0.050907209515571594,
0.012656150385737419,
0.03945595771074295,
-0.0029220113065093756,
-0.033329516649246216,
-0.011359230615198612,
-0.0017552642384544015,
0.05121520534157753,
0.033038023859262466,
0.026756487786769867,
0.04263753443956375,
-0.010673210956156254,
-0.006725998129695654,
0.04184969514608383,
0.030194036662578583,
0.016983691602945328,
-0.018027400597929955,
-0.0025460270699113607,
0.0061374232172966,
-0.03223889693617821,
-0.014750371687114239,
0.0136431148275733,
-0.026842789724469185,
-0.03842112794518471,
-0.004129819571971893,
0.025312889367341995,
0.02330993488430977,
-0.04039894416928291,
0.007809174247086048,
-0.020427806302905083,
0.011669321916997433,
-0.04103895276784897,
0.00020441378001123667,
-0.008060433901846409,
0.04637649655342102,
0.02826603874564171,
0.029870489612221718,
-0.01792205311357975,
-0.04351639002561569,
-0.029574159532785416,
0.03824334591627121,
0.05550862103700638,
-0.0400594063103199,
-0.00602060416713357,
-0.06675496697425842,
0.013908683322370052,
0.03606438636779785,
-0.01933779940009117,
0.030398927628993988,
-0.02654493972659111,
-0.0017008056165650487,
-0.009620727971196175,
-0.03812688589096069,
0.013889415189623833,
0.011030183173716068,
-0.002323542255908251,
-0.008073580451309681,
-0.03519111126661301,
-0.012982564978301525,
-0.01968221180140972,
0.014629744924604893,
-0.010233556851744652,
-0.006247731391340494,
0.03156616538763046,
0.03997357562184334,
-0.004218004178255796,
0.01968494988977909,
-0.005747733172029257,
-0.1001865342259407,
0.024707769975066185,
-0.02227865532040596,
-0.02400093525648117,
0.048053670674562454,
-0.03503968194127083,
-0.022873178124427795,
0.017057746648788452,
0.0055625406093895435,
0.00026807625545188785,
-0.007151837460696697,
-0.059851691126823425,
0.05851351097226143,
0.05731641873717308,
-0.0020552489440888166,
0.007743007969111204,
0.051383987069129944,
-0.03586621209979057,
0.0266588032245636,
-0.047353941947221756,
-0.005492079071700573,
-0.029474720358848572,
0.014398245140910149,
-0.04111523553729057,
0.014776883646845818,
-0.03985057398676872,
0.0548454113304615,
0.01176905632019043,
0.03395902365446091,
0.01818164438009262,
-0.0642998069524765,
-0.026765717193484306,
0.04130984842777252,
0.0014531946508213878,
-0.015805674716830254,
-0.02689456380903721,
0.02270519733428955,
0.017141465097665787,
-0.009025905281305313,
0.03276617452502251,
-0.010886907577514648,
-0.007596287410706282,
-0.0030620819889009,
-0.036979448050260544,
0.014733223244547844,
-0.0255295317620039,
-0.03436799347400665,
0.02542467601597309,
-0.04093417525291443,
0.0407978780567646,
-0.02864699997007847,
-0.006477439776062965,
0.008508846163749695,
-0.03913664445281029,
-0.035128552466630936,
0.02420586533844471,
0.005318829324096441,
-0.028285864740610123,
-0.013671528548002243,
0.009359929710626602,
-0.024336839094758034,
0.006762594450265169,
-0.06330704689025879,
-0.0018182024359703064,
-0.00516451895236969,
0.005615961272269487,
-0.041128214448690414,
-0.04958615452051163,
-0.01726364530622959,
-0.05399816483259201,
-0.01762976497411728,
-0.019830990582704544,
0.06056031957268715,
-0.02988712675869465,
-0.00544513575732708,
0.03502311557531357,
0.04293711110949516,
0.039128709584474564,
0.026101335883140564,
-0.008289676159620285,
0.024367354810237885,
0.009473728947341442,
0.014832882210612297,
0.04639163240790367,
0.01358762290328741,
-0.01060368400067091,
-0.00784197449684143,
0.010045871138572693,
-0.011809478513896465,
0.003762985812500119,
-0.012395908124744892,
0.014545596204698086,
0.050322551280260086,
-0.007159237749874592,
0.0376397930085659,
-0.018709290772676468,
0.02642771229147911,
0.009444169700145721,
0.05218455195426941,
-0.03358981013298035,
0.007897892966866493,
-0.02330608107149601,
-0.018663600087165833,
0.04379233717918396,
0.020705968141555786,
0.0010147623252123594,
-0.0026188474148511887,
-0.020744625478982925,
0.03238799422979355,
-0.02063145861029625,
0.03166995570063591,
-0.017151616513729095,
-0.009415817447006702,
-0.02111375890672207,
0.07929280400276184,
-0.007646767422556877,
0.02101554162800312,
-0.0003158839826937765,
-0.025146406143903732,
0.011719905771315098,
0.031193135306239128,
0.011590832844376564,
0.02293357439339161,
-0.016722649335861206,
-0.03588791564106941,
-0.059098534286022186,
0.006576883140951395,
-0.031055960804224014,
0.015000531449913979,
0.029721638187766075,
-0.01857732981443405,
-0.006179814226925373,
-0.03818203881382942,
0.016692841425538063,
0.06473883241415024,
0.05441302806138992,
-0.027775129303336143,
0.02185863070189953,
0.04906107485294342,
0.01645239070057869,
0.025541050359606743,
-0.038812391459941864,
-0.03571736812591553,
0.06624390929937363,
-0.021987197920680046,
0.026145121082663536,
0.014588897116482258,
-0.0029161081183701754,
0.0035760176833719015,
0.02211521565914154,
0.036834266036748886,
-0.020030179992318153,
-0.005497020669281483,
-0.015199370682239532,
0.007754217833280563,
0.018399640917778015,
-0.0015151569386944175,
0.028291109949350357,
-0.003970685880631208,
0.01958838850259781,
0.05032108724117279,
0.01285461150109768,
-0.015389741398394108,
-0.0809299647808075,
-0.010001533664762974,
-0.02764236554503441,
-0.050061121582984924,
0.05897240340709686,
-0.030665412545204163,
-0.02670271322131157,
0.022087890654802322,
-0.04632341489195824,
-0.00458446703851223,
0.006450308952480555,
0.01450356189161539,
-0.0021273400634527206,
0.0361117385327816,
-0.04313959926366806,
0.047848980873823166,
-0.026728611439466476,
0.03194000571966171,
0.1424434781074524,
0.0633770078420639,
0.01377954799681902,
-0.04570285975933075,
0.056033749133348465,
0.002358838450163603,
0.023409565910696983,
-0.0051926118321716785,
0.041309904307127,
0.003600824624300003,
-0.012951698154211044,
-0.013603371568024158,
0.035838037729263306,
0.007206474430859089,
0.02112753503024578,
0.05066535994410515,
-0.016817662864923477,
-0.06319695711135864,
-0.00181787577457726,
0.029792338609695435,
0.0008857708307914436,
-0.03308432921767235,
0.0009121007169596851,
0.027274582535028458,
-0.002780194627121091,
-0.013931739144027233,
0.015086037106812,
-0.010671409778296947,
-0.0022916195448487997,
0.03675384819507599,
-0.04168297350406647,
-0.016365472227334976,
0.02029094472527504,
-0.014654550701379776,
-0.019778933376073837,
0.0022778615821152925,
0.0026451570447534323,
0.02437104657292366,
0.04193618893623352,
0.036098413169384,
-0.011541186831891537,
0.01507961843162775,
0.028153683990240097,
0.03705717995762825,
-0.02302170917391777,
-0.03093630261719227,
0.013154709711670876,
0.08580662310123444,
-0.02305467426776886,
-0.0442303828895092,
0.04280681908130646,
-0.018060339614748955,
0.056371018290519714,
-0.02167639508843422,
0.0009062745375558734,
-0.03388086333870888,
-0.02795650064945221,
-0.027608530595898628,
-0.02184372767806053,
0.04649151861667633,
0.06837227195501328,
0.021748356521129608,
0.04050341248512268,
0.007765772752463818,
-0.02614239975810051,
-0.014410656876862049,
-0.02515062317252159,
0.029462479054927826,
0.03858935460448265,
-0.02463347837328911,
-0.035783033818006516,
0.014524349011480808,
-0.025105735287070274,
0.004999733995646238,
-0.01776481606066227,
-0.006454928778111935,
0.034271419048309326,
-0.0031081135384738445,
-0.01234758272767067,
-0.055508341640233994,
-0.010110621340572834,
0.028549551963806152,
-0.014912562444806099,
-0.03531127795577049,
-0.006786443293094635,
0.02034788765013218,
-0.003570067696273327,
0.05089973658323288,
-0.012323550879955292,
0.022265803068876266,
0.007612358313053846,
0.05217127874493599,
-0.0027607569936662912,
-0.06872095912694931,
-0.01271553710103035,
-0.0008653692784719169,
-0.047050997614860535,
0.042727332562208176,
0.005281058605760336,
0.0052912416867911816,
0.005934661254286766,
0.02951444685459137,
-0.008909076452255249,
0.024297500029206276,
-0.0017697385046631098,
-0.0039168549701571465,
0.04172602295875549,
-0.015291317366063595,
0.006617644801735878,
0.02079017646610737,
0.028646139428019524,
-0.026857251301407814,
-0.03867164999246597,
-0.024273952469229698,
-0.00238129124045372,
0.002881531370803714,
0.038674309849739075,
-0.05887575447559357,
0.012700840830802917,
-0.012017357163131237,
0.018829187378287315,
-0.04457314684987068,
-0.0006538713350892067,
-0.035002876073122025,
-0.011121949180960655,
-0.016212010756134987,
0.006520411465317011,
-0.014831140637397766,
0.023181652650237083,
-0.012476203963160515,
0.04048261046409607,
0.0001630482147447765,
0.015959694981575012,
-0.0745755136013031,
-0.03901353105902672,
-0.01972367614507675,
-0.0052426960319280624,
0.023639582097530365,
0.0061986795626580715,
-0.02034134417772293,
0.02235451340675354,
-0.01527815219014883,
-0.0619770772755146,
0.036471594125032425,
0.028554042801260948,
0.00821148045361042,
0.00034823670284822583,
-0.03495281562209129,
-0.008272255770862103,
0.014339914545416832,
-0.007936876267194748,
0.020159324631094933,
-0.011425387114286423,
0.012678557075560093,
0.015191181562840939,
-0.001737498096190393,
0.003376719541847706,
0.028245536610484123,
-0.015221365727484226,
0.02177942916750908,
0.030132215470075607,
0.004426590166985989,
-0.03274557366967201,
-0.00856403261423111,
-0.03447388857603073,
0.012222019955515862,
-0.014386043883860111,
0.06960674375295639,
0.02804652415215969,
0.038603637367486954,
-0.06023561954498291,
0.0360465906560421,
0.03279673308134079,
-0.030667772516608238,
-0.06180233508348465,
-0.050666868686676025,
0.05228492245078087,
0.0038814465515315533,
0.04523723945021629,
-0.011996956542134285,
0.05846266448497772,
0.016131505370140076,
-0.05852896720170975,
0.004523600451648235,
-0.0017591543728485703,
0.007841939106583595,
-0.08722608536481857,
-0.050396133214235306,
-0.01644635759294033,
0.02069707028567791,
0.00446814950555563,
0.04003898799419403,
0.01736006885766983,
0.050309717655181885,
0.02221960574388504,
-0.0605018176138401,
-0.006515193730592728,
0.023082183673977852,
-0.008944974280893803,
-0.04029947891831398,
0.10498706996440887,
-0.041141327470541,
-0.029734184965491295,
0.020825160667300224,
0.0015308666042983532,
0.013067170046269894,
-0.016913436353206635,
0.006764013785868883,
0.012146740220487118,
0.0357595831155777,
0.01676381751894951,
-0.011715858243405819,
0.018822001293301582,
0.002253403188660741,
-0.01708199456334114,
0.05369480699300766,
0.016471102833747864,
0.003981711808592081,
-0.051304399967193604,
-0.04031526669859886,
-0.029244326055049896,
0.039031099528074265,
-0.04962582886219025,
0.003384438343346119,
0.00623541884124279,
-0.019360927864909172,
-0.027050262317061424,
0.004367454443126917,
0.013750419020652771,
-0.04382344335317612,
0.013478209264576435,
0.01611282303929329,
0.009310942143201828,
0.01253646519035101,
0.007388175930827856,
-0.0067085763439536095,
0.002248345408588648,
0.01557532325387001,
0.015218764543533325,
-0.03433781489729881,
-0.03380874916911125,
-0.010900887660682201,
-0.008553697727620602,
0.03779715299606323,
0.004189088009297848,
-0.03314241021871567,
-0.006756316404789686,
0.022681336849927902,
0.027004580944776535,
0.045532144606113434,
-0.010980729945003986,
0.0045614722184836864,
0.007961602881550789,
-0.04796769097447395,
0.025372080504894257,
0.02740325964987278,
0.03080258145928383,
-0.02222190983593464,
-0.02763420343399048,
0.0034569278359413147,
-0.03693059831857681,
0.018765000626444817,
0.01262746937572956,
-0.021684836596250534,
0.06680304557085037,
0.027916496619582176,
-0.018424514681100845,
0.004868520423769951,
0.00625277403742075,
0.009267749264836311,
-0.005207272246479988,
-0.013615278527140617,
-0.016490483656525612,
-0.016307726502418518,
0.004049280192703009,
0.06074640899896622,
-0.005079940892755985,
-0.014816652983427048,
-0.007180158980190754,
-0.04544464126229286,
0.05617168918251991,
0.0184829980134964,
-0.01776186190545559,
0.04762015864253044,
0.03332575038075447,
-0.014611472375690937,
0.006036390084773302,
-0.03887211158871651,
-0.028469182550907135,
0.014111869968473911,
-0.018635522574186325,
0.005021919496357441,
0.011159002780914307,
-0.029849013313651085,
0.005752920638769865,
-0.03355279192328453,
0.015721632167696953,
0.05097411200404167,
0.012745958752930164,
-0.024074029177427292,
0.044986557215452194,
0.024576958268880844,
0.01959942653775215,
0.0059251305647194386,
0.008852153085172176,
0.025360533967614174,
-0.03724266588687897,
0.011345330625772476,
0.011921914294362068,
0.037552449852228165,
0.030256852507591248,
-0.00013464469520840794,
0.035601209849119186,
0.0112458486109972,
-0.007519981823861599,
0.048991858959198,
0.04030296951532364,
-0.012826293706893921,
-0.014294560998678207,
0.028779972344636917,
-0.011685548350214958,
0.024615203961730003,
0.004828840494155884,
-0.02431698702275753,
0.06388485431671143,
-0.016555840149521828,
-0.029918646439909935,
-0.019991248846054077,
-0.021244630217552185,
0.015018375590443611,
0.022724837064743042,
-0.004988583270460367,
0.027398547157645226,
0.0025101089850068092,
0.000172672065673396,
-0.0031556806061416864,
0.042522918432950974,
-0.0022296931128948927,
-0.04260125383734703,
-0.026382284238934517,
-0.002347456058487296,
-0.004134595859795809,
-0.0413619726896286,
-0.008407609537243843,
0.009438611567020416,
-0.006263223942369223,
0.03772616758942604,
0.03035002201795578,
-0.009954297915101051,
-0.04061354324221611,
-0.056175291538238525,
-0.02989991381764412,
0.020955277606844902,
-0.00803044717758894,
0.0023945763241499662,
-0.014387175440788269,
0.02403022162616253,
-0.04374003782868385,
-0.011246048845350742
] |
<p>I am trying to wrap my head around how this would work.</p>
<p>The setup is quite simple - there are multiple flat coils sealed in insulated disks, and an active coil with alternating current underneath. All is placed in a cylinder.</p>
<p>The question is, how will the disks behave - all should induce the same magnetic field and thus repel each other. Will this force be stable enough, when the field collapses on each pulse?</p>
<p>Thanks!</p>
| 10,793 |
[
-0.05073174089193344,
-0.028301365673542023,
0.0009406143217347562,
-0.05684848502278328,
0.049530886113643646,
-0.010975147597491741,
-0.007365138735622168,
-0.010994136333465576,
-0.003498362610116601,
-0.018104547634720802,
0.027593489736318588,
0.055392056703567505,
0.04473067447543144,
0.007277932018041611,
0.025206303223967552,
-0.02880748361349106,
0.00005148164927959442,
0.008612466044723988,
-0.0042063151486217976,
-0.05117502436041832,
-0.012622863054275513,
0.015703799203038216,
-0.02074398286640644,
0.01028999499976635,
-0.0337044894695282,
0.019681628793478012,
0.03729432821273804,
-0.010662444867193699,
0.014083873480558395,
0.07480412721633911,
-0.05786801502108574,
-0.024683520197868347,
-0.0508325956761837,
0.030547507107257843,
0.027456363663077354,
0.0038322184700518847,
-0.06924060732126236,
-0.055106550455093384,
-0.034144315868616104,
0.038708899170160294,
-0.026837464421987534,
-0.00457843579351902,
-0.031263742595911026,
0.048641618341207504,
-0.020994562655687332,
-0.00723224738612771,
0.007849887013435364,
0.008231275714933872,
0.037951111793518066,
-0.06822799146175385,
0.05296942964196205,
-0.016339058056473732,
0.05536699667572975,
0.020675620064139366,
-0.00334866251796484,
-0.018894964829087257,
0.0715612843632698,
0.04134790226817131,
-0.0019916603341698647,
-0.016986383125185966,
0.0031450835522264242,
-0.00681855995208025,
-0.018930591642856598,
-0.04904283955693245,
-0.02812735177576542,
0.025683416053652763,
0.0026913387700915337,
-0.0013896857853978872,
0.025848867371678352,
0.022348111495375633,
0.03526104986667633,
0.016272149980068207,
0.008340946398675442,
-0.018301866948604584,
-0.016063468530774117,
-0.018435319885611534,
-0.0019653686322271824,
0.0030561990570276976,
0.03448906168341637,
0.029888538643717766,
-0.02617751806974411,
0.005029959604144096,
0.009519044309854507,
0.07420371472835541,
0.01707269437611103,
0.002375510521233082,
0.05997335910797119,
-0.021341489627957344,
0.04200981184840202,
-0.00950494222342968,
0.0303487591445446,
0.042578715831041336,
0.04909399524331093,
0.0017993677174672484,
-0.07273176312446594,
0.02286522649228573,
0.0035886946134269238,
0.05700377747416496,
-0.0237792506814003,
-0.018251506611704826,
0.019920960068702698,
0.01329833921045065,
-0.0007695219246670604,
0.05953952297568321,
0.018494436517357826,
-0.04530063271522522,
-0.06604477018117905,
0.015615937300026417,
-0.03777221590280533,
-0.00832336489111185,
-0.016163295134902,
0.004430759232491255,
0.027356941252946854,
-0.03782186284661293,
-0.015820620581507683,
-0.03280266746878624,
0.022434482350945473,
-0.008030487224459648,
0.022410092875361443,
0.034645479172468185,
0.05372503399848938,
-0.042559459805488586,
0.0009384768782183528,
-0.052472107112407684,
-0.06285155564546585,
-0.009896558709442616,
0.026584547013044357,
0.015246231108903885,
-0.0262463241815567,
0.04080626368522644,
-0.005982077214866877,
-0.029716527089476585,
-0.016827089712023735,
0.018730035051703453,
0.03333720192313194,
-0.03549627214670181,
-0.07295666635036469,
-0.027287254109978676,
0.021055879071354866,
-0.051119640469551086,
0.031314682215452194,
-0.031208638101816177,
-0.014426291920244694,
0.059769950807094574,
0.07210119068622589,
-0.06066104397177696,
-0.01344304159283638,
0.025614453479647636,
0.04215265437960625,
0.012681274674832821,
-0.02848185785114765,
-0.026341579854488373,
-0.03636791184544563,
-0.03729868680238724,
-0.050507932901382446,
-0.08992369472980499,
0.001830782857723534,
0.03576040267944336,
0.00928931962698698,
0.0071778008714318275,
0.017961516976356506,
-0.03691060468554497,
0.020283421501517296,
0.010016384534537792,
-0.015458371490240097,
-0.0195918045938015,
0.05260377377271652,
-0.02222798764705658,
0.031197642907500267,
0.032815564423799515,
-0.030794501304626465,
0.030857251957058907,
0.018036866560578346,
0.04422183334827423,
0.03634148836135864,
-0.039221394807100296,
0.00004159547825111076,
-0.036503296345472336,
0.018640613183379173,
-0.012468245811760426,
-0.019921476021409035,
-0.06159431114792824,
-0.00004515190812526271,
0.014468587934970856,
-0.006227034144103527,
0.027243293821811676,
-0.005220877937972546,
-0.012442274019122124,
-0.017063342034816742,
-0.05333680287003517,
-0.030650125816464424,
-0.010998259298503399,
0.045161403715610504,
-0.02288205362856388,
-0.04269735887646675,
0.010578876361250877,
-0.00037324868026189506,
0.022720374166965485,
0.010961291380226612,
-0.05867763236165047,
-0.028516370803117752,
0.03726616129279137,
-0.022774919867515564,
0.018290525302290916,
0.008685906417667866,
0.029034972190856934,
0.0004067515837959945,
-0.014036273583769798,
0.04383696988224983,
-0.03417440131306648,
-0.036019906401634216,
-0.02394718863070011,
-0.04851274564862251,
-0.002285232301801443,
0.019568677991628647,
0.018209127709269524,
0.046380411833524704,
0.012272919528186321,
0.034874048084020615,
0.014753293246030807,
-0.022636977955698967,
0.08207885175943375,
0.05693313851952553,
-0.007545183878391981,
0.03290696069598198,
0.028228512033820152,
0.011211756616830826,
0.0025003699120134115,
-0.02943495661020279,
-0.01862814836204052,
-0.06200709939002991,
0.03282187879085541,
0.05821637064218521,
0.04840238392353058,
-0.028280828148126602,
0.04145611822605133,
0.04073156416416168,
0.044553108513355255,
0.018937882035970688,
0.01924782246351242,
-0.00786119420081377,
-0.007779698818922043,
0.00838364940136671,
0.03488791733980179,
-0.02343783713877201,
-0.0004755804839078337,
0.02639077790081501,
0.03324630483984947,
0.00002066403794742655,
0.0052146995440125465,
0.009182173758745193,
0.03777935355901718,
-0.019040117040276527,
0.01901557296514511,
-0.016714880242943764,
-0.0387788787484169,
0.004311058670282364,
-0.030619123950600624,
0.033828478306531906,
-0.02420753799378872,
0.00700733857229352,
-0.007251627743244171,
0.00928227324038744,
0.009328894317150116,
0.002910079900175333,
0.004100668244063854,
0.0017805685056373477,
-0.06206783279776573,
0.014153010211884975,
-0.030913453549146652,
0.02785336785018444,
-0.0007729417993687093,
0.006754747591912746,
-0.011349805630743504,
0.01266065426170826,
0.03580477088689804,
0.013590370304882526,
0.05781196802854538,
-0.04180608317255974,
-0.029744016006588936,
-0.044911373406648636,
-0.027088403701782227,
0.01650005392730236,
0.021712999790906906,
-0.04163794592022896,
-0.010513585060834885,
-0.02074693702161312,
-0.01988643780350685,
0.04261908307671547,
0.004178293980658054,
-0.024342821910977364,
0.03336720913648605,
-0.0018892998341470957,
-0.07421786338090897,
-0.024591196328401566,
-0.031723249703645706,
0.029871866106987,
-0.03528769314289093,
0.014638642780482769,
0.08540359139442444,
0.02783823385834694,
-0.030490988865494728,
-0.0016927962424233556,
-0.02242768369615078,
-0.002862105146050453,
0.013187929056584835,
-0.018048817291855812,
0.027813155204057693,
-0.055418290197849274,
0.04561155289411545,
0.04239296168088913,
-0.03448853641748428,
0.0020572913344949484,
-0.01429517287760973,
-0.03632819280028343,
-0.02133757434785366,
-0.013226865790784359,
0.04666697233915329,
-0.044359758496284485,
-0.03852752968668938,
0.08933721482753754,
-0.013649634085595608,
-0.017789382487535477,
-0.011224532499909401,
-0.05361005291342735,
-0.0390152633190155,
-0.029640670865774155,
0.02940264530479908,
0.023585990071296692,
-0.03684588894248009,
0.006698472425341606,
0.011564294807612896,
-0.01519859116524458,
0.04950232803821564,
0.030025329440832138,
-0.01563786156475544,
0.019281137734651566,
0.059154123067855835,
-0.012158459983766079,
0.05885959789156914,
0.0387750044465065,
-0.04169280827045441,
0.0036926816683262587,
-0.014744755811989307,
0.021257279440760612,
0.0337478443980217,
-0.035438403487205505,
0.049119748175144196,
-0.014481651596724987,
0.004149741027504206,
-0.005515288561582565,
0.024914583191275597,
-0.01063461508601904,
-0.03594933822751045,
-0.009887122549116611,
0.03246533125638962,
0.04720035195350647,
-0.024073822423815727,
-0.016837185248732567,
0.039717476814985275,
0.034904155880212784,
-0.037084996700286865,
-0.03414524346590042,
-0.005925842560827732,
-0.020973222330212593,
-0.031910475343465805,
-0.01713855378329754,
-0.02566004917025566,
0.016024351119995117,
0.004125355277210474,
0.050767578184604645,
0.02310316078364849,
0.0018553208792582154,
-0.0013160726521164179,
-0.08805574476718903,
0.011683221906423569,
-0.003009264590218663,
0.04698263481259346,
0.0049652718007564545,
0.052557263523340225,
0.007633276283740997,
-0.01046479307115078,
0.026824915781617165,
0.01857081800699234,
-0.054545287042856216,
-0.0007652973290532827,
-0.018636660650372505,
-0.006259279791265726,
0.00398867717012763,
-0.002985011786222458,
0.002836475381627679,
0.021725069731473923,
0.011682207696139812,
-0.010680269449949265,
-0.021032223477959633,
-0.058142002671957016,
0.009068374522030354,
-0.027313124388456345,
-0.038648221641778946,
-0.021291295066475868,
0.03599967435002327,
0.03584595397114754,
0.005383932031691074,
0.018033193424344063,
-0.0365351103246212,
-0.058912478387355804,
0.01951133832335472,
-0.005815410520881414,
-0.029213489964604378,
0.005958035122603178,
0.013429849408566952,
0.002189453924074769,
0.012230925261974335,
-0.035357583314180374,
-0.015694785863161087,
0.012300030328333378,
0.04232591763138771,
0.030359268188476562,
-0.013458963483572006,
-0.01680964045226574,
-0.04187909886240959,
-0.04572091996669769,
0.018804209306836128,
0.05275968462228775,
-0.010441087186336517,
-0.004703904967755079,
0.0025376102421432734,
-0.010441696271300316,
-0.032305508852005005,
0.02979259192943573,
0.04847533255815506,
0.007825757376849651,
-0.02554413117468357,
-0.029469793662428856,
-0.012606292963027954,
-0.004968581721186638,
0.017010880634188652,
-0.030503960326313972,
-0.009563990868628025,
-0.044743891805410385,
0.004159083124250174,
0.026393909007310867,
0.044578004628419876,
-0.0002713407448027283,
0.008667469024658203,
-0.022832496091723442,
0.013318280689418316,
-0.033997032791376114,
0.02405894733965397,
0.002192607382312417,
0.04981983080506325,
0.05120513215661049,
0.03809497877955437,
-0.03886260837316513,
-0.10282882302999496,
-0.035760555416345596,
0.038193028420209885,
0.032990071922540665,
0.019341232255101204,
-0.01452354434877634,
-0.027122508734464645,
-0.021106146275997162,
0.04716316610574722,
-0.08791535347700119,
0.03947524353861809,
0.010663256980478764,
-0.04096493870019913,
-0.004488091450184584,
-0.010471870191395283,
-0.016581472009420395,
0.02796727977693081,
-0.024016257375478745,
0.030715493485331535,
-0.01029635313898325,
-0.004609739873558283,
0.0075499326921999454,
0.030763156712055206,
0.033483006060123444,
0.035783689469099045,
-0.020331021398305893,
0.017191581428050995,
-0.014145651832222939,
0.030051443725824356,
-0.023550625890493393,
-0.05466729775071144,
0.01608455739915371,
-0.021573757752776146,
-0.020003579556941986,
0.04887298122048378,
-0.03870868310332298,
-0.05000162869691849,
-0.017427563667297363,
0.028519989922642708,
0.028634339570999146,
-0.028614329174160957,
-0.03533864766359329,
0.04981280863285065,
0.03249403461813927,
-0.013993743807077408,
0.03722105920314789,
0.017947914078831673,
-0.03553275391459465,
0.01920207589864731,
0.01675732247531414,
0.017996422946453094,
-0.03151281923055649,
0.030869167298078537,
-0.02521098405122757,
0.05220409482717514,
-0.06382568180561066,
0.08095604926347733,
-0.04889766126871109,
0.0135415680706501,
0.003009225009009242,
-0.010135430842638016,
0.027293186634778976,
0.03449646756052971,
-0.02559042163193226,
-0.01798427850008011,
0.00922179315239191,
0.031835488975048065,
-0.027259113267064095,
-0.020310141146183014,
0.00015519307635258883,
-0.034908246248960495,
0.02019355446100235,
0.023404492065310478,
-0.000394807051634416,
0.004682708065956831,
-0.04080819711089134,
-0.00613362854346633,
0.01482737623155117,
-0.04664042592048645,
0.051585663110017776,
-0.017516445368528366,
0.029810314998030663,
0.015165220946073532,
-0.033772069960832596,
0.008972304873168468,
-0.015293837524950504,
-0.033609140664339066,
0.04688752442598343,
-0.024506177753210068,
0.024499407038092613,
0.00033103988971561193,
-0.013171046040952206,
-0.03932134807109833,
-0.05758924037218094,
0.05145818740129471,
-0.000533183803781867,
0.025659266859292984,
-0.04224192351102829,
-0.009672817774116993,
-0.015573273412883282,
-0.029152218252420425,
-0.014415008947253227,
0.029855486005544662,
-0.05282970890402794,
0.01917961612343788,
0.027567647397518158,
-0.029052598401904106,
0.031078139320015907,
0.03723552078008652,
-0.0256052203476429,
0.005568627268075943,
-0.026515981182456017,
-0.0073682693764567375,
-0.015557345002889633,
0.008853034116327763,
-0.016370488330721855,
-0.059988945722579956,
0.003320376155897975,
0.03846731781959534,
0.04230600222945213,
-0.023020660504698753,
0.01283725444227457,
0.020968277007341385,
0.013345947489142418,
-0.020023632794618607,
-0.03331372141838074,
0.009406269527971745,
0.0003778334939852357,
-0.016371440142393112,
-0.000841919332742691,
-0.015198026783764362,
-0.04982363060116768,
-0.06624768674373627,
0.03430738300085068,
0.007791201584041119,
-0.020879900082945824,
0.005242099519819021,
0.08887919038534164,
-0.023486925289034843,
-0.013710898347198963,
-0.023258036002516747,
-0.026480957865715027,
0.017794223502278328,
0.01089446246623993,
0.015996335074305534,
0.005541607271879911,
-0.023794103413820267,
-0.0006336579681374133,
-0.03835263103246689,
-0.024852076545357704,
0.017107725143432617,
0.04555550590157509,
-0.026980215683579445,
0.04981429502367973,
0.03564897179603577,
0.010128948837518692,
-0.018954908475279808,
-0.02459731325507164,
0.014861435629427433,
-0.0004700265417341143,
0.009071728214621544,
0.029180025681853294,
0.004151978995651007,
0.007279595825821161,
0.031725943088531494,
0.05455600097775459,
0.02311912178993225,
0.01474315207451582,
0.04182680323719978,
0.022157877683639526,
0.023114092648029327,
0.004018726292997599,
-0.03051341511309147,
0.028884761035442352,
-0.053204409778118134,
0.037897057831287384,
0.012333063408732414,
0.01049550250172615,
0.03196348622441292,
0.02778548188507557,
0.02221846580505371,
-0.012340863235294819,
-0.006415826268494129,
-0.027373945340514183,
0.05120886489748955,
0.022106513381004333,
0.026466794312000275,
0.020437201485037804,
0.04199403524398804,
0.033386439085006714,
0.035189058631658554,
-0.009593376889824867,
-0.0015132384141907096,
-0.04912405088543892,
-0.02892540581524372,
0.011170299723744392,
-0.04315481707453728,
0.03385362774133682,
0.037549570202827454,
-0.022322311997413635,
-0.014391542412340641,
0.018335439264774323,
0.028396595269441605,
0.0332200713455677,
0.011841751635074615,
0.013793237507343292,
0.07250631600618362,
0.012974947690963745,
0.03121139109134674,
-0.03282003849744797,
0.00012912816600874066,
0.11676473915576935,
0.018931496888399124,
0.030831528827548027,
-0.03181369602680206,
-0.015010126866400242,
-0.029227081686258316,
-0.013825783506035805,
-0.012206359766423702,
0.008490638807415962,
0.008906189352273941,
-0.013983502052724361,
0.01557350717484951,
0.0029627978801727295,
-0.0052643525414168835,
-0.004733507055789232,
0.02540791779756546,
-0.0017600293504074216,
-0.004575565457344055,
-0.020064452663064003,
0.011854484677314758,
-0.017537400126457214,
-0.010141734033823013,
-0.046241600066423416,
0.05603978410363197,
-0.012519394978880882,
-0.009172325022518635,
-0.016099929809570312,
-0.04024893790483475,
0.029111972078680992,
-0.0016524577513337135,
0.003445365931838751,
0.009153284132480621,
-0.052606433629989624,
-0.030628403648734093,
-0.044146183878183365,
0.03950488939881325,
0.01277933083474636,
0.013887041248381138,
0.01181543618440628,
0.008679128251969814,
0.029797177761793137,
-0.007377300877124071,
-0.00034231090103276074,
0.01372316014021635,
-0.004543933551758528,
-0.003133654361590743,
-0.04818344488739967,
0.06894033402204514,
-0.012401537969708443,
0.0031231683678925037,
-0.020934846252202988,
0.00975709967315197,
0.028580978512763977,
-0.030513860285282135,
-0.010451625101268291,
0.0013632503105327487,
-0.001499162637628615,
-0.03162221983075142,
-0.014968948438763618,
-0.021661920472979546,
0.01155961211770773,
-0.014658641070127487,
-0.001977953827008605,
-0.023976564407348633,
-0.03128456696867943,
0.0012158231111243367,
-0.02274448052048683,
0.03458961471915245,
-0.014344613067805767,
0.012857277877628803,
-0.05087990686297417,
-0.011936033144593239,
-0.03231072425842285,
0.008436372503638268,
-0.00023428935674019158,
0.02367805689573288,
0.00950352381914854,
-0.005343693774193525,
-0.012738507241010666,
0.028838319703936577,
-0.05777525529265404,
0.055015601217746735,
-0.008857004344463348,
-0.023052645847201347,
0.006615957710891962,
-0.022792816162109375,
0.027485845610499382,
0.03764534741640091,
-0.02151016891002655,
0.04727502539753914,
-0.01895204558968544,
0.03576723486185074,
-0.01828841120004654,
0.007982511073350906,
-0.037632498890161514,
-0.005111899226903915,
-0.06496819108724594,
0.002711155219003558,
0.017905278131365776,
0.06940583884716034,
0.020021166652441025,
-0.004411452449858189,
0.013235610909759998,
0.040961962193250656,
-0.004388218279927969,
-0.0183013416826725,
-0.0024507855996489525,
-0.0273000318557024,
-0.00276378751732409,
-0.00895609986037016,
-0.029060199856758118,
-0.02977837808430195,
-0.034205805510282516,
-0.019338389858603477,
-0.024372205138206482,
0.010093689896166325,
-0.0030829196330159903,
0.01596163958311081,
-0.01925559528172016,
-0.02682744339108467,
0.031245017424225807,
-0.022654157131910324,
-0.00416415324434638,
-0.017968973144888878,
-0.009378856047987938,
0.013466347940266132,
0.009270674549043179,
-0.008367452770471573,
-0.013099953532218933,
-0.016770415008068085,
0.006949059199541807,
0.023612070828676224,
-0.028283892199397087,
-0.008082610554993153,
0.002198816044256091,
0.021576181054115295,
0.02103165164589882,
0.006506281904876232,
0.00981537252664566,
-0.04089430719614029,
0.04663672298192978,
-0.041650135070085526,
-0.03826966881752014,
-0.011686830781400204,
-0.010012832470238209,
0.02558046020567417,
0.07551807910203934,
-0.018503153696656227,
-0.028016746044158936,
0.03939727321267128,
0.006638184189796448,
-0.01912727579474449,
0.024331122636795044,
0.0002744607627391815,
0.02586785890161991,
0.02050108276307583,
0.040407296270132065,
-0.004602676723152399,
-0.025095952674746513,
0.02075774222612381,
0.04823596403002739,
0.012855767272412777,
-0.013520479202270508,
-0.0026202290318906307,
0.05570077523589134,
-0.01036268100142479,
-0.013937617652118206,
-0.005992983002215624,
0.05656201019883156,
0.01374818291515112,
-0.00801234319806099,
-0.030501121655106544,
-0.02881886623799801,
0.008072098717093468,
-0.09575506299734116,
0.0021933207754045725,
0.01334263477474451,
0.011117846705019474,
-0.013960794545710087,
-0.05640019476413727,
-0.021286319941282272,
0.0332375206053257,
-0.05601661279797554,
-0.010870586149394512,
-0.015900328755378723,
-0.017715618014335632,
-0.050850480794906616,
0.02385653555393219,
-0.012251432985067368,
0.035445861518383026,
0.02753102406859398,
0.0198017880320549,
0.013549321331083775,
-0.012862036935985088,
-0.035267286002635956,
-0.0022551347501575947,
-0.03299374133348465,
0.020658394321799278,
0.00967331137508154,
0.021192576736211777,
0.06155967339873314,
-0.012785380706191063,
-0.027093008160591125,
0.01710399240255356,
-0.03131329268217087,
-0.007258608005940914,
-0.007214910350739956,
0.018536988645792007,
0.015978846698999405,
0.02602592669427395,
-0.022559095174074173,
0.0022247042506933212,
0.026212219148874283,
0.031225599348545074,
0.04945174604654312,
0.01982489600777626,
-0.0026545573491603136,
0.027927888557314873,
0.0711243599653244,
-0.007561755366623402,
0.003054960398003459,
0.042897749692201614,
-0.0033306037075817585,
-0.004524027928709984,
-0.03881854563951492,
0.013722334057092667,
0.03399933502078056,
0.006444142200052738,
0.005478444043546915,
-0.0419410802423954,
-0.01786809042096138,
0.016267899423837662,
-0.004833444021642208,
0.009818395599722862,
0.04563871771097183,
-0.015170438215136528,
-0.023186875507235527,
0.02806571125984192,
0.011059727519750595,
-0.020788535475730896,
-0.029513409361243248,
-0.0001340118469670415,
0.020108776167035103,
0.011916456744074821,
-0.003710805904120207,
-0.025841809809207916,
-0.00652170367538929,
0.020001480355858803,
0.04076974093914032,
0.02968471869826317,
0.04995586350560188,
-0.08484525233507156,
-0.011228648945689201,
-0.02720644325017929,
0.05956282839179039,
-0.041705358773469925,
-0.05906466022133827,
-0.04936940595507622,
-0.10017130523920059,
-0.01362970843911171,
0.029160065576434135,
0.01500653475522995,
0.012670367024838924,
-0.01942862570285797,
0.031514912843704224,
-0.02950436621904373,
0.040395647287368774,
-0.06371535360813141,
0.024069298058748245,
0.004866133909672499,
-0.007616750430315733,
0.0015812271740287542,
0.028865495696663857,
-0.01336362399160862,
0.0032818650361150503,
0.020249981433153152,
-0.03434363752603531,
0.006094297394156456,
-0.019007153809070587,
-0.04215770214796066,
0.014142075553536415,
-0.014266466721892357,
-0.016773756593465805,
0.030268393456935883,
-0.026247642934322357,
0.00823900941759348,
-0.027254614979028702,
-0.024206576868891716,
-0.0388721339404583,
0.00899331271648407,
-0.055118147283792496,
0.04140172153711319,
-0.03685218095779419,
-0.00962667167186737,
0.012003453448414803,
-0.033211369067430496,
-0.004562066867947578,
0.024338167160749435,
-0.03286159783601761,
0.004446964245289564,
0.055987387895584106,
0.02802000194787979,
0.01341636199504137,
-0.027877431362867355,
0.042606107890605927,
-0.0037252118345350027,
0.017814289778470993,
-0.040135644376277924,
0.05808160826563835,
0.001016271417029202,
0.027471624314785004,
0.00881396047770977,
0.014707167632877827,
0.023280538618564606,
0.02398703619837761,
0.0027919893618673086,
0.035758521407842636,
-0.01889481209218502,
0.015591229312121868,
-0.0023926959838718176,
-0.01312954630702734,
-0.01889643445611,
0.03367267921566963,
-0.01410884503275156,
0.10168276727199554,
-0.04951195418834686,
-0.005671312566846609,
-0.04024989902973175,
0.030551154166460037,
0.05241420492529869,
0.019253268837928772,
0.045347198843955994,
0.05896146968007088,
-0.03306863084435463,
0.023433813825249672,
0.01020814012736082,
-0.015951042994856834,
0.08216486871242523,
-0.04147055372595787,
0.053671907633543015,
-0.01588733308017254,
0.014633086510002613,
-0.018649492412805557,
-0.01971982792019844,
-0.028487926349043846,
-0.050049591809511185,
0.0024995962157845497,
0.01831337995827198,
0.005212989170104265,
0.00833510048687458,
0.016331495717167854,
0.013561741448938847,
0.05610452964901924,
-0.04190859571099281,
0.014307470992207527,
-0.020845968276262283,
0.030231352895498276,
0.05586843565106392,
0.04756985604763031
] |
<p>I am trying to locate peak in a data set by numerically calculating the peak using <a href="http://mathworld.wolfram.com/FunctionCentroid.html" rel="nofollow">centroid method</a>. How can I estimate the error associated with this peak determination?</p>
| 10,794 |
[
-0.002614127704873681,
-0.011509371921420097,
-0.002280276268720627,
-0.005400586873292923,
0.016219384968280792,
0.010796874761581421,
-0.032653674483299255,
-0.03756428137421608,
0.03543597459793091,
-0.021391741931438446,
0.07598771899938583,
0.06703052669763565,
0.06048224866390228,
0.06521318852901459,
0.025387652218341827,
-0.009859896264970303,
-0.0323537215590477,
0.01613626256585121,
0.0020835078321397305,
-0.037821464240550995,
0.023607896640896797,
0.03313330188393593,
-0.017601314932107925,
-0.017253106459975243,
-0.03561565652489662,
0.017949530854821205,
0.012905328534543514,
0.00012536445865407586,
-0.0012987758964300156,
0.06919161230325699,
-0.05908104032278061,
-0.0378449484705925,
0.03203810378909111,
0.02729782462120056,
0.039953526109457016,
0.0046970597468316555,
-0.04085661843419075,
-0.029483623802661896,
-0.022866930812597275,
0.029102375730872154,
0.00632231030613184,
-0.03830748796463013,
0.006970817688852549,
0.04076630249619484,
-0.013429244980216026,
-0.011332926340401173,
0.01347428746521473,
-0.03505378216505051,
0.01861426793038845,
-0.03979349136352539,
0.06993068009614944,
0.027794133871793747,
0.011926780454814434,
0.03455571457743645,
-0.02965281344950199,
0.020557411015033722,
0.011120222508907318,
0.06552191823720932,
-0.014406457543373108,
-0.09069448709487915,
-0.0534663088619709,
-0.04717499762773514,
0.016715405508875847,
-0.02048667147755623,
-0.022606519982218742,
0.044919367879629135,
-0.02657156251370907,
-0.02332562766969204,
0.018595777451992035,
-0.030602991580963135,
0.005338877439498901,
0.025090698152780533,
0.0006765829166397452,
-0.010954177007079124,
0.001302551245316863,
-0.04199701547622681,
0.014223987236618996,
0.011759157292544842,
0.03268440067768097,
0.009483817964792252,
0.03405240178108215,
0.033469218760728836,
0.011458752676844597,
-0.0027492432855069637,
0.021665560081601143,
0.0010521974181756377,
0.05126532167196274,
-0.0003001915756613016,
0.027585020288825035,
0.011722235940396786,
-0.03156276419758797,
-0.007546841632574797,
0.03333623707294464,
-0.017905229702591896,
-0.02885354869067669,
0.009117914363741875,
-0.010513991117477417,
0.060321252793073654,
-0.006005532573908567,
-0.021497471258044243,
0.023048395290970802,
-0.029149334877729416,
0.006756845861673355,
0.06603725254535675,
-0.028161929920315742,
-0.008582904003560543,
-0.003064762568101287,
-0.021541381254792213,
-0.016833269968628883,
-0.032578546553850174,
-0.00792111735790968,
0.007397995330393314,
0.020584233105182648,
0.01043415442109108,
0.03426659479737282,
0.03108077123761177,
-0.007719838991761208,
-0.024217771366238594,
0.05628664419054985,
0.006657048128545284,
0.03196583315730095,
-0.030798083171248436,
0.01710909605026245,
-0.011010966263711452,
-0.04315102845430374,
0.027711905539035797,
0.02498326450586319,
-0.036669470369815826,
-0.07847583293914795,
0.0033785635605454445,
-0.01361999474465847,
-0.028228264302015305,
0.038202349096536636,
0.005666246172040701,
0.028214531019330025,
0.010961486957967281,
-0.06636612117290497,
-0.08753468841314316,
0.0038506402634084225,
0.00990896113216877,
-0.01911095902323723,
-0.0366537906229496,
0.012560003437101841,
0.042067620903253555,
0.044661954045295715,
0.028885407373309135,
0.028187740594148636,
0.057087235152721405,
0.045391958206892014,
0.012336871586740017,
-0.0031827830243855715,
-0.027070272713899612,
0.006751460023224354,
-0.03509838879108429,
-0.05600584298372269,
-0.05819471552968025,
-2.443227913317969e-7,
-0.011416574008762836,
-0.010357007384300232,
-0.02559487335383892,
0.031778451055288315,
0.02304387465119362,
-0.005439566448330879,
-0.0015430287458002567,
-0.0031097163446247578,
-0.0022449123207479715,
0.06796016544103622,
0.024592485278844833,
0.005092787556350231,
0.02256929688155651,
0.007431307341903448,
0.04271133616566658,
-0.017057573422789574,
-0.017136238515377045,
0.08360161632299423,
-0.0510055311024189,
-0.0009041411685757339,
-0.02259873040020466,
0.01163420919328928,
0.015506437979638577,
-0.04948330670595169,
-0.037790823727846146,
0.0229343194514513,
0.017058759927749634,
0.00740191200748086,
0.056040406227111816,
-0.018390009179711342,
-0.027372783049941063,
0.03539940342307091,
-0.010891457088291645,
0.006049199029803276,
-0.042822010815143585,
0.021319404244422913,
-0.012481103651225567,
-0.013810542412102222,
-0.010776311159133911,
-0.0005965158343315125,
-0.01800111122429371,
-0.009341695345938206,
0.00019579871150199324,
0.0013315045507624745,
-0.005423885770142078,
0.04696885868906975,
-0.03282077983021736,
0.007287873420864344,
0.0356331430375576,
0.03962568938732147,
-0.007017232943326235,
0.043521322309970856,
-0.0067935846745967865,
0.012635739520192146,
0.011509527452290058,
-0.04706856608390808,
-0.007543934974819422,
-0.010917275212705135,
-0.026319559663534164,
0.0046722604893147945,
-0.008109981194138527,
0.009894799441099167,
0.043606776744127274,
-0.02453404664993286,
0.08423525840044022,
0.06151872128248215,
0.005471645388752222,
0.017537977546453476,
-0.014395378530025482,
0.011401871219277382,
0.021271971985697746,
-0.0009073172695934772,
-0.029589125886559486,
-0.05114154517650604,
-0.007087846286594868,
0.045757535845041275,
0.015263459645211697,
-0.026782924309372902,
-0.019586216658353806,
0.10188557207584381,
-0.0187455452978611,
0.0446731336414814,
-0.0063630398362874985,
-0.03353360295295715,
-0.00022297207033261657,
0.018364742398262024,
0.037617940455675125,
-0.021912910044193268,
0.016866695135831833,
0.007434165570884943,
0.02069004625082016,
0.030091220512986183,
-0.013721945695579052,
0.0004251104546710849,
0.03298637643456459,
-0.03949741646647453,
0.017792243510484695,
0.009072590619325638,
0.017355898395180702,
0.06183862313628197,
-0.0341116301715374,
0.041106969118118286,
0.016795990988612175,
-0.051320094615221024,
0.01749483309686184,
0.0042687831446528435,
-0.027391444891691208,
0.02962297759950161,
0.03900111839175224,
-0.0642959475517273,
-0.012921473942697048,
0.017884377390146255,
-0.045159075409173965,
0.001089489902369678,
-0.031595464795827866,
-0.02263604663312435,
-0.018844550475478172,
0.003410391043871641,
0.03931320086121559,
0.00886895414441824,
0.016636531800031662,
-0.01948060840368271,
-0.020097922533750534,
-0.023316914215683937,
-0.04414377361536026,
0.011448103934526443,
-0.0021797800436615944,
-0.04514097422361374,
-0.027008064091205597,
-0.03252984583377838,
-0.020922578871250153,
0.0006933685508556664,
0.02000530995428562,
0.00978263933211565,
0.00964084267616272,
0.004098106175661087,
-0.04651375114917755,
0.021598387509584427,
-0.020989077165722847,
0.013923834078013897,
-0.027910251170396805,
0.007515335455536842,
0.02310786210000515,
-0.014753023162484169,
-0.009587246924638748,
0.05193006619811058,
-0.0025828653015196323,
-0.01924658752977848,
-0.07129352539777756,
0.024790344759821892,
0.03740805760025978,
-0.06208265945315361,
0.011938618496060371,
-0.010777153074741364,
0.015745803713798523,
0.007411609869450331,
-0.08146647363901138,
-0.040857166051864624,
0.004563177935779095,
-0.019410986453294754,
0.03086760826408863,
0.009836800396442413,
-0.012926490046083927,
0.0662529468536377,
0.014063932001590729,
-0.06553507596254349,
-0.04104328900575638,
0.0008499825489707291,
-0.013258997350931168,
0.02526756376028061,
0.004523251671344042,
0.002129784319549799,
-0.00005275689181871712,
-0.014462042599916458,
-0.011791692115366459,
0.008399942889809608,
0.07960588485002518,
0.010265079326927662,
-0.009985902346670628,
0.01495162770152092,
0.016936862841248512,
0.018226953223347664,
0.03954996541142464,
0.008817890658974648,
-0.0034070140682160854,
0.047391876578330994,
-0.015872381627559662,
-0.0018968952354043722,
0.0363130196928978,
-0.020625971257686615,
-0.0029597764369100332,
-0.0077336449176073074,
-0.000017634871255722828,
-0.024837302044034004,
0.025841768831014633,
0.03536690026521683,
0.01660921424627304,
-0.007382082752883434,
0.05090269073843956,
0.07472356408834457,
-0.020229605957865715,
-0.025798089802265167,
0.04412708058953285,
0.01085405983030796,
-0.018611304461956024,
-0.017305895686149597,
0.01129607018083334,
-0.03622214123606682,
0.006855762097984552,
-0.017276011407375336,
-0.06167445331811905,
0.044991642236709595,
0.0472227968275547,
-0.008148927241563797,
0.04335068166255951,
-0.04084222391247749,
-0.0052605378441512585,
-0.05358479171991348,
-0.01450763363391161,
-0.028047025203704834,
0.051828112453222275,
-0.001337238005362451,
0.05457204952836037,
0.06997985392808914,
-0.026524493470788002,
0.012527389451861382,
0.03211775794625282,
-0.08336876332759857,
0.014269139617681503,
-0.01792191155254841,
-0.013858680613338947,
-0.031776126474142075,
-0.040227264165878296,
0.028385715559124947,
-0.008644569665193558,
0.01094751711934805,
-0.021212130784988403,
0.02371029369533062,
-0.04700570926070213,
0.024186257272958755,
0.007862658239901066,
0.023890148848295212,
-0.028591958805918694,
0.0254853256046772,
0.03876957669854164,
-0.0002307347021996975,
0.03036065772175789,
0.006762781646102667,
0.0032947929576039314,
-0.038654547184705734,
-0.015024622902274132,
-0.027291227132081985,
-0.018381351605057716,
0.04206974804401398,
-0.006881393492221832,
0.03926223888993263,
-0.03645298257470131,
0.019887162372469902,
-0.024116363376379013,
0.058428067713975906,
0.061554454267024994,
0.007442295551300049,
-0.014639381319284439,
-0.029769862070679665,
-0.005119957961142063,
0.014381617307662964,
0.002629814902320504,
-0.03739272803068161,
-0.020886942744255066,
0.04244022071361542,
0.010251796804368496,
-0.01827133074402809,
0.025540772825479507,
0.03824334591627121,
0.04827641323208809,
0.01572193205356598,
-0.05942729115486145,
-0.014753942377865314,
-0.02911340817809105,
-0.02734297700226307,
0.02758573554456234,
-0.0282655768096447,
-0.020737983286380768,
0.006499936804175377,
0.053907234221696854,
-0.004340003710240126,
-0.03085053525865078,
-0.0009051958913914859,
0.02040388062596321,
0.015981173142790794,
-0.02306056022644043,
-0.03467555344104767,
0.030444277450442314,
0.016676928848028183,
0.084712915122509,
-0.015475773252546787,
0.009043787606060505,
-0.10909285396337509,
-0.028906384482979774,
0.044804178178310394,
0.009495433419942856,
-0.06448645144701004,
0.02099682204425335,
-0.047779228538274765,
0.007177358027547598,
0.05910031870007515,
-0.039540935307741165,
0.04733872041106224,
-0.031300608068704605,
0.02863544039428234,
0.010065155103802681,
-0.01854100078344345,
-0.03693769872188568,
-0.009141202084720135,
-0.02856343984603882,
0.036910638213157654,
-0.044759608805179596,
0.0017007555579766631,
-0.008994931355118752,
-0.0017925896681845188,
0.034491315484046936,
0.09406626224517822,
0.025218404829502106,
-0.011070678941905499,
-0.007911036722362041,
0.008345022797584534,
-0.007922527380287647,
-0.04674558341503143,
0.0018264779355376959,
-0.01853819191455841,
0.011668592691421509,
0.022526664659380913,
-0.014673905447125435,
-0.030357658863067627,
0.01441541500389576,
0.021372565999627113,
-0.013391663320362568,
-0.02509494498372078,
-0.023549387231469154,
0.040640346705913544,
0.06915697455406189,
0.0079259742051363,
0.09075397253036499,
-0.00316201732493937,
0.007742639165371656,
-0.00048418596270494163,
-0.03203916177153587,
-0.001846756786108017,
0.004118616227060556,
-0.014974942430853844,
0.0034333965741097927,
0.013837405480444431,
-0.03274371847510338,
0.01673857308924198,
-0.008074328303337097,
0.019020196050405502,
-0.033674970269203186,
0.003326136153191328,
0.017801333218812943,
0.035150084644556046,
-0.005286474712193012,
0.025373779237270355,
0.009258352220058441,
0.03463306650519371,
0.013689514249563217,
-0.018857093527913094,
-0.0021424898877739906,
-0.028857838362455368,
-0.01399289071559906,
0.00764087587594986,
-0.03376633673906326,
0.0016209814930334687,
-0.04561826214194298,
-0.022156141698360443,
-0.006301545538008213,
-0.05047021806240082,
0.025263795629143715,
-0.04158594831824303,
0.0007050399435684085,
-0.01571081206202507,
-0.011356310918927193,
-0.044222526252269745,
-0.004304294474422932,
-0.0078085241839289665,
0.05837467312812805,
-0.052542950958013535,
0.0154422577470541,
0.007939045317471027,
0.019374601542949677,
-0.066852867603302,
-0.040180008858442307,
0.03595273569226265,
0.04002918675541878,
-0.030542857944965363,
-0.043412644416093826,
0.011891670525074005,
0.011196493171155453,
-0.03154730424284935,
-0.014599044807255268,
0.05496750771999359,
0.004287034273147583,
-0.032814618200063705,
-0.0025282837450504303,
-0.013291271403431892,
0.06961430609226227,
-0.027391407638788223,
0.05311880260705948,
0.011087445542216301,
0.013837704434990883,
-0.03308474272489548,
-0.007255898788571358,
0.005053930915892124,
-0.04050620272755623,
-0.032095395028591156,
-0.017172224819660187,
-0.01012304425239563,
0.026691989973187447,
-0.0006034269463270903,
-0.011662852019071579,
0.03764771670103073,
0.03604097664356232,
-0.017333155497908592,
-0.02550283446907997,
0.0006922847242094576,
-0.01910402998328209,
-0.010133788920938969,
-0.006149335764348507,
-0.01176593080163002,
-0.027645988389849663,
0.03955024853348732,
0.020005792379379272,
0.025593427941203117,
-0.02273406833410263,
-0.007868312299251556,
0.09799124300479889,
-0.013644765131175518,
0.011256898753345013,
-0.002234288491308689,
-0.03295457363128662,
0.033104319125413895,
0.016126109287142754,
0.013256192207336426,
0.018064390867948532,
0.0471160002052784,
-0.029162727296352386,
0.014306553639471531,
-0.05355450510978699,
0.024627886712551117,
0.09795863181352615,
0.03684322535991669,
0.05317278578877449,
0.02867847867310047,
0.028451813384890556,
-0.017888978123664856,
0.003671651938930154,
-0.03435080870985985,
-0.01582770235836506,
0.021259842440485954,
0.045028116554021835,
-0.003732100361958146,
-0.023656805977225304,
0.04835302755236626,
0.020591314882040024,
-0.002321705687791109,
0.04211825504899025,
0.013360950164496899,
0.03960469737648964,
-0.0047067198902368546,
-0.006190314888954163,
-0.013967243023216724,
-0.0012777256779372692,
-0.002823217073455453,
0.02617913857102394,
-0.010378474369645119,
-0.026887673884630203,
0.0386493057012558,
0.00517928646877408,
0.018165722489356995,
-0.008929976262152195,
-0.021174417808651924,
-0.024944543838500977,
0.01511768251657486,
-0.03267572447657585,
-0.027933809906244278,
-0.016433024778962135,
0.04411236569285393,
0.006922518368810415,
-0.015410460531711578,
0.012264419347047806,
-0.03749772906303406,
-0.07588081806898117,
0.010455148294568062,
-0.03911595791578293,
-0.07241491973400116,
0.037065137177705765,
0.02364109829068184,
-0.05563125014305115,
0.060049399733543396,
0.005465919151902199,
0.022251278162002563,
0.03698056563735008,
0.052414197474718094,
-0.008433136157691479,
0.05350622907280922,
0.010910875163972378,
-0.014925895258784294,
0.043434374034404755,
-0.02148212119936943,
0.10470573604106903,
0.0953737124800682,
-0.029801076278090477,
-0.09001877158880234,
0.005895791109651327,
-0.010206305421888828,
0.011795812286436558,
-0.029664190486073494,
0.00891026109457016,
0.012325006537139416,
0.0009085768251679838,
0.05467583239078522,
0.029184669256210327,
0.0009780836990103126,
0.01508531253784895,
0.042242102324962616,
0.012438983656466007,
-0.02169235236942768,
0.012991641648113728,
-0.014660759828984737,
0.009411368519067764,
-0.009832202456891537,
-0.02344813197851181,
0.057617537677288055,
-0.03598326817154884,
-0.02207602560520172,
-0.05601390078663826,
-0.011548097245395184,
0.009462457150220871,
-0.0055521223694086075,
-0.05295293405652046,
0.004772346466779709,
0.04446522146463394,
-0.02707996778190136,
-0.03981892392039299,
0.005617585964500904,
-0.020835690200328827,
-0.006699457764625549,
0.018977070227265358,
0.027207979932427406,
0.01752103678882122,
0.014367739669978619,
-0.011330164968967438,
0.027312178164720535,
-0.043217774480581284,
-0.04166393727064133,
-0.028770674020051956,
0.026643307879567146,
0.008029458113014698,
0.0058017815463244915,
0.006481154356151819,
0.006766432896256447,
-0.04300548881292343,
-0.03752511739730835,
0.014236677438020706,
-0.0016096803592517972,
-0.012752183713018894,
-0.03653635457158089,
-0.01906631886959076,
-0.0342029444873333,
0.0068036699667572975,
-0.0162742231041193,
0.007303347811102867,
0.046891696751117706,
-0.026620756834745407,
-0.009219096042215824,
-0.014122969470918179,
0.04474826902151108,
-0.009588557295501232,
-0.027208734303712845,
-0.03281111642718315,
-0.03579334542155266,
-0.011533518321812153,
-0.0037076210137456656,
0.001360071124508977,
-0.003938016016036272,
0.011015789583325386,
0.009345272555947304,
-0.009417482651770115,
0.000760754628572613,
-0.06748783588409424,
0.02416236139833927,
-0.006985639221966267,
-0.0029375385493040085,
-0.028030719608068466,
0.020474741235375404,
0.051722656935453415,
0.02642020769417286,
-0.0034994243178516626,
0.015201724134385586,
-0.02501889131963253,
0.01732628047466278,
0.011848698370158672,
-0.052355214953422546,
-0.025958187878131866,
-0.015787066891789436,
-0.03284864127635956,
0.013636324554681778,
0.0029312926344573498,
0.041822586208581924,
0.024274194613099098,
0.010364741086959839,
0.006959141697734594,
0.005174597259610891,
-0.0437699519097805,
-0.0003798532416112721,
0.002217184752225876,
-0.02957451343536377,
-0.006836257874965668,
-0.04799136146903038,
-0.001076610991731286,
-0.046746931970119476,
-0.00021076100529171526,
-0.044431429356336594,
-0.019808901473879814,
0.03249921649694443,
0.019441889598965645,
-0.053283385932445526,
0.023170800879597664,
0.023630663752555847,
-0.029908111318945885,
0.026636255905032158,
0.01758299581706524,
-0.01511319074779749,
0.003594348207116127,
-0.01115476991981268,
0.021761704236268997,
-0.0079458924010396,
-0.017119206488132477,
-0.015487894415855408,
0.01643950864672661,
0.00604544160887599,
0.027636263519525528,
0.024480825290083885,
0.008165432140231133,
-0.008879992179572582,
0.0189348217099905,
0.057473599910736084,
-0.032700907438993454,
-0.008414376527071,
0.04122777283191681,
-0.058543603867292404,
-0.030824819579720497,
0.033356498926877975,
-0.021446561440825462,
0.012066191993653774,
0.015697086229920387,
-0.005560373421758413,
0.012259160168468952,
0.03110656887292862,
0.018619535490870476,
-0.011241082102060318,
0.005417336709797382,
0.01724120043218136,
-0.0071751419454813,
0.034626852720975876,
0.011758803389966488,
-0.005132630933076143,
0.01619821786880493,
0.00021095317788422108,
0.04567737877368927,
-0.01816266030073166,
-0.0032706093043088913,
0.011228909716010094,
-0.008282609283924103,
-0.008823709562420845,
0.015678947791457176,
-0.006228170823305845,
0.03235810250043869,
0.0486249141395092,
-0.044562797993421555,
0.017460256814956665,
-0.027118586003780365,
0.007425531279295683,
-0.10538486391305923,
-0.029459526762366295,
0.008968396112322807,
-0.005432221572846174,
0.0036946905311197042,
-0.029601987451314926,
-0.00051456707296893,
0.0672077015042305,
-0.01199029665440321,
0.022780224680900574,
-0.0232740119099617,
-0.02129998803138733,
-0.017424218356609344,
-0.01647847704589367,
0.010523674078285694,
0.007184798363596201,
0.051687441766262054,
0.045929960906505585,
0.03229167312383652,
0.005802921950817108,
-0.00901744794100523,
-0.03446090966463089,
0.016122380271553993,
0.03235648199915886,
0.00152604712639004,
-0.0723615437746048,
0.035447534173727036,
-0.013759828172624111,
-0.03336586430668831,
0.015934523195028305,
-0.04400132969021797,
-0.004251605831086636,
0.025360042229294777,
0.016993289813399315,
-0.009973989799618721,
0.05784090980887413,
0.017300715669989586,
-0.030792972072958946,
-0.040153320878744125,
0.00307771610096097,
0.011664900928735733,
0.0073945713229477406,
-0.04459086433053017,
0.03969883546233177,
-0.0034879979211837053,
0.015807634219527245,
-0.042841602116823196,
0.054921120405197144,
0.0029765989165753126,
-0.003553285263478756,
-0.005746909882873297,
-0.0010625127470120788,
0.0056794979609549046,
-0.07051113992929459,
0.023913370445370674,
-0.0177091546356678,
0.027268875390291214,
0.03557509183883667,
0.03403406962752342,
-0.01974336802959442,
-0.00011919256940018386,
-0.014081714674830437,
-0.044244710355997086,
0.023725638166069984,
0.01640443317592144,
-0.05415096506476402,
-0.05970440432429314,
0.022640671581029892,
0.006046743132174015,
-0.022852541878819466,
-0.00676328968256712,
-0.021298175677657127,
-0.004124361556023359,
0.04935619235038757,
-0.0051639145240187645,
-0.008850791491568089,
0.017735913395881653,
0.0037289883475750685,
-0.025374414399266243,
-0.1256636381149292,
0.0428517684340477,
-0.009046671912074089,
-0.01909559965133667,
-0.0030450308695435524,
-0.017046377062797546,
-0.03216955438256264,
0.0062659564428031445,
0.039096467196941376,
0.012387667782604694,
-0.029543522745370865,
0.01515293214470148,
0.015265606343746185,
-0.022173788398504257,
-0.04988434165716171,
-0.015870805829763412,
0.015320828184485435,
-0.026076283305883408,
-0.00983350072056055,
-0.014397682622075081,
0.00401488458737731,
0.007622371427714825,
-0.0031134781893342733,
0.02367471531033516,
0.021959654986858368,
0.023249344900250435,
0.0019855136051774025,
0.046003423631191254,
0.02162874862551689,
0.011613914743065834,
0.06791915744543076,
0.015658654272556305,
-0.0002889350289478898,
0.04604753479361534,
-0.014256148599088192,
-0.04695672541856766,
0.017563439905643463,
-0.027599094435572624,
-0.024995911866426468,
-0.004842708818614483,
0.023412786424160004,
-0.013574899174273014,
-0.04759940132498741,
-0.014004027470946312,
0.031097615137696266,
-0.023404760286211967,
-0.034102194011211395,
0.015022086910903454,
0.01006776187568903,
0.04264577478170395,
0.01764407567679882,
0.03738667815923691,
0.009993217885494232,
-0.04028114676475525,
0.003872960340231657,
0.008346479386091232,
0.022329863160848618,
-0.010180609300732613,
0.04045391455292702,
0.026675695553421974,
0.021632120013237,
-0.009292129427194595,
-0.012531437911093235,
0.010108061134815216,
-0.01849493756890297,
-0.03940776735544205,
0.0002965360472444445,
-0.024231642484664917,
0.005255028605461121,
-0.023090261965990067,
-0.018656503409147263,
0.06581076979637146,
-0.013337722979485989,
0.012247482314705849,
-0.03403189778327942,
-0.03838701546192169,
-0.0337667278945446,
0.012998498976230621,
0.007392168510705233,
0.0383252315223217,
0.005826006643474102,
0.028888199478387833,
0.050519950687885284,
0.02110046148300171,
0.03888621926307678,
0.006289367564022541,
0.02936125546693802,
-0.040752511471509933,
-0.007458132691681385,
-0.02899894304573536,
-0.016565537080168724,
-0.022417131811380386,
-0.02450108900666237,
0.00883243978023529,
0.060757480561733246,
0.0229767058044672,
0.007600945886224508,
-0.0013983952812850475,
-0.00624286150559783,
0.03829158842563629,
-0.0709492489695549,
-0.030891574919223785,
-0.011312616989016533,
-0.008427399210631847,
-0.036541376262903214,
-0.04000123590230942
] |
<p>I have a system of particles with equal distance with each other and another at random positions which is moving with time. What I want to know is :</p>
<ol>
<li><p>The method by which I can reduce the number of particles from the first system, as I know the maximum motion of any particle is X (<strong>Meaning: Maximum displacement from starting to end of simulation is X)</strong>.</p></li>
<li><p>How to efficiently calculate the collision between them, I have heard about quadtree and octree but (as per I understood till now) they are for collision of particle from each other. In my problem,second system of particles doesn't collide with each other.</p></li>
</ol>
<p>Note: Sorry, if it is a very basic question, I am (very) new to this field.</p>
<p><strong>Update:</strong></p>
<p><img src="http://i.stack.imgur.com/ZTixa.png" alt="enter image description here"></p>
<h2><strong>The combined System</strong></h2>
<p><img src="http://i.stack.imgur.com/uEgwX.png" alt="enter image description here"></p>
<h2><strong>Movable parts (Same color means same radius and mass)</strong></h2>
<p><img src="http://i.stack.imgur.com/i3whf.png" alt="enter image description here"></p>
<h2><strong>Unmovable Grid (Colors means nothing and yes, it's a cube of spheres)</strong></h2>
| 10,795 |
[
0.01079187449067831,
-0.0382067933678627,
-0.005478984210640192,
-0.024244949221611023,
0.010287705808877945,
-0.0019398719305172563,
-0.004682112485170364,
-0.058862194418907166,
0.029849927872419357,
-0.0025065827649086714,
0.03773212060332298,
0.056136053055524826,
0.07028002291917801,
0.03180171549320221,
0.034258853644132614,
-0.01798201911151409,
-0.014115669764578342,
-0.03365591540932655,
0.019289135932922363,
-0.05395925045013428,
-0.01903526857495308,
-0.02683321386575699,
0.05030353367328644,
-0.018241243436932564,
0.0074060880579054356,
0.068369060754776,
0.03625398501753807,
-0.042756084352731705,
-0.03018445149064064,
0.04862874001264572,
-0.033390358090400696,
-0.02042989805340767,
-0.005861095618456602,
-0.0055839670822024345,
0.04386897385120392,
0.0014210863737389445,
-0.028437310829758644,
-0.0011249564122408628,
-0.005844629369676113,
-0.0163500364869833,
-0.03659772127866745,
-0.030867649242281914,
-0.054148782044649124,
0.07332029938697815,
0.00501085352152586,
0.04113731533288956,
0.01653541997075081,
0.011959986761212349,
0.053662244230508804,
-0.07025894522666931,
0.04109964147210121,
0.01768294721841812,
0.06868908554315567,
0.0057501462288200855,
0.009402401745319366,
-0.025057312101125717,
0.03939693048596382,
0.09094388037919998,
-0.039350155740976334,
-0.02832239866256714,
-0.010309906676411629,
-0.006516197230666876,
-0.00012804467405658215,
-0.022958623245358467,
0.0012480563018471003,
0.027451854199171066,
-0.025633065029978752,
-0.007148989010602236,
0.004712461028248072,
0.006065342575311661,
0.0013319867430254817,
-0.02270282804965973,
0.0535685159265995,
-0.02510451339185238,
0.02394094131886959,
0.015754513442516327,
0.007010823115706444,
0.01592858135700226,
0.005925080273300409,
0.013554452918469906,
-0.027641544118523598,
0.036702509969472885,
0.032554782927036285,
0.020756158977746964,
-0.012768418528139591,
-0.03184990957379341,
0.04151877760887146,
-0.009264807216823101,
-0.008279172703623772,
0.02513691410422325,
-0.011400140821933746,
0.008454916067421436,
0.06627222150564194,
0.015174333937466145,
-0.024022024124860764,
0.007493542041629553,
0.026819201186299324,
0.03311769664287567,
-0.01507126446813345,
-0.029937462881207466,
-0.022634752094745636,
-0.04575469344854355,
-0.0013497101608663797,
0.05591148883104324,
0.001025930978357792,
0.023440562188625336,
-0.011586437933146954,
0.0009553865529596806,
-0.01505746878683567,
0.02761814184486866,
-0.0112682543694973,
-0.006403136067092419,
0.008125538006424904,
-0.0038127191364765167,
0.01190485805273056,
-0.025261562317609787,
-0.02473457157611847,
-0.01269743125885725,
0.02092142589390278,
0.04700467735528946,
0.039573416113853455,
-0.02790062502026558,
-0.0018813068745657802,
-0.052375152707099915,
-0.10351672023534775,
-0.011924012564122677,
0.02301028184592724,
0.014578103087842464,
-0.060019079595804214,
0.06352344155311584,
0.035451654344797134,
-0.0032950080931186676,
0.014337464235723019,
-0.01639145240187645,
0.003485621651634574,
-0.0169884841889143,
-0.06293539702892303,
-0.05683521181344986,
0.053490977734327316,
-0.018530214205384254,
0.031720276921987534,
-0.04011085629463196,
-0.03854592889547348,
0.02572094462811947,
0.08511946350336075,
0.01678141951560974,
-0.022128017619252205,
0.01059381291270256,
0.07051615417003632,
-0.009118454530835152,
-0.013926884159445763,
0.012939734384417534,
-0.014950631186366081,
0.020048581063747406,
0.03213541582226753,
-0.052518080919981,
0.04280439764261246,
0.030015505850315094,
-0.010353093966841698,
-0.0014128773473203182,
0.026174873113632202,
-0.026534270495176315,
0.005822877399623394,
0.03082691691815853,
0.01957164704799652,
-0.024489138275384903,
0.04603562876582146,
-0.00572600681334734,
-0.004707696381956339,
0.032808367162942886,
-0.017413640394806862,
0.021499576047062874,
0.016088662669062614,
0.03829001262784004,
0.0418098047375679,
0.010222313925623894,
-0.012844223529100418,
-0.00636501656845212,
-0.034184880554676056,
0.011321758851408958,
-0.020726235583424568,
-0.03318443521857262,
-0.018776830285787582,
0.0040339636616408825,
0.013725116848945618,
0.030415544286370277,
0.013079372234642506,
-0.0008112129289656878,
0.003952357918024063,
-0.009972105734050274,
-0.06462905555963516,
-0.06748991459608078,
0.022470468655228615,
0.010957441292703152,
0.0009927572682499886,
0.02912210114300251,
0.009868428111076355,
-0.004546490032225847,
0.011167321354150772,
-0.004171326290816069,
-0.05534644424915314,
0.007972140796482563,
0.009091942571103573,
-0.011287353001534939,
-0.019339917227625847,
0.06172342970967293,
0.04861023649573326,
-0.01857033558189869,
-0.0022715663071721792,
-0.009360680356621742,
-0.021624263375997543,
-0.04076428338885307,
-0.04654304310679436,
-0.007249395828694105,
0.0038162285927683115,
-0.025810422375798225,
0.03567644581198692,
0.0031587237026542425,
0.0026730422396212816,
0.013967392966151237,
-0.007972495630383492,
0.08939898014068604,
0.07145066559314728,
-0.00239867833442986,
0.0002649306261446327,
0.03129245713353157,
-0.019956856966018677,
-0.0076898373663425446,
0.03067607246339321,
-0.043940044939517975,
-0.04073333740234375,
-0.009985637851059437,
0.02438046783208847,
0.03337375819683075,
-0.053491391241550446,
0.006138307973742485,
0.012600943446159363,
-0.0036129471845924854,
0.04913482069969177,
0.012729445472359657,
-0.0006654207245446742,
-0.003990516532212496,
0.039488937705755234,
0.04037940874695778,
0.01891995593905449,
0.027800697833299637,
0.005388404242694378,
0.01146331150084734,
-0.0006677790661342442,
-0.008872686885297298,
-0.04180120304226875,
-0.015105600468814373,
0.0555536262691021,
0.027964681386947632,
-0.020312871783971786,
-0.05053131654858589,
-0.01562657207250595,
0.005150144454091787,
0.006459887605160475,
0.03555932641029358,
0.007267969194799662,
-0.01279689371585846,
-0.04226767644286156,
0.009224850684404373,
0.0027633137069642544,
0.03649790957570076,
-0.022849243134260178,
0.015123858116567135,
0.03107522428035736,
-0.06105278804898262,
0.02448219060897827,
0.030178150162100792,
-0.03006109967827797,
-0.052944887429475784,
0.010080898180603981,
0.028303498402237892,
0.005345400422811508,
0.02593928948044777,
-0.0563877671957016,
-0.0034431307576596737,
-0.011324629187583923,
-0.03713228181004524,
-0.01204685214906931,
0.03213624283671379,
-0.0686686709523201,
0.013324872590601444,
-0.034709058701992035,
-0.09267047047615051,
0.03732514753937721,
-0.010446522384881973,
-0.011936617083847523,
0.07268214225769043,
0.00010767581989057362,
-0.03865242749452591,
-0.014199801720678806,
-0.027187421917915344,
0.008868018165230751,
-0.019024671986699104,
0.013736655004322529,
0.006693023722618818,
0.030289849266409874,
-0.058238763362169266,
-0.008937074802815914,
-0.06808629631996155,
-0.021687207743525505,
-0.0615624338388443,
-0.02171103097498417,
0.036501575261354446,
-0.038221653550863266,
-0.03792531415820122,
0.025844598188996315,
-0.008365384303033352,
0.011388885788619518,
-0.04713917896151543,
-0.03935958817601204,
-0.0229193028062582,
-0.004624731373041868,
0.08519601821899414,
0.010782933793962002,
-0.02390870451927185,
0.05508985370397568,
-0.00415967870503664,
-0.040991317480802536,
-0.027642475441098213,
0.010985616594552994,
-0.009701229631900787,
0.00651793135330081,
0.015294991433620453,
0.027182936668395996,
0.008929352276027203,
0.003037063404917717,
0.00417302455753088,
-0.0038050576113164425,
0.053361665457487106,
0.006185474805533886,
0.031341418623924255,
-0.03955186903476715,
0.005408626049757004,
-0.044556744396686554,
0.037692535668611526,
-0.0014100491534918547,
-0.031063204631209373,
0.051247335970401764,
0.004946400411427021,
0.023123065009713173,
0.02231910452246666,
-0.06328579783439636,
-0.006417779251933098,
0.021671967580914497,
0.00031608931021764874,
0.035157036036252975,
0.0023577697575092316,
-0.005874407943338156,
-0.02938571572303772,
0.00998228695243597,
0.04478326439857483,
0.0434444323182106,
0.011492722667753696,
-0.044924307614564896,
0.015411360189318657,
0.03495749458670616,
-0.023373836651444435,
0.006771046202629805,
-0.04229963198304176,
0.005389729514718056,
0.025032004341483116,
-0.0027961181476712227,
-0.017181305214762688,
0.022038239985704422,
0.008731554262340069,
0.048391178250312805,
0.005998531356453896,
-0.006757230032235384,
-0.007654188666492701,
-0.0385282076895237,
-0.004819557070732117,
-0.031861625611782074,
0.08434507995843887,
-0.007619868032634258,
0.03590535745024681,
0.007445233874022961,
0.006846180651336908,
0.006166783627122641,
-0.010670289397239685,
-0.07662073522806168,
0.031538765877485275,
0.014989407733082771,
-0.004952902905642986,
-0.006085070315748453,
-0.02539829909801483,
-0.036315515637397766,
-0.010306808166205883,
0.014290569350123405,
0.02582402713596821,
0.03755412623286247,
-0.06245560571551323,
-0.009227263741195202,
-0.041256826370954514,
0.002834976650774479,
0.0019647458102554083,
0.028137408196926117,
0.004642685875296593,
-0.04232429340481758,
0.036080893129110336,
0.0327468104660511,
-0.035949479788541794,
0.00478784367442131,
-0.039205022156238556,
0.012348054908216,
0.05089128017425537,
0.03495795652270317,
-0.0012869654456153512,
0.06347192078828812,
-0.006230075843632221,
-0.01489501167088747,
-0.008370649069547653,
0.0475962795317173,
-0.02465292625129223,
0.00937173143029213,
-0.022596243768930435,
-0.01997467689216137,
0.006724092178046703,
0.0019600207451730967,
0.03861748054623604,
-0.03506678342819214,
0.02372898906469345,
0.026904655620455742,
0.023404991254210472,
-0.012118732556700706,
0.0389120988547802,
0.07179342955350876,
0.014946741051971912,
-0.00634251581504941,
-0.021008826792240143,
-0.007838176563382149,
0.006533638574182987,
-0.01360827311873436,
0.06368633359670639,
0.023004353046417236,
-0.002309961710125208,
0.005380128975957632,
0.029115254059433937,
0.0429939404129982,
-0.06254987418651581,
0.03588954731822014,
-0.044304341077804565,
0.020979050546884537,
-0.06343425065279007,
0.024531109258532524,
-0.002678393153473735,
0.010184086859226227,
0.010628361254930496,
0.004934967495501041,
0.004525469616055489,
-0.0659143254160881,
-0.013494748622179031,
0.0500728115439415,
0.015104392543435097,
-0.0061511206440627575,
0.004562323912978172,
-0.029294751584529877,
-0.01052539050579071,
0.04808318614959717,
0.00014149484923109412,
-0.01004751119762659,
-0.010538381524384022,
-0.007433554157614708,
-0.02212127298116684,
-0.03296925500035286,
0.004216759465634823,
-0.0006110131507739425,
0.001966200303286314,
0.032262638211250305,
0.006013659294694662,
-0.014179928228259087,
0.007432702463120222,
0.030822571367025375,
0.012420661747455597,
0.04466188699007034,
-0.017895523458719254,
-0.025048714131116867,
-0.019956737756729126,
0.004898893181234598,
-0.045006901025772095,
-0.06590662151575089,
0.02820289134979248,
-0.010048280470073223,
-0.046036526560783386,
0.06384337693452835,
-0.025517966598272324,
0.015080058947205544,
0.00985574908554554,
0.016227643936872482,
0.010869977064430714,
-0.017971346154808998,
-0.018234895542263985,
0.04144514724612236,
0.04712352901697159,
-0.0067974599078297615,
0.014651279896497726,
0.026904264464974403,
-0.016545290127396584,
0.005267444998025894,
-0.028643937781453133,
0.037273257970809937,
-0.022909218445420265,
-0.010260417126119137,
-0.020861266180872917,
0.012046517804265022,
-0.017550962045788765,
-0.011710559949278831,
-0.010531800799071789,
0.013470439240336418,
-0.02707207202911377,
-0.015505349263548851,
0.008803273551166058,
0.054360661655664444,
0.00023596726532559842,
0.0510878823697567,
-0.04970802366733551,
0.021018976345658302,
0.004066252149641514,
-0.035125020891427994,
0.01545227412134409,
-0.008047067560255527,
0.0035805150400847197,
0.007248420733958483,
-0.053711362183094025,
0.00038020522333681583,
-0.04512409865856171,
-0.0058445618487894535,
0.0044092112220823765,
-0.06619314104318619,
0.042877450585365295,
-0.003399086417630315,
0.031862545758485794,
0.026754779741168022,
-0.06414220482110977,
-0.0593053437769413,
0.03401318937540054,
-0.024337871000170708,
-0.007855920121073723,
-0.056910596787929535,
0.041240155696868896,
-0.013648726977407932,
0.03296489268541336,
-0.04974993318319321,
-0.0561615452170372,
0.0027364585548639297,
0.018338438123464584,
0.013937602750957012,
-0.08612065017223358,
-0.0272207111120224,
-0.040729548782110214,
-0.03290525823831558,
-0.012453209608793259,
0.02752816304564476,
0.041985075920820236,
-0.008360341191291809,
0.03545629233121872,
-0.005224120337516069,
0.02632434107363224,
0.012332150712609291,
0.03657323867082596,
0.0017634727992117405,
0.013552862219512463,
-0.021725328639149666,
-0.012906591407954693,
0.05586133524775505,
-0.022398512810468674,
-0.03028208017349243,
0.014325767755508423,
0.028678622096776962,
0.034838661551475525,
-0.04247814789414406,
0.01412301417440176,
0.02961118333041668,
0.040566734969615936,
-0.002578330459073186,
-0.00833501759916544,
-0.020543405786156654,
-0.02858990617096424,
0.01279810257256031,
-0.003420851891860366,
0.012047293595969677,
-0.005618755705654621,
-0.056312717497348785,
0.014905497431755066,
-0.01767268404364586,
0.005106335040181875,
0.017244240269064903,
0.03509920462965965,
-0.016406023874878883,
-0.046392008662223816,
0.007145392708480358,
-0.011489597149193287,
0.06694130599498749,
-0.046124767512083054,
-0.016344580799341202,
0.045535970479249954,
-0.004674041643738747,
-0.011562064290046692,
-0.010232084430754185,
-0.05012185871601105,
0.02046450413763523,
0.05002535507082939,
-0.06895791739225388,
0.0762677863240242,
0.014391511678695679,
-0.015565897338092327,
-0.009059276431798935,
-0.007463887799531221,
-0.00017560308333486319,
0.02507452294230461,
0.01746070384979248,
0.0604877695441246,
-0.025106972083449364,
0.001096922205761075,
0.01541978120803833,
0.011558090336620808,
0.0038670499343425035,
0.024259019643068314,
-0.014588150195777416,
0.025613436475396156,
0.013756181113421917,
-0.07382535934448242,
0.010567713528871536,
0.013717416673898697,
-0.06214657053351402,
0.02871882915496826,
-0.02441411092877388,
-0.012101479806005955,
0.025999093428254128,
0.03640616312623024,
0.01055553276091814,
0.0016762558370828629,
-0.0024081498850136995,
-0.033613525331020355,
0.028934253379702568,
0.008186237886548042,
-0.008430288173258305,
0.016409730538725853,
0.04496431723237038,
0.05718565359711647,
0.03649013116955757,
0.020389456301927567,
-0.06345075368881226,
-0.07364504039287567,
-0.011830129660665989,
-0.06327314674854279,
-0.0619700588285923,
0.02958124503493309,
0.05151098221540451,
0.0011419522343203425,
0.013909787870943546,
-0.009837621822953224,
-0.004569978918880224,
-0.002130750101059675,
0.04407301917672157,
-0.024294862523674965,
0.06940315663814545,
0.018400412052869797,
0.049839217215776443,
-0.002894526580348611,
0.029389262199401855,
0.12738631665706635,
0.051332131028175354,
0.002916455501690507,
-0.03259386867284775,
0.010642253793776035,
-0.0008581317379139364,
-0.026245247572660446,
-0.060614269226789474,
0.007244238629937172,
0.031873807311058044,
-0.005166037939488888,
0.004425651393830776,
0.03127242252230644,
0.024905802682042122,
-0.02277822047472,
0.009395409375429153,
-0.036083877086639404,
-0.031111814081668854,
-0.007445385679602623,
0.0014168061316013336,
-0.0019333019154146314,
0.022750727832317352,
-0.03542809933423996,
0.03598647564649582,
-0.03056338243186474,
-0.015053781680762768,
-0.02176945097744465,
-0.01551657635718584,
0.0328923836350441,
0.029750151559710503,
-0.015592877753078938,
0.05196642875671387,
0.02312140353024006,
-0.02499319054186344,
-0.0026142336428165436,
0.029325546696782112,
0.01341085322201252,
-0.04283658042550087,
0.007407249417155981,
0.010832182131707668,
-0.02734522894024849,
-0.0005308941472321749,
0.0038706939667463303,
0.024248046800494194,
-0.01282882783561945,
0.012810853309929371,
-0.07353325933218002,
0.06238877400755882,
-0.0027846512384712696,
0.0018722922541201115,
0.04344741627573967,
0.012610957957804203,
0.0013407167280092835,
-0.05635790526866913,
-0.016810158267617226,
-0.013148319907486439,
0.04680435732007027,
-0.024688255041837692,
0.006600235588848591,
-0.03142491355538368,
0.03668254241347313,
-0.023938775062561035,
0.008613502606749535,
0.010334455408155918,
0.0022394966799765825,
-0.015657000243663788,
-0.021187996491789818,
0.07214447855949402,
-0.023406654596328735,
-0.01299805473536253,
-0.019742028787732124,
0.020226331427693367,
0.024720801040530205,
-0.015129533596336842,
0.007531114853918552,
0.03839782997965813,
0.014493049122393131,
0.014396649785339832,
-0.023915953934192657,
0.00117678742390126,
-0.04616749659180641,
0.02452819049358368,
-0.02232632040977478,
-0.031586311757564545,
-0.04700932651758194,
-0.0468326210975647,
0.025115203112363815,
0.03936108201742172,
-0.014995777979493141,
-0.049511589109897614,
-0.015599912032485008,
0.01759001426398754,
-0.006124493665993214,
0.006919600535184145,
-0.04762640222907066,
-0.010440411977469921,
-0.015835007652640343,
0.03551425039768219,
-0.009774726815521717,
0.05708501860499382,
-0.0038162709679454565,
-0.008010122925043106,
-0.0003225388645660132,
0.04371821880340576,
-0.02429969795048237,
0.011239088140428066,
0.014567375183105469,
-0.038590315729379654,
-0.017917543649673462,
0.021770525723695755,
-0.013749868609011173,
-0.0016401124885305762,
0.01058897189795971,
-0.014761095866560936,
-0.04153062030673027,
0.009384812787175179,
0.023646339774131775,
-0.03227948769927025,
-0.0167223047465086,
-0.029953712597489357,
0.03519735485315323,
0.016761425882577896,
0.0018198640318587422,
-0.028220264241099358,
-0.024313537403941154,
0.0037128443364053965,
-0.038747724145650864,
-0.05523381382226944,
-0.0013136881170794368,
0.030365603044629097,
-0.0031912149861454964,
0.000263840687694028,
0.024445125833153725,
0.03486433997750282,
-0.005594119429588318,
0.006546643562614918,
-0.0014197338605299592,
0.05712110549211502,
-0.015126777812838554,
-0.0111177247017622,
0.031802885234355927,
-0.059373173862695694,
-0.0452842190861702,
0.0051046255975961685,
-0.04735656455159187,
0.0449984148144722,
0.04008105397224426,
-0.012061964720487595,
-0.03270435333251953,
0.09973380714654922,
-0.04291733726859093,
-0.05317263305187225,
-0.026516860350966454,
-0.030921416357159615,
-0.0327717624604702,
-0.031604550778865814,
0.004199428483843803,
-0.019453207030892372,
-0.05208656191825867,
0.04054544121026993,
0.041745398193597794,
0.017357362434267998,
-0.0002401219680905342,
-0.016219856217503548,
-0.01029493659734726,
0.012918424792587757,
0.03660089150071144,
0.009527238085865974,
0.049497779458761215,
0.06733664125204086,
-0.02781675197184086,
-0.015657788142561913,
0.0006439326098188758,
-0.021008867770433426,
-0.06755679845809937,
-0.003758006729185581,
-0.0066549996845424175,
-0.01596405729651451,
0.0594838447868824,
-0.0434064082801342,
0.047489557415246964,
0.058733392506837845,
-0.03733909875154495,
0.00954141840338707,
-0.031924985349178314,
0.010583548806607723,
-0.03873353824019432,
-0.04165850207209587,
-0.013538702391088009,
0.01621866598725319,
0.016093648970127106,
0.004396497271955013,
0.03910456970334053,
0.039873965084552765,
-0.03199053928256035,
-0.033879928290843964,
0.013552257791161537,
-0.011055143550038338,
-0.0300371702760458,
-0.03170032054185867,
0.02707425318658352,
-0.04518875479698181,
-0.005332150496542454,
-0.002364000305533409,
-0.02784169651567936,
-0.02201136201620102,
-0.005879430565983057,
0.016495684161782265,
0.007736922707408667,
0.037877585738897324,
0.007056417874991894,
-0.011478875763714314,
0.00013518185005523264,
-0.016793640330433846,
0.03296815603971481,
-0.029417453333735466,
-0.011158116161823273,
0.03235465660691261,
0.05220864340662956,
0.041736532002687454,
-0.006372929085046053,
0.028980299830436707,
0.014101158827543259,
-0.0045223236083984375,
-0.020168090239167213,
0.014895815402269363,
0.030622299760580063,
-0.014436742290854454,
-0.015998823568224907,
0.0006564560462720692,
0.02840401418507099,
0.023934613913297653,
-0.021768411621451378,
-0.019051015377044678,
-0.005527828354388475,
-0.03423693776130676,
-0.003553439863026142,
-0.031701136380434036,
-0.021756082773208618,
-0.023087158799171448,
-0.0003465375630185008,
-0.008197154849767685,
0.017552360892295837,
0.00961537566035986,
-0.025720007717609406,
-0.011519405990839005,
-0.014069722034037113,
0.020154431462287903,
-0.025938982143998146,
0.030711419880390167,
0.022859876975417137,
0.005142996087670326,
-0.01210949569940567,
-0.07032252103090286,
0.0286019966006279,
-0.001984878908842802,
-0.01627967320382595,
-0.03853714093565941,
-0.03124174475669861,
0.03753450885415077,
0.012683876790106297,
0.027202051132917404,
-0.011004296131432056,
0.042784396559000015,
-0.01270066574215889,
0.035603005439043045,
0.046901602298021317,
-0.006747877690941095,
-0.014313442632555962,
-0.028895510360598564,
-0.006983347237110138,
0.016847796738147736,
-0.01280828844755888,
0.03386080265045166,
-0.01656348817050457,
0.017752980813384056,
-0.017376534640789032,
-0.019225304946303368,
0.027429664507508278,
-0.022377248853445053,
-0.004563734866678715,
-0.02102581039071083,
0.04155716300010681,
0.06455785036087036,
-0.03683704137802124,
0.011693576350808144,
0.017496900632977486,
-0.001982039073482156,
0.004742397926747799,
0.039874691516160965,
-0.05859129875898361,
-0.028016215190291405,
-0.0038422970101237297,
-0.012140880338847637,
-0.011801237240433693,
-0.06859228760004044,
0.007591931149363518,
0.004227806814014912,
-0.04326332360506058,
-0.010373130440711975,
0.032735105603933334,
0.004830701742321253,
0.05037737265229225,
0.015316180884838104,
0.010603148490190506,
0.01085587777197361,
-0.015820803120732307,
0.038006000220775604,
0.0395573154091835,
-0.015952562913298607,
0.012861580587923527,
0.004708318971097469,
0.024416998028755188,
0.02741583250463009,
0.017064111307263374,
-0.010088067501783371,
0.016145169734954834,
0.03452848270535469,
-0.012121829204261303,
0.006044025532901287,
-0.015109310857951641,
0.04293558746576309,
0.006069621536880732,
0.030714573338627815,
0.07687249034643173,
-0.035498086363077164,
0.01615755632519722,
-0.028121663257479668,
0.020445510745048523,
-0.035254403948783875,
0.020719533786177635,
-0.0010152463801205158,
0.04121626541018486,
-0.022510556504130363,
-0.001038558199070394,
-0.01901041343808174,
0.01284161675721407,
0.000544403912499547,
-0.018605822697281837,
0.05991644412279129,
0.017773067578673363,
-0.005548982881009579,
0.03688272833824158,
-0.036248430609703064,
-0.013983744196593761,
-0.019956229254603386,
0.031770482659339905,
0.041808318346738815,
0.00968533381819725,
0.03194189816713333,
-0.013134564273059368,
-0.032051730901002884,
0.0018110864330083132,
-0.05234634503722191,
-0.01722935400903225,
-0.030589889734983444,
-0.01616857200860977,
-0.03685326501727104,
0.048832833766937256
] |
<p>I'm just curious what causes radioactivity. I've been told that in the case of alpha decay, since the nucleus is quantum mechanical, there is a probability that the configuration of protons and neutrons is in such a way as to have an alpha particle outside the nucleus, and then the electric repulsion pushes it away. Is this true? Does quantum mechanics give a probability of this sort of thing happening which would be connected to the half life. Also the second part of my question is,why we don't have many other kinds of decay, why alpha particles or beta only (and fission etc artificially)? Thanks a lot in advance, if you can point to articles or books I can read on the subject it would also be a plus.</p>
<p>edit: for the configuration , I mean some kind of quantum entanglement or uncertainty principle.</p>
| 10,796 |
[
-0.006224778480827808,
-0.03832053765654564,
0.028789719566702843,
-0.039562009274959564,
0.004037655424326658,
0.008101885206997395,
-0.025463221594691277,
-0.03102630004286766,
0.007606936618685722,
-0.06021934002637863,
0.00002920794941019267,
0.03294961154460907,
0.042516596615314484,
-0.0010502514196559787,
0.02061445266008377,
0.0033623259514570236,
0.012676605023443699,
-0.051868122071027756,
-0.008133878000080585,
-0.013305582106113434,
0.030969163402915,
0.00115313904825598,
-0.018355000764131546,
0.007314637769013643,
-0.011923566460609436,
0.02023107185959816,
0.009243854321539402,
0.04107172042131424,
0.025477709248661995,
0.05643472447991371,
0.027452649548649788,
-0.04067889228463173,
0.02922341600060463,
0.022527607157826424,
0.013998212292790413,
-0.014415954239666462,
0.004001034889370203,
-0.0388234406709671,
-0.04238281026482582,
0.04293646290898323,
-0.030493559315800667,
-0.04412427544593811,
-0.014032014645636082,
0.024977315217256546,
-0.011357417330145836,
0.0076410165056586266,
0.02902664802968502,
-0.011266986839473248,
0.06437895447015762,
-0.05296580493450165,
0.043543435633182526,
-0.015809016302227974,
0.040568359196186066,
0.035779405385255814,
0.026560014113783836,
0.012786677107214928,
0.08157403767108917,
0.07175682485103607,
-0.033777832984924316,
-0.05937734246253967,
-0.04841627925634384,
-0.03309216722846031,
-0.006172711029648781,
-0.011608417145907879,
-0.014890910126268864,
0.03407799080014229,
-0.01957749016582966,
-0.0427435040473938,
0.01774967648088932,
0.018106264993548393,
0.051226262003183365,
0.015864666551351547,
0.021266598254442215,
-0.01048580463975668,
0.009608677588403225,
0.001442172797396779,
0.03147502988576889,
0.01333555206656456,
0.03785453736782074,
0.038245465606451035,
-0.010412084870040417,
-0.007321557495743036,
0.019643407315015793,
0.0012210906716063619,
-0.010154654271900654,
0.0015237430343404412,
0.07627460360527039,
-0.0354461707174778,
-0.005438040941953659,
0.01847114786505699,
-0.03198578953742981,
0.012452642433345318,
0.048708509653806686,
0.03994586691260338,
-0.03959649056196213,
0.023666292428970337,
0.0272482018917799,
0.09293573349714279,
0.02717738226056099,
0.013012757524847984,
0.04485011100769043,
-0.029312055557966232,
0.01691659912467003,
0.08162414282560349,
-0.028553767129778862,
-0.00966673530638218,
-0.028928782790899277,
0.006688656285405159,
-0.0012259137583896518,
-0.026427658274769783,
-0.0102026192471385,
0.027916964143514633,
0.01429764088243246,
-0.003290112130343914,
0.027636906132102013,
-0.02378983050584793,
-0.00622584531083703,
-0.03018283098936081,
0.055359866470098495,
0.07557695358991623,
0.023581363260746002,
-0.03556934371590614,
0.029866477474570274,
-0.01571604050695896,
-0.06299496442079544,
-0.014538045041263103,
0.031059961766004562,
0.0043442039750516415,
-0.03949333354830742,
0.044719450175762177,
-0.008621565997600555,
-0.041823118925094604,
0.0002599596045911312,
-0.007176593877375126,
0.06540745496749878,
-0.02113855816423893,
-0.11044525355100632,
-0.04322371631860733,
0.0377938449382782,
-0.0008371297153644264,
-0.029978714883327484,
-0.08784345537424088,
0.03147665411233902,
0.034652940928936005,
0.06526605039834976,
0.00131415412761271,
-0.0374189056456089,
0.017900394275784492,
0.028004111722111702,
0.016545793041586876,
-0.00042400165693834424,
-0.011162437498569489,
0.010868136771023273,
-0.007967724464833736,
0.0062405201606452465,
-0.09127733111381531,
0.003837779862806201,
0.015351202338933945,
-0.018965821713209152,
0.0017779116751626134,
0.02958017960190773,
-0.027705064043402672,
0.004297757055610418,
0.024551715701818466,
0.012125663459300995,
-0.044212739914655685,
0.08457807451486588,
0.056374795734882355,
-0.023804349824786186,
0.05602424591779709,
0.008963802829384804,
0.052614230662584305,
-0.0011937334202229977,
0.04001571983098984,
0.010752188041806221,
-0.05073933303356171,
-0.04244834929704666,
-0.007781680207699537,
-0.0019097138429060578,
0.0030791694298386574,
-0.042088717222213745,
0.02368425950407982,
-0.005093648564070463,
0.03154078125953674,
-0.001714778714813292,
0.020874209702014923,
-0.001259418553672731,
-0.018980400636792183,
0.015185251832008362,
0.0018413529032841325,
-0.03684328496456146,
-0.050074879080057144,
0.017581531777977943,
-0.0008161762962117791,
-0.021715927869081497,
-0.0034999579656869173,
0.02401076816022396,
-0.017218545079231262,
-0.024587402120232582,
-0.023869527503848076,
-0.024098196998238564,
0.03186454996466637,
0.004165003076195717,
-0.011444002389907837,
0.03402578830718994,
0.05446001887321472,
0.0066531929187476635,
-0.017771940678358078,
0.045688845217227936,
-0.02049786038696766,
-0.03128904476761818,
-0.02780759148299694,
-0.039190709590911865,
-0.0027887560427188873,
-0.014137344434857368,
-0.017029600217938423,
-0.006438092328608036,
-0.024761410430073738,
0.002993432804942131,
0.043846506625413895,
-0.007910051383078098,
0.07392797619104385,
-0.0002607341739349067,
0.03503727167844772,
-0.011821456253528595,
0.059348199516534805,
0.004715769551694393,
-0.001882955082692206,
-0.019093887880444527,
-0.05363733693957329,
-0.05188728868961334,
-0.015561011619865894,
0.0027704674284905195,
-0.017142927274107933,
-0.028748679906129837,
0.04882857948541641,
-0.022504914551973343,
0.06278432905673981,
0.008350304327905178,
0.035464126616716385,
-0.029437938705086708,
-0.004785496275871992,
-0.02738620527088642,
-0.003309227991849184,
0.00380942365154624,
0.023291930556297302,
-0.0032955154310911894,
0.03182287886738777,
0.022440092638134956,
-0.019164184108376503,
-0.02117433398962021,
0.025472497567534447,
-0.039953239262104034,
0.005878014490008354,
-0.021679705008864403,
-0.04699999466538429,
0.03887102007865906,
-0.007172787562012672,
0.026980159804224968,
-0.022338546812534332,
-0.00856804009526968,
0.001396647305227816,
-0.016409726813435555,
-0.025815226137638092,
0.011712940409779549,
0.036429066210985184,
-0.018175790086388588,
-0.016965162009000778,
0.0019877932500094175,
-0.009155470877885818,
0.02261386066675186,
-0.012907998636364937,
-0.004620394669473171,
0.006706210318952799,
-0.009553952142596245,
0.05528528615832329,
0.013348851352930069,
0.01353692077100277,
-0.018210845068097115,
-0.04359573498368263,
-0.014553495682775974,
-0.04300038516521454,
0.007631506770849228,
0.025833560153841972,
-0.037999361753463745,
0.0411795936524868,
-0.06422465294599533,
-0.0019985842518508434,
0.05066835507750511,
-0.008831963874399662,
0.0382908396422863,
0.02320794202387333,
-0.013674447312951088,
-0.05995635688304901,
-0.010971239767968655,
-0.03538595512509346,
-0.024445001035928726,
0.006865663919597864,
-0.01569547690451145,
0.056774064898490906,
-0.00899417046457529,
-0.031062722206115723,
0.004513112362474203,
-0.059038594365119934,
-0.04334094747900963,
-0.02372964471578598,
0.001649322104640305,
0.03288579732179642,
-0.023510117083787918,
0.015684783458709717,
0.027527667582035065,
-0.07544682919979095,
0.005794040858745575,
-0.022555474191904068,
-0.05185486003756523,
0.028118398040533066,
-0.0026959471870213747,
0.004928947426378727,
0.008336707949638367,
-0.025131376460194588,
0.0714162066578865,
0.04107964038848877,
-0.04490543529391289,
0.010232364758849144,
-0.014836912974715233,
-0.011786079965531826,
-0.026891585439443588,
0.009921394288539886,
0.008088824339210987,
0.021924402564764023,
0.03617144376039505,
-0.0025095429737120867,
0.03781126067042351,
-0.023449862375855446,
-0.0009392836363986135,
-0.004605107940733433,
0.026659786701202393,
0.038137372583150864,
-0.014262900687754154,
0.019826147705316544,
-0.005508843343704939,
-0.038771647959947586,
0.015465947799384594,
0.001095685875043273,
0.05346573516726494,
-0.008675284683704376,
-0.04635387286543846,
0.022541366517543793,
0.009945988655090332,
0.02807300165295601,
-0.04584307596087456,
0.047689568251371384,
-0.003768311580643058,
0.0026827321853488684,
0.02276885323226452,
0.0015519497683271766,
0.05412457883358002,
-0.02316433936357498,
0.040676429867744446,
0.02468487061560154,
0.03761779144406319,
-0.029327452182769775,
-0.047557540237903595,
-0.035692572593688965,
-0.00402502715587616,
0.003301626769825816,
-0.008889904245734215,
-0.03263058513402939,
0.04674674943089485,
0.011617183685302734,
0.033785317093133926,
-0.028916016221046448,
-0.04544325917959213,
-0.029166558757424355,
-0.06106102094054222,
-0.014720873907208443,
-0.0052552130073308945,
0.04581629857420921,
-0.014717181213200092,
0.028528206050395966,
0.04142693057656288,
-0.007540449500083923,
-0.012188408523797989,
-0.026660844683647156,
-0.06782396137714386,
0.05281193554401398,
-0.05246002972126007,
-0.025796644389629364,
-0.007923043332993984,
-0.015295310877263546,
-0.005911159794777632,
-0.003288369858637452,
-0.07589616626501083,
-0.010888881050050259,
-0.004475732333958149,
-0.07481233775615692,
0.0006717853830195963,
-0.048518285155296326,
-0.04026471823453903,
-0.046622928231954575,
0.0672982707619667,
0.006414742209017277,
-0.017227424308657646,
-0.00044753256952390075,
0.007553524803370237,
-0.04711345210671425,
-0.006067371927201748,
-0.028426874428987503,
0.014586579985916615,
-0.0038519680965691805,
0.00537059735506773,
0.06581193953752518,
0.003835405921563506,
-0.018340840935707092,
-0.02432885579764843,
0.04449159651994705,
0.05369751527905464,
0.008828622289001942,
-0.006628257222473621,
-0.008710999973118305,
-0.038760166615247726,
0.0020185811445116997,
0.0005641593015752733,
0.000842713750898838,
0.0132944630458951,
0.05869615823030472,
0.018574757501482964,
-0.00884916726499796,
-0.043058689683675766,
0.04312464967370033,
0.02158425748348236,
0.020399969071149826,
-0.019979797303676605,
-0.024391062557697296,
-0.01889711804687977,
-0.01294085755944252,
-0.014107336290180683,
0.020121896639466286,
-0.009592958725988865,
-0.03770897909998894,
0.024081546813249588,
0.0026323357596993446,
-0.007135685067623854,
0.001845218357630074,
-0.020137345418334007,
0.0022963781375437975,
-0.00562287075445056,
-0.0039168838411569595,
-0.03750268369913101,
0.04114304855465889,
0.008944397792220116,
0.06199784204363823,
0.039294201880693436,
0.004216612782329321,
-0.047633763402700424,
0.0100456727668643,
0.05580619350075722,
0.06642752885818481,
-0.023408852517604828,
-0.01249497290700674,
-0.03292296454310417,
-0.048660509288311005,
0.07563283294439316,
-0.05036626756191254,
0.0115425456315279,
-0.04313592612743378,
-0.018953939899802208,
0.018440108746290207,
-0.05040143430233002,
0.006439688615500927,
0.011910309083759785,
0.00868488010019064,
0.008667001500725746,
-0.027862926945090294,
-0.01978902891278267,
-0.036130208522081375,
-0.0017827923875302076,
0.033808618783950806,
0.07078146189451218,
-0.005176359321922064,
0.020029166713356972,
-0.007294122129678726,
0.043725259602069855,
0.010912374593317509,
-0.09632836282253265,
0.01700161211192608,
-0.03738940879702568,
-0.021134518086910248,
0.03829554468393326,
-0.056218862533569336,
-0.055609945207834244,
0.011016245000064373,
0.007587937172502279,
-0.010328748263418674,
-0.03029472380876541,
-0.05453253909945488,
0.0073009575717151165,
0.02172873541712761,
-0.01615300215780735,
0.052209679037332535,
0.043561920523643494,
-0.03353940322995186,
-0.005428595468401909,
-0.021770447492599487,
0.023611826822161674,
-0.032874222844839096,
0.0025390966329723597,
-0.03058798611164093,
-0.011233056895434856,
0.011756950989365578,
0.062067244201898575,
-0.013654202222824097,
-0.0025705217849463224,
0.04003387689590454,
-0.04207351431250572,
0.008275902830064297,
0.03842267766594887,
-0.012328090146183968,
0.0025641010142862797,
-0.01006339956074953,
0.02950195036828518,
-0.004035830497741699,
-0.04356925189495087,
0.025132259353995323,
-0.014026081189513206,
-0.005051514599472284,
0.018968014046549797,
-0.030319733545184135,
0.013780117966234684,
-0.010609102435410023,
-0.0346573181450367,
0.045363303273916245,
-0.05616181716322899,
0.025587575510144234,
-0.01580902934074402,
-0.0006535855936817825,
-0.014235423877835274,
-0.0672505721449852,
-0.024003705009818077,
0.0013947770930826664,
-0.02802744135260582,
0.07835938781499863,
-0.034898072481155396,
0.037578754127025604,
0.00765384454280138,
-0.007809214759618044,
-0.07636132836341858,
-0.056343138217926025,
0.009484321810305119,
0.0480615608394146,
-0.020334342494606972,
-0.03185533359646797,
0.002503474010154605,
-0.020063690841197968,
-0.039794404059648514,
0.01130611915141344,
0.042840924113988876,
-0.012163487263023853,
0.019260548055171967,
0.03151920437812805,
0.002453174674883485,
0.04267468675971031,
-0.008383152075111866,
-0.025630254298448563,
0.017021026462316513,
0.009134005755186081,
-0.01442012470215559,
-0.0033902255818247795,
0.07012776285409927,
-0.027768537402153015,
-0.0334719754755497,
0.022762952372431755,
0.009950253181159496,
0.02013198845088482,
-0.03050227276980877,
-0.02188628539443016,
0.023520374670624733,
0.024715308099985123,
0.037671979516744614,
-0.0046807206235826015,
0.02697662077844143,
0.037601448595523834,
0.027649492025375366,
0.04318135604262352,
0.007572945673018694,
-0.0365152582526207,
-0.04828139394521713,
0.01699915900826454,
-0.01003373134881258,
0.0320182703435421,
0.03374725207686424,
0.013529006391763687,
0.028537632897496223,
-0.007627734448760748,
-0.004197502043098211,
-0.026936914771795273,
0.021031901240348816,
-0.015611784532666206,
0.015706101432442665,
0.017433006316423416,
0.005949842277914286,
-0.018352394923567772,
-0.022690115496516228,
-0.04992608353495598,
0.009726996533572674,
0.05901338905096054,
-0.010363351553678513,
0.03321194276213646,
0.007884593680500984,
0.03217240422964096,
-0.005651857238262892,
-0.014680522494018078,
-0.029284467920660973,
0.0006948005175217986,
0.0010233799694105983,
0.0026828693225979805,
-0.002814339706674218,
-0.0031009544618427753,
0.02230788953602314,
0.034385502338409424,
-0.017608845606446266,
0.025429680943489075,
0.021652575582265854,
0.059803690761327744,
-0.011667242273688316,
0.011935699731111526,
-0.029852649196982384,
0.046335045248270035,
-0.023550722748041153,
0.021939711645245552,
0.022654980421066284,
-0.02362695522606373,
0.020534465089440346,
-0.0028419033624231815,
0.024328729137778282,
-0.04665057361125946,
-0.033715128898620605,
-0.029739325866103172,
0.013868405483663082,
-0.01578926295042038,
0.04648672044277191,
-0.027203431352972984,
0.028966151177883148,
0.0013689190382137895,
0.007167982403188944,
-0.000453158572781831,
0.013671780936419964,
-0.08934495598077774,
-0.030118100345134735,
-0.05419830232858658,
-0.05011943355202675,
0.036951348185539246,
-0.023912133648991585,
-0.04317827150225639,
-0.019910726696252823,
-0.031237486749887466,
0.03493201732635498,
0.02311498485505581,
0.020074177533388138,
-0.009060504846274853,
0.05739467591047287,
0.009064819663763046,
0.011110993102192879,
-0.019760914146900177,
0.03159134089946747,
0.08956006914377213,
0.059725698083639145,
-0.001408686046488583,
-0.050393976271152496,
-0.02101028524339199,
-0.04937702417373657,
0.04849076271057129,
-0.004420978482812643,
0.01303918194025755,
0.03744863346219063,
0.02669980376958847,
0.024950947612524033,
0.05376976728439331,
0.04869697988033295,
0.022868605330586433,
0.056007079780101776,
-0.03809988126158714,
-0.07250002026557922,
-0.01972421631217003,
-0.0027650734409689903,
-0.01162373274564743,
-0.0027901814319193363,
-0.05031631886959076,
-0.004948606714606285,
-0.01002577692270279,
-0.00023929275630507618,
-0.027071310207247734,
0.003788498928770423,
0.007439202629029751,
0.01745866797864437,
-0.029790546745061874,
-0.014555505476891994,
-0.014324689283967018,
-0.0031978830229490995,
-0.023509178310632706,
0.028574170544743538,
0.036174654960632324,
-0.0204301867634058,
-0.010544017888605595,
0.004280492197722197,
0.012642208486795425,
-0.008818352594971657,
-0.01377391628921032,
0.005658244714140892,
-0.03766206279397011,
-0.017361799255013466,
-0.016748853027820587,
0.06368367373943329,
-0.05015679821372032,
-0.010958938859403133,
-0.011072246357798576,
-0.0007295377436093986,
-0.01469687931239605,
-0.028602629899978638,
-0.02091650292277336,
0.0023145703598856926,
0.006749493535608053,
-0.03230717405676842,
-0.00844074971973896,
-0.010291815735399723,
0.021939082071185112,
-0.0392930693924427,
0.0452224463224411,
0.002482905052602291,
-0.030568737536668777,
-0.02796432562172413,
0.0008151077199727297,
-0.009707637131214142,
-0.023362040519714355,
-0.005142431240528822,
-0.02766246534883976,
0.01935296691954136,
-0.05188639089465141,
-0.013767141848802567,
0.055274687707424164,
0.02042464353144169,
0.0457318052649498,
0.031027566641569138,
0.00967663899064064,
0.009484437294304371,
-0.018343592062592506,
0.07111284136772156,
-0.025431044399738312,
-0.01152143906801939,
-0.017542025074362755,
0.007669598329812288,
0.016308177262544632,
0.043951645493507385,
-0.02483346499502659,
-0.0013241847045719624,
0.0011266324436292052,
-0.03221167251467705,
-0.0015927382046356797,
-0.04831017926335335,
0.004905328620225191,
0.0414891317486763,
-0.04321165010333061,
0.014238049276173115,
-0.018964799121022224,
0.01440515834838152,
0.018739011138677597,
0.0030346557032316923,
0.01774902455508709,
0.02992650493979454,
-0.018708834424614906,
-0.015011494047939777,
0.0016603082185611129,
-0.04487869516015053,
-0.011519409716129303,
0.0019715228118002415,
0.019021637737751007,
-0.0566556379199028,
-0.03037487342953682,
-0.024493100121617317,
0.01794220320880413,
0.0178897213190794,
0.03333631902933121,
-0.031796395778656006,
-0.0020543516147881746,
-0.011030200868844986,
0.03360658511519432,
-0.0012873226078227162,
0.02012123540043831,
-0.04664771631360054,
-0.016926167532801628,
0.01207682117819786,
-0.025273269042372704,
-0.03614570200443268,
0.002914291573688388,
0.0023379060439765453,
-0.03358535096049309,
0.027016369625926018,
0.04636850953102112,
-0.014834407716989517,
0.03547116369009018,
0.029591349884867668,
-0.007621120661497116,
0.04417441785335541,
-0.00023864072863943875,
0.014704993925988674,
0.0009587797685526311,
-0.012527192942798138,
-0.05748958885669708,
0.008436866104602814,
-0.05410071834921837,
0.0028809518553316593,
0.02589484304189682,
-0.010135460644960403,
0.004825395066291094,
0.06556002795696259,
-0.008678920567035675,
-0.00009436001710128039,
-0.008358587510883808,
0.04103165119886398,
-0.02063322626054287,
0.0006568582030013204,
-0.008271090686321259,
0.0072074709460139275,
-0.002283791545778513,
0.014209677465260029,
0.021901864558458328,
-0.010594726540148258,
0.0036756463814526796,
-0.018714623525738716,
-0.013477502390742302,
0.041369739919900894,
0.03055758960545063,
0.06273624300956726,
0.013344267383217812,
0.04349954426288605,
-0.01316895056515932,
0.07308340817689896,
0.0229132492095232,
-0.0020773864816874266,
-0.06351974606513977,
-0.004797374829649925,
-0.0023918929509818554,
-0.013700810261070728,
0.04257553815841675,
-0.02746857888996601,
0.012243262492120266,
0.029195822775363922,
-0.06737574934959412,
0.025194372981786728,
-0.008871871046721935,
-0.04159734770655632,
0.0003391169593669474,
0.011700761504471302,
-0.0024427874013781548,
0.07617338746786118,
0.0444658137857914,
0.046495623886585236,
0.02059200406074524,
-0.018817836418747902,
0.00858211424201727,
-0.00005831590169691481,
-0.03292323276400566,
0.011306296102702618,
0.00541897676885128,
0.004639907274395227,
0.0738634541630745,
-0.02237991988658905,
-0.006378698628395796,
0.04845660924911499,
-0.03506441414356232,
0.016637345775961876,
-0.010450419038534164,
-0.0005214591510593891,
-0.031148454174399376,
0.04200596734881401,
-0.0017052986659109592,
0.018850484862923622,
-0.009416921064257622,
0.02911011129617691,
0.01230099331587553,
0.015923654660582542,
0.0158773772418499,
0.028521040454506874,
0.01809212565422058,
-0.054458413273096085,
-0.014793273992836475,
-0.009102112613618374,
0.02282562106847763,
-0.006811374332755804,
-0.0071978638879954815,
0.017486386001110077,
0.02815820463001728,
-0.043818652629852295,
0.0008234725100919604,
-0.025187674909830093,
0.012177023105323315,
-0.008405559696257114,
0.050136253237724304,
0.03137699142098427,
0.019874870777130127,
0.0005041843978688121,
-0.02921147458255291,
-0.002519905334338546,
0.018321169540286064,
-0.039747413247823715,
-0.06284459680318832,
0.006123009137809277,
0.010000131092965603,
0.013679925352334976,
0.02163601666688919,
-0.03496113792061806,
-0.05428474023938179,
0.03501492738723755,
0.022026794031262398,
0.04086405411362648,
-0.008087622001767159,
-0.030398746952414513,
-0.031246665865182877,
-0.04367096349596977,
0.06592953205108643,
-0.05009138584136963,
0.03293422609567642,
-0.056549299508333206,
-0.02575756423175335,
0.003924140706658363,
0.007525552995502949,
0.041201893240213394,
-0.008608298376202583,
0.0028500398620963097,
0.01286964863538742,
0.0012343194102868438,
0.0049125016666948795,
-0.031716518104076385,
0.019566278904676437,
0.008428151719272137,
-0.019823485985398293,
-0.0062454137951135635,
0.012454359792172909,
-0.022110532969236374,
0.05406351387500763,
-0.0034809077624231577,
-0.027686579152941704,
0.01289501041173935,
0.004754139110445976,
-0.0017205142648890615,
0.06441740691661835,
-0.017299512401223183,
-0.0015351022593677044,
0.04978371411561966,
-0.04107508435845375,
0.034488875418901443,
0.018763288855552673,
-0.03186403959989548,
-0.013703263364732265,
0.04184902831912041,
0.010256657376885414,
-0.0076870727352797985,
0.00005804277679999359,
-0.010613654740154743,
0.017743131145834923,
-0.01513753179460764,
-0.004178410861641169,
0.015599541366100311,
-0.03192725405097008,
0.002579351421445608,
0.01534064207226038,
0.0020619328133761883,
0.03991308435797691,
0.006010542158037424,
0.010411991737782955,
0.009037822484970093,
0.012550504878163338,
0.005386095494031906,
0.04438941925764084,
0.007478360552340746,
-0.010030918754637241,
0.04435567930340767,
0.006608132738620043,
0.02913971059024334,
0.02675331011414528,
0.013639386743307114,
0.02278825268149376,
-0.024118568748235703,
-0.005186579655855894,
0.017600156366825104,
-0.018163759261369705,
0.005686100106686354,
0.0042827134020626545,
-0.05548790469765663,
0.08206633478403091,
-0.031938742846250534,
0.03461639955639839,
0.0012549248058348894,
0.00174251280259341,
0.009779129177331924,
0.011582991108298302,
0.021469570696353912,
0.05309731140732765,
-0.015689421445131302,
-0.0014255887363106012,
-0.009027943946421146,
0.039519988000392914,
0.029144741594791412,
-0.02582676336169243,
0.014679496176540852,
-0.03277236968278885,
-0.017372775822877884,
-0.03381466493010521,
-0.005934723187237978,
-0.03674854338169098,
-0.03332486003637314,
0.0192112997174263,
0.07229068875312805,
0.05075324699282646,
-0.001252041314728558,
-0.029930470511317253,
-0.056099485605955124,
0.06748238950967789,
-0.029058832675218582,
-0.020663894712924957,
-0.050551142543554306,
0.028682276606559753,
-0.03266363963484764,
0.012693116441369057
] |
<p>I would like to know the following:</p>
<ol>
<li><p>What is the angle at which water gets splashed when I ride my vehicle through a water on the road?</p></li>
<li><p>How does angle of water varies with speed?</p></li>
<li><p>What is the relation between the distance the water goes with the speed of the vehicle?</p></li>
</ol>
<p>Thanks!</p>
| 10,797 |
[
-0.03953362628817558,
-0.05302324891090393,
-0.009386340156197548,
0.03654695302248001,
0.03055625781416893,
-0.00897655263543129,
-0.024348730221390724,
-0.015857044607400894,
0.030354565009474754,
0.0099897226318717,
0.028273945674300194,
0.09421005845069885,
0.0016278796829283237,
0.03890581429004669,
0.03531520068645477,
0.020319340750575066,
0.00937410444021225,
-0.011386734433472157,
0.02445809356868267,
-0.012610059231519699,
-0.005371071398258209,
-0.023666778579354286,
0.027226485311985016,
0.015677226707339287,
-0.023527752608060837,
0.02570219896733761,
0.0499606691300869,
-0.028805535286664963,
0.020198939368128777,
0.011194689199328423,
0.0008209176012314856,
-0.027023030444979668,
-0.00021567144722212106,
0.005468546412885189,
0.01408417709171772,
0.016191864386200905,
-0.031802948564291,
-0.0035988769959658384,
-0.01346336118876934,
0.022763818502426147,
-0.012476579286158085,
0.0027305230032652617,
-0.011958615854382515,
0.06244365870952606,
-0.02716311253607273,
0.034823935478925705,
0.0009686241392046213,
-0.032827120274305344,
0.02475595846772194,
-0.04490872099995613,
0.06117219850420952,
-0.022770138457417488,
-0.003909003455191851,
0.037088435143232346,
0.011585956439375877,
0.008059806190431118,
0.08021929115056992,
0.07036237418651581,
-0.05793818086385727,
-0.06068748980760574,
0.011088022962212563,
-0.014287899248301983,
-0.008284898474812508,
0.00391533924266696,
-0.04944969713687897,
0.016338905319571495,
-0.021731460466980934,
-0.03660581260919571,
0.006772508844733238,
0.006692135240882635,
-0.02403084747493267,
-0.0016050866106525064,
0.03127928450703621,
-0.00548651535063982,
0.018155405297875404,
-0.07556819170713425,
0.02473095990717411,
0.05661897361278534,
0.043338529765605927,
0.051777616143226624,
-0.0016890037804841995,
-0.004392952658236027,
0.02286955527961254,
0.008046375587582588,
0.017114683985710144,
-0.029630986973643303,
0.07038605213165283,
0.053629063069820404,
0.006634700112044811,
0.014362846501171589,
0.03068523108959198,
0.013609237968921661,
-0.013813929632306099,
0.013635852374136448,
0.003365925746038556,
0.045096151530742645,
-0.015783902257680893,
0.05598287656903267,
0.023036271333694458,
-0.05651099607348442,
0.014389877207577229,
-0.03208116441965103,
-0.015533003956079483,
0.06554572284221649,
0.004085213411599398,
-0.010081027634441853,
-0.02756258100271225,
0.025416266173124313,
-0.024566899985074997,
-0.007378668989986181,
-0.011290661990642548,
-0.010973085649311543,
-0.025418397039175034,
-0.025501932948827744,
-0.023830406367778778,
-0.02446982078254223,
0.033393826335668564,
-0.0008933577337302268,
0.05141555517911911,
0.053887203335762024,
0.044324841350317,
-0.03489222005009651,
-0.009441365487873554,
0.008032885380089283,
-0.05487056076526642,
0.011468085460364819,
0.010451871901750565,
0.016078809276223183,
-0.04270661994814873,
0.03599490225315094,
-0.01781451143324375,
0.0330878309905529,
-0.011260603554546833,
-0.0017138501862064004,
-0.00455097621306777,
-0.008595705963671207,
-0.07468792051076889,
-0.06940463185310364,
0.038457468152046204,
0.02359125018119812,
-0.05566259101033211,
-0.06450126320123672,
0.03784693032503128,
0.02971811778843403,
0.046530283987522125,
-0.019300144165754318,
0.042354270815849304,
0.0074278125539422035,
-0.0011684047058224678,
-0.0034016508143395185,
-0.0011269244132563472,
-0.018413390964269638,
0.011474593542516232,
-0.024240029975771904,
0.013645624741911888,
-0.03199177607893944,
0.004134643357247114,
0.024897024035453796,
0.0018656859174370766,
-0.030924055725336075,
0.0410800464451313,
0.003742532106116414,
-0.010590996593236923,
0.025384794920682907,
-0.01855573244392872,
-0.0031678746454417706,
0.04732965677976608,
0.02627555839717388,
0.004119887016713619,
-0.0006478350260294974,
0.005312892142683268,
0.03840898349881172,
-0.004415511153638363,
-0.013422825373709202,
0.071952223777771,
-0.02008027769625187,
-0.03856585919857025,
-0.008308854885399342,
0.006104322150349617,
-0.009666281752288342,
-0.04867475852370262,
-0.03261428326368332,
-0.01633431948721409,
0.03800225630402565,
-0.0017851967131718993,
0.026221586391329765,
0.03121950663626194,
0.0384649820625782,
-0.013772465288639069,
-0.010026954114437103,
-0.008734991773962975,
-0.04570746421813965,
0.03564503788948059,
-0.031808093190193176,
0.011735848151147366,
-0.009467857889831066,
-0.013797423802316189,
0.029498251155018806,
-0.049208760261535645,
-0.00031471537658944726,
-0.006893244106322527,
0.022439563646912575,
0.026574376970529556,
-0.006166423205286264,
-0.02165002003312111,
0.07404742389917374,
0.03705025091767311,
-0.04026258736848831,
-0.018854010850191116,
-0.01312934048473835,
-0.028392916545271873,
-0.031227560713887215,
-0.03137613832950592,
0.000524527276866138,
-0.016723133623600006,
0.023547010496258736,
0.02353241853415966,
0.018699446693062782,
0.012391392141580582,
0.004221691749989986,
-0.019956333562731743,
0.10894986242055893,
0.06752389669418335,
0.021409520879387856,
0.032272953540086746,
0.039094265550374985,
-0.009740492329001427,
0.0035840999335050583,
0.028282353654503822,
-0.004381822422146797,
-0.044074054807424545,
-0.0038203345611691475,
-0.002155319321900606,
-0.010179598815739155,
-0.03209155797958374,
-0.030089039355516434,
0.0457647368311882,
0.02807827852666378,
0.011296414770185947,
-0.007701970171183348,
0.0019391769310459495,
-0.042335957288742065,
0.009237957186996937,
0.046059925109148026,
-0.002466152422130108,
0.01700156182050705,
0.01006181538105011,
0.01462861243635416,
0.031192220747470856,
-0.017999034374952316,
-0.023544792085886,
0.02451978623867035,
0.012488610111176968,
0.01416520681232214,
-0.016342010349035263,
-0.011706304736435413,
0.041380658745765686,
-0.030200602486729622,
-0.03487858176231384,
0.03754926845431328,
0.024488139897584915,
-0.007148921024054289,
-0.026009006425738335,
0.0052689299918711185,
0.01543725747615099,
0.0009440330904908478,
-0.019761577248573303,
-0.016093848273158073,
0.04672052338719368,
-0.03503353148698807,
0.02876480296254158,
-0.04343750327825546,
-0.01830618642270565,
-0.009059960022568703,
0.011873742565512657,
0.04335916042327881,
-0.00443309498950839,
0.008945760317146778,
-0.01286562904715538,
-0.024022212252020836,
0.000028689733881037682,
-0.00307313515804708,
-0.03916781768202782,
-0.020053980872035027,
-0.08026767522096634,
-0.0014405485708266497,
-0.0024216254241764545,
-0.01015031524002552,
0.03977581858634949,
-0.009134338237345219,
0.0020696655847132206,
0.04438477009534836,
0.025039171800017357,
-0.015398144721984863,
-0.036477282643318176,
-0.03110286220908165,
0.049357302486896515,
-0.05094362050294876,
-0.0164199061691761,
0.018821248784661293,
-0.053825851529836655,
-0.029403280466794968,
0.02950236387550831,
-0.04220230504870415,
-0.01922168955206871,
-0.026784317567944527,
0.0004325775953475386,
0.027331583201885223,
-0.008433734066784382,
-0.01728581264615059,
0.021817853674292564,
-0.04464619979262352,
-0.0005968849291093647,
-0.03377693518996239,
-0.06241840869188309,
0.018402425572276115,
0.006949232425540686,
0.05118181183934212,
-0.011343535035848618,
-0.008118853904306889,
0.03714819997549057,
-0.010827108286321163,
-0.07289943099021912,
-0.03036990575492382,
-0.00941462628543377,
-0.018318964168429375,
-0.04315926879644394,
0.016692262142896652,
0.050282493233680725,
-0.04214772582054138,
0.012382573448121548,
0.027488788589835167,
0.051822416484355927,
0.022759249433875084,
0.02339692786335945,
0.022480180487036705,
-0.025988515466451645,
0.014241288416087627,
0.034810423851013184,
0.04496391862630844,
0.04385576397180557,
-0.05977272987365723,
0.00869641825556755,
0.010515387170016766,
0.026371747255325317,
0.04792065545916557,
-0.04692601412534714,
0.05247588828206062,
0.01302006933838129,
-0.0250870194286108,
-0.027718527242541313,
0.03915959969162941,
-0.0031472856644541025,
0.0021798734087496996,
-0.008267533034086227,
0.013768005184829235,
0.06853324174880981,
-0.0034156807232648134,
-0.012009848840534687,
0.05831112340092659,
0.04764462262392044,
-0.04203319922089577,
-0.0425063781440258,
-0.022615494206547737,
0.017168156802654266,
0.00608364911749959,
-0.05048737674951553,
-0.010019608773291111,
0.036670979112386703,
0.03070267289876938,
0.020042404532432556,
0.029982609674334526,
-0.043417591601610184,
0.008349446579813957,
-0.06220386549830437,
-0.02517017535865307,
0.007272662594914436,
0.03917234390974045,
0.0042190332897007465,
0.0636671632528305,
0.030290206894278526,
0.004777253605425358,
0.006153803318738937,
0.009713123552501202,
-0.03031497821211815,
0.04086346924304962,
-0.040280673652887344,
-0.024434292688965797,
0.012489428743720055,
0.008835922926664352,
0.015720238909125328,
-0.06593295186758041,
-0.031602658331394196,
0.00859894324094057,
-0.005207564681768417,
-0.010823225602507591,
0.03136690706014633,
-0.011804002337157726,
-0.07298427075147629,
-0.019089069217443466,
0.028584031388163567,
0.021873274818062782,
-0.03127945959568024,
0.05352244898676872,
0.06434647738933563,
-0.014027073979377747,
-0.021634167060256004,
0.0015150955878198147,
0.0075512719340622425,
-0.03471574932336807,
0.033170185983181,
0.015520978718996048,
-0.01957669109106064,
0.03173590451478958,
0.02653566189110279,
-0.02311665005981922,
0.043355200439691544,
0.01479280460625887,
0.011784737929701805,
-0.042570848017930984,
-0.06777650862932205,
0.010981743223965168,
0.017782675102353096,
0.027724064886569977,
-0.016643337905406952,
-0.030024733394384384,
0.03362750634551048,
-0.017258064821362495,
-0.03578914329409599,
0.07846958190202713,
0.03968885540962219,
0.005210269242525101,
0.02224084921181202,
-0.03951757773756981,
-0.03318800777196884,
-0.006151048932224512,
-0.008811074309051037,
0.006581438239663839,
0.03818606957793236,
0.002304635476320982,
-0.0049281916581094265,
0.0439695343375206,
-0.018512073904275894,
-0.023842433467507362,
-0.000487770710606128,
-0.02177622728049755,
-0.007614696864038706,
-0.012551228515803814,
0.00022342010925058275,
-0.021428311243653297,
0.01228380762040615,
0.06183089315891266,
-0.021250832825899124,
-0.01993066631257534,
-0.08064392954111099,
-0.03975466266274452,
0.03255946561694145,
0.04420264810323715,
-0.016529230400919914,
-0.02404705621302128,
-0.026475466787815094,
0.007875999435782433,
0.059225354343652725,
-0.020774181932210922,
0.016325006261467934,
-0.021367138251662254,
0.015474528074264526,
-0.0431416779756546,
-0.014453992247581482,
-0.029126377776265144,
0.00894081499427557,
-0.01681884378194809,
0.018695438280701637,
-0.048892293125391006,
-0.016843516379594803,
-0.031033402308821678,
0.017141645774245262,
0.018251607194542885,
0.046933311969041824,
0.005246724467724562,
-0.021677780896425247,
-0.01831684820353985,
0.028495309874415398,
-0.049357641488313675,
-0.06951276957988739,
0.024758443236351013,
0.0072840009815990925,
0.00929300207644701,
0.03343885391950607,
-0.0267301257699728,
-0.009245106019079685,
0.028784334659576416,
0.014112805016338825,
-0.025516165420413017,
0.03744770586490631,
-0.06544625014066696,
-0.00129125255625695,
-0.0009089685627259314,
0.06836855411529541,
0.010816703550517559,
0.04627569392323494,
-0.01791933923959732,
-0.030674442648887634,
-0.014447207562625408,
0.04896127060055733,
0.02042284607887268,
-0.03305315971374512,
-0.03438637778162956,
0.016353309154510498,
-0.04376423358917236,
0.04679619520902634,
-0.016720304265618324,
0.01460901740938425,
-0.021927043795585632,
-0.03573227673768997,
-0.04417767748236656,
0.042742256075143814,
0.00853932648897171,
-0.03616580739617348,
0.05040397122502327,
-0.020351475104689598,
0.005271369591355324,
0.00990330334752798,
0.03720061853528023,
-0.03258855268359184,
0.005609551910310984,
0.0017389386193826795,
0.00653507886454463,
0.015247100032866001,
-0.019860757514834404,
0.002319508697837591,
0.012962340377271175,
-0.03986077755689621,
0.038755565881729126,
0.006208622828125954,
0.014703352004289627,
0.039732735604047775,
-0.030302798375487328,
-0.006061475723981857,
0.06540755927562714,
-0.0170577485114336,
0.05534818395972252,
-0.03025507926940918,
0.028215935453772545,
0.027539968490600586,
0.023058203980326653,
-0.0122012784704566,
-0.062471747398376465,
0.0660974457859993,
0.034124955534935,
-0.01421487145125866,
-0.0323609933257103,
0.017768526449799538,
-0.043010413646698,
-0.02283426932990551,
0.022098200395703316,
0.015719344839453697,
-0.048324353992938995,
-0.003149696160107851,
-0.006111314985901117,
-0.03324386104941368,
0.07242884486913681,
0.01010898593813181,
0.02189774066209793,
0.017520083114504814,
-0.04476052522659302,
-0.01604248210787773,
-0.044525012373924255,
0.04809356480836868,
-0.023767028003931046,
-0.004863298032432795,
-0.013904905878007412,
0.012609833851456642,
0.034825801849365234,
-0.004157714545726776,
0.006260777823626995,
-0.03812548890709877,
0.02788141556084156,
-0.05674358457326889,
-0.02192278392612934,
0.012285043485462666,
0.028095943853259087,
-0.0008930244948714972,
-0.026833437383174896,
0.01200865302234888,
-0.048876792192459106,
-0.025858279317617416,
-0.013393452391028404,
-0.017581718042492867,
0.0211798083037138,
-0.03946062922477722,
0.046513672918081284,
-0.04344724863767624,
0.030993448570370674,
0.031929582357406616,
-0.0021951477974653244,
0.02808445505797863,
-0.008217248134315014,
-0.03917147219181061,
0.015359773300588131,
0.015480715781450272,
0.02035413309931755,
-0.05543394386768341,
-0.010537931695580482,
0.003280223347246647,
0.060473088175058365,
-0.013145217671990395,
0.048891156911849976,
0.04386039823293686,
0.009733837097883224,
-0.013309458270668983,
0.0007909229607321322,
-0.046956438571214676,
0.01160226110368967,
0.00704019982367754,
0.03827890008687973,
-0.014939980581402779,
-0.015185256488621235,
-0.0015591250266879797,
0.03927217796444893,
-0.010616867803037167,
-0.0003414923558011651,
0.04370378330349922,
-0.013128655962646008,
0.038049764931201935,
-0.000469120655907318,
-0.054518911987543106,
0.030460381880402565,
-0.0003098110610153526,
0.04221978411078453,
-0.0258096344769001,
-0.015735914930701256,
0.09594324976205826,
0.005748715251684189,
0.0033630961552262306,
-0.03426361456513405,
0.03854060545563698,
-0.03350561484694481,
-0.008051612414419651,
-0.002172524342313409,
0.021374419331550598,
-0.038766417652368546,
0.02514655515551567,
0.047916896641254425,
-0.05331454426050186,
0.022109411656856537,
-0.031930048018693924,
-0.06870158016681671,
0.015757331624627113,
-0.01517373789101839,
-0.06068388372659683,
0.020588427782058716,
0.005268590524792671,
-0.017286304384469986,
0.03369303047657013,
-0.038429759442806244,
0.0011580020654946566,
0.01330565381795168,
0.042170796543359756,
-0.045278772711753845,
0.03123495914041996,
-0.016273533925414085,
-0.00425591180101037,
0.006715456489473581,
-0.051693934947252274,
0.11814548075199127,
0.04164661839604378,
0.026029156520962715,
-0.0051903678104281425,
-0.004098434932529926,
-0.007201141212135553,
0.007390325423330069,
-0.024037331342697144,
-0.00426902761682868,
0.011332702822983265,
0.007435549981892109,
0.030583838000893593,
0.014572170563042164,
0.010780081152915955,
-0.03239912912249565,
0.0164602342993021,
-0.0372781902551651,
-0.033935826271772385,
0.009194516576826572,
0.016976982355117798,
-0.019178858026862144,
0.04421453922986984,
-0.04170404374599457,
0.030810970813035965,
-0.012661375105381012,
0.0051558963023126125,
-0.030464494600892067,
-0.05863451957702637,
0.03523586690425873,
-0.004288853146135807,
-0.04479620233178139,
0.06001244857907295,
0.025769295170903206,
-0.03623485192656517,
-0.0597057119011879,
0.04083538055419922,
0.038344189524650574,
0.006256798282265663,
-0.03856273740530014,
0.05006643012166023,
0.020783856511116028,
-0.021959392353892326,
0.0013114864705130458,
0.03519832715392113,
-0.04520615562796593,
-0.007190984208136797,
-0.04043305665254593,
0.03920518606901169,
0.005976147949695587,
-0.014702171087265015,
-0.06523359566926956,
0.022331958636641502,
0.006848101504147053,
-0.0754641741514206,
-0.0062611340545117855,
0.024393998086452484,
0.04751969128847122,
-0.033678632229566574,
-0.034171152859926224,
-0.026878133416175842,
0.009866470471024513,
-0.018072931095957756,
0.0036584599874913692,
0.025160830467939377,
-0.009372690692543983,
-0.026636652648448944,
-0.005881277844309807,
0.04123574122786522,
-0.005313487723469734,
-0.01473243162035942,
-0.001122174900956452,
-0.036241065710783005,
-0.06311933696269989,
0.008656264282763004,
0.021303214132785797,
0.01852891780436039,
0.0011362230870872736,
0.028120052069425583,
0.0117917126044631,
0.008248677477240562,
-0.016301004216074944,
0.021939629688858986,
-0.008245652541518211,
-0.005175542552024126,
-0.05453285202383995,
0.02825244888663292,
0.017059504985809326,
0.013391080312430859,
-0.017267687246203423,
0.001000983640551567,
0.005049186758697033,
0.03648534417152405,
-0.0009429636993445456,
0.00004517043271334842,
-0.045572392642498016,
-0.004573581274598837,
-0.00949852354824543,
-0.0013404516503214836,
0.006219004280865192,
0.03802516311407089,
0.035583313554525375,
0.011006082408130169,
0.03361552208662033,
-0.012000113725662231,
-0.030242083594202995,
0.005767057649791241,
0.05157821998000145,
-0.02759181335568428,
-0.02059479057788849,
0.005737052299082279,
0.012112843804061413,
-0.017787763848900795,
0.030853498727083206,
-0.02243984118103981,
-0.009924530051648617,
-0.002548672491684556,
-0.007098406553268433,
-0.036218252032995224,
0.034363407641649246,
-0.05669907480478287,
0.035135164856910706,
-0.022633235901594162,
0.010718527249991894,
-0.02852204442024231,
-0.009050942026078701,
0.004027308896183968,
0.002503979252651334,
-0.033423226326704025,
0.03676079213619232,
-0.03644641861319542,
0.00297452206723392,
-0.0006019127322360873,
0.022166481241583824,
-0.0038797762244939804,
0.0011817826889455318,
0.022925296798348427,
0.000720671727322042,
0.05469828099012375,
-0.04177975654602051,
-0.045170243829488754,
0.05527766793966293,
-0.017659123986959457,
0.0252748541533947,
0.013024975545704365,
-0.020070260390639305,
0.028714798390865326,
0.0177156925201416,
-0.017481982707977295,
-0.00124446046538651,
0.07376448065042496,
0.017967654392123222,
0.013279338367283344,
-0.014944221824407578,
-0.0035265940241515636,
-0.008909182623028755,
-0.01838544011116028,
0.025127913802862167,
-0.033476460725069046,
-0.006334678269922733,
0.025420894846320152,
0.036771006882190704,
0.00092107686214149,
-0.011167295277118683,
0.0035780032631009817,
0.006020136643201113,
-0.026898058131337166,
0.028370104730129242,
-0.012940454296767712,
0.010868466459214687,
0.021754346787929535,
-0.023285159841179848,
0.03212219849228859,
-0.02478691004216671,
0.004289267119020224,
-0.10739631205797195,
0.02025158889591694,
0.01049826666712761,
0.014212794601917267,
0.03593461588025093,
-0.05924809351563454,
-0.029628213495016098,
0.047792837023735046,
-0.08239041268825531,
0.009262344799935818,
-0.01007016934454441,
-0.0023294941056519747,
-0.02880636788904667,
0.02204209566116333,
-0.0010518021881580353,
0.04484373703598976,
0.011704964563250542,
0.03871387988328934,
0.018871955573558807,
-0.010252563282847404,
-0.015601380728185177,
-0.03065500594675541,
0.0107102170586586,
0.016345232725143433,
-0.0032786300871521235,
0.004494968801736832,
0.045301150530576706,
-0.029559563845396042,
-0.002709841588512063,
0.014113555662333965,
-0.0369926281273365,
0.06221279501914978,
0.027775386348366737,
-0.028339311480522156,
-0.0042995791882276535,
0.009984211064875126,
0.014565817080438137,
0.005592248402535915,
-0.018416378647089005,
0.006732061970978975,
-0.008248862810432911,
0.03669371083378792,
0.02119102142751217,
0.01706821657717228,
0.011355339549481869,
-0.04255141317844391,
-0.049786753952503204,
0.040296707302331924,
-0.04222877696156502,
0.006253606174141169,
0.011946266517043114,
-0.0009748393786139786,
0.00035341971670277417,
-0.0369553379714489,
0.0036569719668477774,
-0.025472816079854965,
0.0033010991755872965,
0.028528284281492233,
-0.021102871745824814,
-0.00564795034006238,
0.013523939065635204,
0.0032367324456572533,
-0.004844367504119873,
-0.054650723934173584,
-0.043387386947870255,
-0.011702388525009155,
-0.0597207210958004,
0.011706656776368618,
0.003863108577206731,
-0.006447006482630968,
0.0030051032081246376,
-0.007509992923587561,
-0.0017569618066772819,
0.021759003400802612,
0.03553798422217369,
-0.01436038501560688,
0.05505743622779846,
0.004252532962709665,
-0.0045126681216061115,
-0.05886302515864372,
0.026570124551653862,
0.02024378813803196,
-0.035025570541620255,
-0.048766233026981354,
-0.01367648970335722,
0.018894458189606667,
0.033286768943071365,
0.04319735988974571,
-0.006772181484848261,
-0.019378986209630966,
-0.012234194204211235,
-0.008399817161262035,
0.03514076769351959,
0.016991060227155685,
-0.00911539327353239,
-0.016528459265828133,
-0.04660689830780029,
0.026243962347507477,
0.004857418593019247,
0.006797001697123051,
-0.0063255964778363705,
0.017003871500492096,
-0.030064065009355545,
0.05664334446191788,
-0.022733813151717186,
-0.03594078868627548,
-0.02717234008014202,
0.0131607037037611,
-0.017386557534337044,
0.07496389001607895,
0.0051877559162676334,
0.016670065000653267,
0.02011709287762642,
-0.010761241428554058,
-0.03881572559475899,
0.02045634016394615,
-0.03375733271241188,
-0.00843836646527052,
-0.010699938982725143,
-0.04584642872214317,
0.03962769731879234,
-0.05517186224460602,
0.059083499014377594,
0.009795499965548515,
-0.0617387481033802,
-0.013557602651417255,
0.05660148337483406,
0.054612547159194946,
0.009831870906054974,
-0.0005199263687245548,
0.010950969532132149,
0.00747977290302515,
-0.0842185765504837,
-0.0015451515791937709,
0.04341699555516243,
0.0590682178735733,
-0.005215482320636511,
-0.011362683959305286,
0.0360235832631588,
0.03618933632969856,
0.0481911227107048,
0.012381299398839474,
0.02398557960987091,
0.005453088786453009,
-0.01705855131149292,
0.022421589121222496,
-0.013275278732180595,
0.028181619942188263,
0.04296484217047691,
-0.010882429778575897,
0.005808651447296143,
-0.01990552991628647,
-0.014826339669525623,
-0.016334207728505135,
0.003247758373618126,
-0.02590944431722164,
-0.002803949872031808,
-0.01105574518442154,
0.027213387191295624,
-0.01004642341285944,
-0.04459444060921669,
-0.00651219068095088,
0.0036723774392157793,
0.041426628828048706,
-0.0038325367495417595,
0.045709505677223206,
-0.02924094721674919,
0.00757855037227273,
-0.020902058109641075,
-0.006596022751182318,
-0.0301491841673851,
-0.01377952378243208,
0.0460604764521122,
0.01481760386377573,
-0.010342582128942013,
-0.030430398881435394,
-0.007557128556072712,
-0.03723851218819618,
0.06679423153400421,
-0.0869576558470726,
-0.022781576961278915,
-0.021598221734166145,
-0.0007543766987510026,
0.012342430651187897,
-0.05431123077869415
] |
<p>I know the hypothesis that the light speed is constant is retained by experiments. But is there any theory explaining why the light speed is constant no matter how an observer moves relative to light?</p>
<p>My question is, specifically: Suppose an observer $O$ launches a light and $O$ starts to move at the same time with a uniform velocity $v$ in the same direction that light points. Then why $c$ is still the light speed that $O$ will measure rather than $c-v$? </p>
| 348 |
[
-0.013016576878726482,
-0.010068484582006931,
-0.008224398829042912,
-0.039464980363845825,
0.051653098315000534,
0.02553602121770382,
-0.022518055513501167,
-0.02733265422284603,
-0.0040952726267278194,
-0.02112441323697567,
0.0029308197554200888,
0.06391335278749466,
0.0578460730612278,
-0.0159988421946764,
0.02705124206840992,
-0.011442233808338642,
-0.010110174305737019,
0.009387106634676456,
-0.03631237894296646,
-0.03827998414635658,
-0.006453627720475197,
0.03271593526005745,
0.04737788066267967,
0.009201150387525558,
-0.03235429525375366,
0.007874159142374992,
-0.003815510543063283,
0.010324967093765736,
0.02069268375635147,
0.035787466913461685,
0.009871491231024265,
-0.0025742254219949245,
-0.0050152745097875595,
0.05315540358424187,
-0.00915243849158287,
-0.010998706333339214,
0.006680713966488838,
-0.005915780086070299,
-0.00052481988677755,
0.007597574032843113,
-0.022219913080334663,
-0.00477992370724678,
-0.032960280776023865,
0.06593702733516693,
-0.002449105493724346,
0.023283815011382103,
0.013925645500421524,
0.010232275351881981,
0.0710565373301506,
-0.06159922480583191,
0.070792056620121,
-0.037719402462244034,
0.028620967641472816,
0.032389141619205475,
-0.011713368818163872,
0.004200452007353306,
0.10962682962417603,
0.05999629572033882,
-0.012044459581375122,
0.0023844765964895487,
-0.016110096126794815,
-0.019399108365178108,
0.055715467780828476,
-0.008543926291167736,
-0.01751895621418953,
0.028212888166308403,
-0.01582673378288746,
0.006795171648263931,
0.011042248457670212,
-0.007213882636278868,
-0.002091831760481,
0.01573858968913555,
0.02722984552383423,
0.010052874684333801,
0.01058711763471365,
-0.025022689253091812,
0.014744539745151997,
0.02283678948879242,
0.0341980904340744,
0.025396093726158142,
-0.014699554070830345,
-0.01596534065902233,
0.03716852143406868,
0.03438118100166321,
-0.003496891353279352,
-0.012277217581868172,
0.035095490515232086,
0.011110643856227398,
-0.01764925941824913,
0.033905863761901855,
-0.004834707826375961,
0.007792293559759855,
0.02092384733259678,
-0.006797729525715113,
0.0005123090813867748,
0.05240277200937271,
-0.0048770597204566,
0.03263750672340393,
0.023010777309536934,
-0.033590834587812424,
0.007663413416594267,
0.003645676653832197,
-0.0024236354511231184,
0.050399139523506165,
-0.011636468581855297,
-0.06874930113554001,
-0.036211807280778885,
0.028332442045211792,
-0.046368133276700974,
0.007138749118894339,
-0.0318588986992836,
0.0163398589938879,
0.006106812972575426,
0.024750791490077972,
0.040525659918785095,
-0.02569560706615448,
0.024247338995337486,
-0.0424981452524662,
0.10682500153779984,
0.030359871685504913,
0.02763574942946434,
-0.043974462896585464,
-0.005366994999349117,
-0.01765546202659607,
-0.01715122163295746,
0.009769388474524021,
0.010597252286970615,
-0.010800761170685291,
0.007427623029798269,
0.014449844136834145,
0.004075082950294018,
-0.031868599355220795,
0.0036178247537463903,
0.007739721797406673,
0.0379321463406086,
-0.00954439677298069,
-0.1307346373796463,
-0.0663929432630539,
0.06411920487880707,
-0.02004893496632576,
-0.026149317622184753,
-0.10654238611459732,
-0.0027439361438155174,
0.005225284956395626,
0.08829750120639801,
-0.017875565215945244,
-0.008986758068203926,
-0.010122479870915413,
0.011185422539710999,
0.005139930639415979,
0.01891258731484413,
-0.03472762182354927,
0.011523162014782429,
-0.043725982308387756,
-0.003318607807159424,
-0.07111083716154099,
-0.03279998153448105,
0.03784316033124924,
-0.000849959789775312,
-0.019766880199313164,
0.07793021202087402,
-0.021753137931227684,
0.011893169023096561,
0.009586799889802933,
0.019093256443738937,
-0.027908481657505035,
0.09356328099966049,
0.03916836529970169,
-0.017561297863721848,
0.04691572114825249,
0.027858803048729897,
0.05277571827173233,
-0.0018309673760086298,
0.0010178959928452969,
0.04115726053714752,
-0.060847628861665726,
-0.029084399342536926,
0.026527956128120422,
0.0007833333220332861,
0.005301967728883028,
-0.018380193039774895,
-0.041791509836912155,
-0.011058018542826176,
-0.009412654675543308,
0.018029697239398956,
0.048559606075286865,
-0.03684607520699501,
0.028894905000925064,
0.0004468626284506172,
-0.06100256368517876,
0.021392352879047394,
-0.07219918072223663,
0.007837647572159767,
0.029613953083753586,
-0.0246576014906168,
0.03544294089078903,
0.02583305537700653,
0.022578202188014984,
-0.008072388358414173,
-0.044326700270175934,
-0.00883452408015728,
0.0499940924346447,
0.008496729657053947,
-0.014524786733090878,
0.06262671202421188,
0.028364982455968857,
0.05106222257018089,
0.018321022391319275,
-0.004585090558975935,
0.02218790166079998,
-0.03940541297197342,
0.03177514299750328,
-0.020467786118388176,
0.0020021582022309303,
-0.013745498843491077,
0.01849447190761566,
-0.02508031763136387,
0.012582805939018726,
0.007439614739269018,
0.04739644005894661,
-0.0218175258487463,
0.0632890835404396,
0.016751809045672417,
-0.025389669463038445,
-0.003193566109985113,
0.05705544725060463,
0.002893799915909767,
0.001064916024915874,
-0.009452426806092262,
-0.05039118975400925,
-0.0032047247514128685,
-0.002863881643861532,
0.0417717881500721,
-0.0013055913150310516,
-0.04623012617230415,
0.008165906183421612,
0.023982373997569084,
0.0722208321094513,
0.03264675661921501,
0.03832795098423958,
-0.04528170824050903,
-0.08327071368694305,
0.0034640715457499027,
0.021343881264328957,
0.005051805637776852,
0.02666328102350235,
0.04645548388361931,
0.007585891522467136,
-0.012719441205263138,
-0.016983339563012123,
-0.022153805941343307,
0.014180174097418785,
0.011706451885402203,
-0.010402978397905827,
0.006974596995860338,
-0.017080238088965416,
0.02040606178343296,
-0.011226814240217209,
0.035967469215393066,
0.04436914250254631,
0.014750566333532333,
0.03460139408707619,
-0.04661025479435921,
-0.021633649244904518,
0.020604470744729042,
-0.009944058023393154,
-0.03174062445759773,
-0.0024506421759724617,
0.017532432451844215,
-0.019958430901169777,
0.00926436297595501,
-0.03801671788096428,
0.0075766523368656635,
-0.00387782440520823,
-0.01861565001308918,
0.010161667130887508,
0.027103254571557045,
0.025490371510386467,
-0.02583143673837185,
-0.04705840349197388,
-0.003319632029160857,
-0.03735581040382385,
-0.009304099716246128,
0.011254625394940376,
-0.012627571821212769,
0.05383947864174843,
-0.011280767619609833,
-0.04173050448298454,
0.03324902802705765,
-0.0059190778993070126,
0.04615616425871849,
0.037232592701911926,
-0.000004372581770439865,
-0.07077241688966751,
-0.014528845436871052,
-0.0366596020758152,
-0.040647171437740326,
-0.01737041212618351,
0.02902289479970932,
0.03461000323295593,
-0.02795076183974743,
-0.028893087059259415,
0.0022236837539821863,
-0.05513095483183861,
-0.04501905292272568,
-0.0011515584774315357,
-0.016637681052088737,
0.03899367153644562,
-0.05489348620176315,
0.038984742015600204,
0.0032742556650191545,
-0.05614370480179787,
0.00754177151247859,
-0.016282685101032257,
-0.03266917169094086,
0.05342836678028107,
-0.004993268754333258,
0.05075278505682945,
-0.007681448012590408,
-0.029224414378404617,
0.07567692548036575,
0.03225482627749443,
-0.012301688082516193,
-0.03640253096818924,
0.022510968148708344,
-0.019658299162983894,
-0.021626869216561317,
-0.011288410052657127,
0.02889701910316944,
-0.010283990763127804,
0.025186767801642418,
0.051028430461883545,
-0.004592158365994692,
0.01680039055645466,
0.023870855569839478,
-0.002170021878555417,
-0.004912875592708588,
-0.00704962108284235,
0.01945801079273224,
0.014912762679159641,
0.026657413691282272,
-0.05418599396944046,
-0.011793436482548714,
0.0249656792730093,
0.04035542905330658,
-0.016467198729515076,
-0.03676114231348038,
0.07003695517778397,
0.016555992886424065,
0.01814945973455906,
-0.02364668995141983,
0.02033381536602974,
-0.0006946910289116204,
0.020532462745904922,
-0.0026449698489159346,
0.026794925332069397,
0.00936037115752697,
-0.0007583176484331489,
0.007438653614372015,
0.01070853229612112,
-0.004685965832322836,
-0.024172218516469002,
-0.030490875244140625,
-0.02112603187561035,
-0.02412419579923153,
0.027119185775518417,
-0.02065286599099636,
-0.01643597148358822,
0.05341142416000366,
0.023237332701683044,
0.0003497922734823078,
0.00132184277754277,
-0.05933527275919914,
0.003397261258214712,
-0.04534545913338661,
0.004161111544817686,
0.016065435484051704,
0.006386712659150362,
0.0033097700215876102,
0.048642393201589584,
0.038492247462272644,
0.018984587863087654,
0.016329221427440643,
-0.012493005022406578,
-0.08315862715244293,
0.015388436615467072,
-0.055560868233442307,
-0.026545066386461258,
-0.04225590452551842,
-0.011858992278575897,
-0.030117692425847054,
-0.022246887907385826,
-0.028997274115681648,
-0.031846027821302414,
-0.023759491741657257,
-0.03366668522357941,
0.0014098454266786575,
-0.03241347894072533,
-0.03381171077489853,
-0.035221971571445465,
0.02860235795378685,
0.015178529545664787,
-0.03511347994208336,
0.009737788699567318,
0.023954614996910095,
-0.03184689208865166,
-0.01221418846398592,
-0.02378099411725998,
-0.014170896261930466,
0.017324095591902733,
0.0023814982268959284,
0.044902194291353226,
0.004647664725780487,
-0.014867745339870453,
0.031072160229086876,
0.011399620212614536,
0.01554380264133215,
0.009084329009056091,
-0.027650341391563416,
-0.0435422882437706,
-0.049046505242586136,
-0.02071099914610386,
0.014289378188550472,
0.05266968533396721,
0.026075230911374092,
-0.002586473012343049,
0.0436018705368042,
0.02418564446270466,
-0.005146718118339777,
0.002128743100911379,
0.04300295189023018,
-0.005001137498766184,
-0.0009344690479338169,
-0.03900196775794029,
-0.011409752070903778,
-0.023158909752964973,
-0.00449711736291647,
0.021635258570313454,
-0.024461405351758003,
-0.02031555026769638,
-0.007384876720607281,
-0.013339275494217873,
0.028523774817585945,
0.00713615957647562,
-0.01744185946881771,
-0.0182399470359087,
0.023124290630221367,
0.03628707304596901,
0.00701944762840867,
-0.017607232555747032,
0.029916085302829742,
0.025152573361992836,
0.005602412391453981,
-0.007133773062378168,
-0.062330856919288635,
-0.015804817900061607,
0.0016247547464445233,
0.02891482040286064,
-0.019273634999990463,
0.015608803369104862,
-0.0338868722319603,
-0.01147068664431572,
0.026189913973212242,
-0.01707012951374054,
0.027205033227801323,
-0.006911266129463911,
-0.025475580245256424,
-0.020099634304642677,
0.011689651757478714,
-0.03285079449415207,
0.007623517420142889,
-0.009698037058115005,
-0.016019219532608986,
-0.03644738346338272,
0.011051276698708534,
-0.01019425131380558,
0.003937603905797005,
0.030702661722898483,
0.05175770819187164,
0.01470514852553606,
-0.004006217233836651,
0.0021691324654966593,
0.025032516568899155,
-0.017523078247904778,
-0.06061309576034546,
-0.008594504557549953,
0.024334657937288284,
0.005647188052535057,
0.015437708236277103,
-0.015485205687582493,
-0.0643153041601181,
0.025502884760499,
-0.011188097298145294,
-0.022466199472546577,
0.019998567178845406,
-0.0237283818423748,
0.00039802625542506576,
0.000435724388808012,
-0.021407483145594597,
0.05154795944690704,
0.01718762516975403,
-0.02402562089264393,
-0.0451401062309742,
0.00005145204340806231,
0.0459003672003746,
-0.04010625183582306,
-0.012677101418375969,
-0.01326348353177309,
0.019349711015820503,
-0.017287753522396088,
0.06328769773244858,
-0.014848705381155014,
-0.00680745393037796,
0.00045898917596787214,
-0.025252318009734154,
-0.02541615255177021,
0.03789237141609192,
0.018847720697522163,
0.008176648057997227,
-0.018164414912462234,
0.0011513655772432685,
-0.014451875351369381,
-0.022745653986930847,
0.010036839172244072,
0.010873066261410713,
0.0038687465712428093,
0.009828831069171429,
-0.002251946832984686,
-0.0003791970666497946,
-0.027196962386369705,
-0.014234829694032669,
0.026858558878302574,
-0.036493174731731415,
0.0076534077525138855,
-0.006120611913502216,
-0.01356319710612297,
0.031291231513023376,
-0.056923434138298035,
-0.06653100252151489,
0.011312266811728477,
-0.025912350043654442,
0.03783129155635834,
-0.08153004199266434,
0.004442778415977955,
-0.003950310871005058,
0.024992560967803,
-0.08590839058160782,
-0.040415629744529724,
0.030506597831845284,
-0.009303472936153412,
0.010037983767688274,
-0.027690932154655457,
0.0198301300406456,
-0.033199526369571686,
-0.016169650480151176,
-0.027787525206804276,
0.04170192778110504,
0.01689007319509983,
-0.02503957785665989,
-0.02027907595038414,
0.006382932420819998,
0.030143987387418747,
-0.031835101544857025,
-0.030288197100162506,
0.0020445920526981354,
-0.018081912770867348,
-0.009951114654541016,
0.004348373040556908,
0.09912250936031342,
-0.01809753105044365,
-0.052232589572668076,
-0.008479665964841843,
0.011741134338080883,
0.011105046607553959,
-0.04705660417675972,
0.0069489553570747375,
0.04005565866827965,
0.006959117017686367,
0.0038998827803879976,
-0.01901349611580372,
0.013479824177920818,
0.008352451957762241,
0.03459760174155235,
0.007779271341860294,
0.00037523542414419353,
-0.024354804307222366,
-0.06380505859851837,
0.03877226635813713,
0.001906280405819416,
0.021424168720841408,
-0.02502588927745819,
0.010472609661519527,
0.01465197280049324,
-0.0356510691344738,
-0.0005286145024001598,
0.019242698326706886,
-0.01429575402289629,
0.003985986113548279,
0.011183565482497215,
0.00848606787621975,
-0.017474785447120667,
-0.040937308222055435,
-0.023078816011548042,
-0.003991936333477497,
-0.007782649714499712,
0.05967380851507187,
-0.008226940408349037,
0.08499117195606232,
0.015110993757843971,
-0.006325514521449804,
-0.020379725843667984,
-0.006682599429041147,
-0.010030727833509445,
-0.0019554952159523964,
0.03217446431517601,
0.028264537453651428,
-0.03973875567317009,
-0.0022155805490911007,
0.0160895474255085,
0.06923621147871017,
0.005700880195945501,
0.011002087965607643,
0.035546958446502686,
0.04615207761526108,
0.037271175533533096,
0.011484263464808464,
-0.03716297820210457,
0.03302039951086044,
-0.0033347720745950937,
0.010568929836153984,
-0.003656348679214716,
-0.013893995434045792,
0.028858890756964684,
-0.009340059012174606,
0.014949523843824863,
-0.016622653231024742,
-0.03318088501691818,
-0.06309513002634048,
0.01607985608279705,
0.014969654381275177,
0.05198149010539055,
-0.0004948429414071143,
0.018754340708255768,
0.0075621106661856174,
0.014220898039638996,
0.035664722323417664,
-0.03466864302754402,
-0.0583481527864933,
-0.051163751631975174,
-0.007846520282328129,
-0.007187407463788986,
0.04424025118350983,
0.007009097374975681,
-0.03676369786262512,
-0.012959026731550694,
-0.028533900156617165,
0.010473842732608318,
0.034074779599905014,
0.03140092268586159,
-0.015792427584528923,
0.07930970191955566,
0.006898064166307449,
-0.01133094634860754,
-0.012371809221804142,
0.007688537240028381,
0.08017921447753906,
0.03490513935685158,
0.0022066934034228325,
-0.06654814630746841,
0.04680325835943222,
-0.01242693979293108,
0.03056117333471775,
-0.06542851775884628,
0.06715085357427597,
-0.0012572333216667175,
0.031625837087631226,
0.034638527780771255,
0.05689969286322594,
-0.002046348061412573,
-0.022482121363282204,
0.06845050305128098,
-0.02088528871536255,
-0.03213858604431152,
-0.002553724916651845,
0.034012872725725174,
-0.001744166249409318,
0.02332957647740841,
0.001248106942512095,
0.020918095484375954,
-0.029937829822301865,
-0.026453150436282158,
-0.015483054332435131,
-0.04040658846497536,
-0.0032691278029233217,
0.0003653811290860176,
-0.06103505194187164,
0.008853538893163204,
0.029242128133773804,
-0.03173689916729927,
-0.09174039959907532,
0.005883139558136463,
0.020008085295557976,
-0.010266805067658424,
0.01743781752884388,
0.010780749842524529,
0.022194767370820045,
0.03135918453335762,
0.009635495953261852,
-0.009037698619067669,
-0.05251128971576691,
0.009693977423012257,
-0.025596603751182556,
0.05163436755537987,
-0.016979428008198738,
0.026918085291981697,
0.022676585242152214,
0.01529175229370594,
-0.010614833794534206,
-0.06757360696792603,
-0.020293131470680237,
-0.00041337506263516843,
0.005358593538403511,
0.002020796062424779,
0.0003605865640565753,
-0.019875621423125267,
0.022313691675662994,
-0.012422878295183182,
-0.0067072403617203236,
-0.0007977227796800435,
-0.001323208911344409,
-0.0193560179322958,
-0.014040113426744938,
0.008719045668840408,
-0.015035453252494335,
-0.028747953474521637,
0.01691691391170025,
-0.0023712681140750647,
-0.04535653814673424,
0.0014822252560406923,
0.023464340716600418,
0.01051273476332426,
0.022478759288787842,
-0.007030976936221123,
-0.0006576690939255059,
-0.006258372683078051,
-0.0757579654455185,
0.0013132210588082671,
-0.03162923827767372,
-0.0352826751768589,
-0.031222447752952576,
0.027249984443187714,
0.05361201614141464,
0.049213897436857224,
-0.031378135085105896,
0.023501424118876457,
-0.035572294145822525,
0.027737801894545555,
0.01318857166916132,
-0.018713882192969322,
-0.018627507612109184,
-0.016143377870321274,
0.002880341373383999,
-0.01433618739247322,
-0.041133493185043335,
0.03346734866499901,
0.04386100545525551,
0.02993789315223694,
0.012133915908634663,
0.002898699603974819,
-0.007181365974247456,
0.024692656472325325,
0.00762746250256896,
-0.04199432581663132,
0.018115617334842682,
0.01581696979701519,
0.014639665372669697,
-0.017710091546177864,
-0.04495510831475258,
-0.01061944104731083,
0.0030710373539477587,
-0.014125204645097256,
0.008774860762059689,
-0.022749299183487892,
0.011820579878985882,
-0.033601030707359314,
0.007319052238017321,
-0.06705968081951141,
-0.0331309512257576,
-0.025647569447755814,
0.026482468470931053,
-0.011107109487056732,
-0.008137132041156292,
0.0017510611796751618,
0.06079520657658577,
-0.00649090064689517,
-0.029635241255164146,
0.016287337988615036,
0.022002847865223885,
0.024741988629102707,
0.01651662588119507,
0.030611326918005943,
0.005817945580929518,
0.04484529420733452,
-0.034373510628938675,
-0.041628021746873856,
0.02831709012389183,
-0.03412151709198952,
-0.07694384455680847,
0.051926154643297195,
-0.0389607734978199,
0.013496050611138344,
0.029315827414393425,
-0.00808931514620781,
0.029320355504751205,
0.04612386226654053,
-0.023543644696474075,
0.01558155007660389,
0.0011164635652676225,
-0.022664792835712433,
-0.013550521805882454,
-0.017231086269021034,
0.035857055336236954,
-0.00464458717033267,
-0.033374059945344925,
0.05257805436849594,
0.021749204024672508,
-0.03891913592815399,
0.050576526671648026,
0.0009388479520566761,
-0.03158077597618103,
-0.013674652203917503,
0.04111848026514053,
0.030966095626354218,
0.001186869922094047,
0.02982969768345356,
-0.009341183118522167,
0.057669077068567276,
0.022194739431142807,
0.006789505016058683,
-0.13892892003059387,
0.007695922628045082,
-0.01505204290151596,
0.042579155415296555,
0.04192705079913139,
-0.04161963611841202,
0.031421106308698654,
0.0477459616959095,
-0.0722641870379448,
0.007114166859537363,
-0.04839044809341431,
-0.022968195378780365,
-0.0402979739010334,
-0.034722644835710526,
0.0049103801138699055,
0.06573667377233505,
0.03454212844371796,
0.02795754186809063,
0.03353895992040634,
0.01792123168706894,
-0.014314739033579826,
-0.032117340713739395,
-0.011389457620680332,
0.026431526988744736,
-0.008393495343625546,
0.014674408361315727,
0.06739860028028488,
-0.0017548028845340014,
-0.00832410529255867,
0.03663714975118637,
0.02097153849899769,
0.009234176017343998,
-0.009078944101929665,
0.023997677490115166,
0.014362895861268044,
0.01836417429149151,
0.014263655059039593,
-0.00978543609380722,
-0.041292473673820496,
0.024609241634607315,
0.014632747508585453,
0.025764834135770798,
-0.006580012384802103,
-0.014977408573031425,
0.0011629271320998669,
-0.07371081411838531,
-0.03168042376637459,
0.032248806208372116,
-0.004138014744967222,
-0.019896576181054115,
0.0448731929063797,
0.025851208716630936,
0.020022856071591377,
-0.029092902317643166,
0.0009471934172324836,
-0.06530937552452087,
-0.008083375170826912,
0.025934016332030296,
0.0025719639379531145,
-0.014167160727083683,
-0.02860112302005291,
0.009422726929187775,
-0.013866073451936245,
0.011067389510571957,
0.02945737913250923,
0.03362174332141876,
-0.0570838563144207,
-0.021476825699210167,
0.018833378329873085,
-0.035996075719594955,
0.022276313975453377,
-0.053887367248535156,
-0.007103134412318468,
0.04539119452238083,
0.01196789275854826,
-0.006296812556684017,
-0.023133130744099617,
-0.023343242704868317,
-0.04515618830919266,
-0.06387219578027725,
0.046638086438179016,
-0.005663692951202393,
0.018492765724658966,
-0.05732729658484459,
-0.01267516240477562,
-0.053084686398506165,
0.014020298607647419,
0.06066508591175079,
-0.0016619644593447447,
-0.023359354585409164,
0.026155047118663788,
0.0009960049064829946,
0.013780899345874786,
-0.05516098439693451,
-0.021085286512970924,
-0.00022539829660672694,
-0.037471722811460495,
-0.015957433730363846,
-0.027594435960054398,
-0.022167116403579712,
0.019525736570358276,
-0.006447322200983763,
-0.01004039403051138,
0.02044801041483879,
0.012206020765006542,
-0.04418226704001427,
0.05169016495347023,
0.022661441937088966,
-0.0050777895376086235,
0.05955500155687332,
0.028712360188364983,
0.02987743727862835,
0.04512582719326019,
-0.01646324247121811,
-0.05152668431401253,
0.0009898848365992308,
-0.021737128496170044,
-0.02524084411561489,
-0.0026292353868484497,
0.03161164000630379,
0.016837462782859802,
-0.015126786194741726,
0.01185780018568039,
0.037525251507759094,
-0.037282995879650116,
-0.0031989694107323885,
0.03920220211148262,
-0.017282862216234207,
0.00464903749525547,
0.023510953411459923,
0.023817457258701324,
0.04037458822131157,
0.024089986458420753,
-0.0008895794744603336,
0.04385538771748543,
0.032108742743730545,
0.002305269008502364,
0.046022411435842514,
0.027426239103078842,
0.012669683434069157,
0.03270480036735535,
-0.013452786020934582,
0.04003008455038071,
-0.018135562539100647,
0.004607281181961298,
-0.003000314347445965,
-0.026951638981699944,
0.01332676038146019,
0.01566201262176037,
-0.03795921057462692,
0.06391184777021408,
-0.03453049063682556,
0.022082915529608727,
0.0038458281196653843,
0.03622167930006981,
-0.019233237951993942,
0.011329513974487782,
-0.00005600478471023962,
0.03603959456086159,
-0.0033021685667335987,
0.006747106555849314,
0.013157404959201813,
-0.016785645857453346,
0.025574546307325363,
-0.05376224219799042,
0.02839679643511772,
-0.0018496798584237695,
-0.04364210367202759,
-0.011252781376242638,
0.009793605655431747,
-0.028591984882950783,
-0.024810075759887695,
0.015318389981985092,
0.048911914229393005,
0.03442675620317459,
0.014983353205025196,
-0.011564278975129128,
-0.014791877008974552,
0.07342493534088135,
-0.07368620485067368,
0.00047435995656996965,
-0.019583940505981445,
0.023745229467749596,
-0.02020694687962532,
-0.012541350908577442
] |
<p>Given the lowest eigenvalue $E_0$ of an Schrödinguer operator, do the other energies $ E_{n} $ for $ n >0 $ depend strongly on the lowest eigenvalue of the system? I mean, if we somehow fixed the eigenvalue $E_{0}$, could we get more or at least better approximations to the other eigenenergies of the system?</p>
<p>thanks</p>
| 10,798 |
[
-0.013170862570405006,
-0.007363514509052038,
-0.007266993168741465,
-0.008177297189831734,
0.029331475496292114,
-0.003261835314333439,
-0.05778733640909195,
-0.08788749575614929,
0.009331371635198593,
-0.05790204927325249,
0.014215391129255295,
-0.006129876710474491,
0.02958417311310768,
0.01530916802585125,
0.060646090656518936,
0.022256745025515556,
-0.0334416925907135,
-0.016919808462262154,
-0.007036508060991764,
-0.015265729278326035,
-0.013890824280679226,
0.027831489220261574,
0.024032974615693092,
0.013270036317408085,
-0.053390875458717346,
-0.004285129718482494,
0.014000874012708664,
0.001924664480611682,
0.03098742663860321,
0.0330081470310688,
0.004421452526003122,
0.008186763152480125,
0.00045965504250489175,
0.07583235204219818,
0.028478657826781273,
0.011860682629048824,
-0.0400235578417778,
-0.03627623990178108,
-0.029944492504000664,
0.01437376532703638,
-0.03157076984643936,
-0.04770627245306969,
0.004308407194912434,
0.032450489699840546,
0.031168736517429352,
0.004051423631608486,
0.01781024970114231,
-0.053938087075948715,
0.04458710923790932,
-0.0383550263941288,
0.07717998325824738,
-0.00585170229896903,
0.023058418184518814,
0.027913695201277733,
0.0053576575592160225,
-0.01033581793308258,
0.07805774360895157,
0.06962627172470093,
0.024307172745466232,
-0.035921331495046616,
-0.027398748323321342,
-0.0286219771951437,
-0.006983851082623005,
-0.015269216150045395,
-0.03794728219509125,
0.0002792823943309486,
0.011164694093167782,
-0.030589766800403595,
0.027874093502759933,
-0.007877440191805363,
-0.031451739370822906,
0.025162752717733383,
0.039447687566280365,
-0.008773698471486568,
0.011873102746903896,
-0.007096271961927414,
0.037105489522218704,
0.002240973524749279,
0.03471534699201584,
0.00905959215015173,
-0.01463585626333952,
0.004095938988029957,
0.01544464286416769,
0.05679088458418846,
0.0017870375886559486,
0.012644989416003227,
0.0640975758433342,
-0.022492583841085434,
0.026978259906172752,
0.04028676077723503,
0.0027964995242655277,
0.021148817613720894,
0.03408609703183174,
-0.040232498198747635,
-0.02168267033994198,
-0.0016637775115668774,
0.010960111394524574,
0.0041745430789887905,
0.008468563668429852,
-0.031688474118709564,
-0.006995401810854673,
-0.05676082521677017,
-0.009396351873874664,
0.04967237263917923,
0.03073582798242569,
-0.020458104088902473,
-0.0629710927605629,
0.013617005199193954,
-0.0041781761683523655,
0.003836109535768628,
-0.006206693593412638,
-0.0007240608101710677,
0.0010105367982760072,
0.0131745096296072,
0.00485585629940033,
0.005051037296652794,
0.0009715864434838295,
-0.028836173936724663,
0.03271010145545006,
0.06933869421482086,
0.027305733412504196,
-0.04413957893848419,
0.030157750472426414,
-0.021132709458470345,
-0.06550733745098114,
0.016160422936081886,
0.031735390424728394,
-0.02597884275019169,
-0.05921178683638573,
-0.005524561274796724,
0.009041884914040565,
-0.008923857472836971,
-0.0007392520201392472,
-0.005234711337834597,
0.044938184320926666,
-0.026064490899443626,
-0.08263266831636429,
-0.020556187257170677,
0.003918993286788464,
-0.0472862608730793,
-0.008542868308722973,
-0.056997623294591904,
-0.035720668733119965,
0.01919076032936573,
0.06061461567878723,
-0.00033687177347019315,
0.027333106845617294,
0.009604917839169502,
0.026898041367530823,
0.01853312738239765,
0.012058273889124393,
-0.01830730214715004,
-0.003725202288478613,
-0.05705421790480614,
0.03105662763118744,
-0.034052833914756775,
0.0323895700275898,
0.021346502006053925,
0.004580313805490732,
-0.02036658674478531,
0.05948302522301674,
-0.03973528370261192,
0.020606501027941704,
0.009706107899546623,
0.029043128713965416,
0.004944761749356985,
0.06329917162656784,
0.01960151642560959,
0.024393286556005478,
0.012459042482078075,
-0.013512179255485535,
0.003988847602158785,
0.0023526386357843876,
0.054697953164577484,
0.0346902459859848,
-0.04356272518634796,
-0.020534923300147057,
-0.0390738919377327,
0.0400221161544323,
0.022860178723931313,
-0.038576122373342514,
-0.012368721887469292,
0.023458091542124748,
-0.006022660061717033,
0.0014044794952496886,
0.07480786740779877,
0.0007996378117240965,
-0.0252386461943388,
-0.03351762145757675,
-0.046268951147794724,
0.022105703130364418,
-0.017308812588453293,
0.020942049100995064,
0.02580326609313488,
-0.021977467462420464,
0.06360898911952972,
0.012493977323174477,
0.0174424909055233,
-0.004438359290361404,
0.0004240405687596649,
-0.016663843765854836,
0.012665187940001488,
-0.02548036351799965,
-0.053056128323078156,
0.0396338552236557,
0.034754518419504166,
0.026101119816303253,
0.0040877689607441425,
0.06830725073814392,
-0.03702384606003761,
-0.04697667434811592,
-0.00558884721249342,
-0.011664843186736107,
0.05824020504951477,
0.02145148068666458,
0.00013444361684378237,
-0.0191724244505167,
-0.02566119097173214,
0.004335274454206228,
0.026707984507083893,
-0.04992690682411194,
0.035272613167762756,
0.020148051902651787,
0.0026775484438985586,
-0.0027235071174800396,
0.039371196180582047,
0.03828989714384079,
0.022773252800107002,
0.0026774646248668432,
-0.035595137625932693,
-0.035402633249759674,
0.03110615536570549,
0.02094162628054619,
0.07075166702270508,
-0.07149304449558258,
0.00988415814936161,
0.017923999577760696,
0.012074100784957409,
0.030641743913292885,
-0.008550980128347874,
-0.050410717725753784,
0.001961236586794257,
0.02920786663889885,
0.04336046800017357,
0.003205551067367196,
0.002458147704601288,
0.04262195900082588,
0.01983550563454628,
0.034964773803949356,
0.015337055549025536,
-0.02816191501915455,
0.03892512619495392,
-0.030067523941397667,
0.00815920252352953,
-0.0014776404714211822,
-0.0033757127821445465,
0.0028106917161494493,
-0.06371688842773438,
0.039305441081523895,
0.011134806089103222,
-0.025454163551330566,
-0.004207584075629711,
-0.0008407357381656766,
-0.048508305102586746,
0.044965051114559174,
-0.030682077631354332,
-0.022456690669059753,
-0.013029933907091618,
0.019538547843694687,
-0.015718679875135422,
0.01885989122092724,
-0.0582532063126564,
-0.012399292550981045,
-0.020471474155783653,
0.004582853522151709,
0.0811467096209526,
-0.015119634568691254,
0.008126555941998959,
-0.05497466400265694,
-0.0210754182189703,
0.00799753051251173,
-0.012929925695061684,
0.005936944391578436,
0.010177829302847385,
-0.046699874103069305,
-0.000373105431208387,
-0.03144795447587967,
-0.02182784117758274,
0.02865322306752205,
-0.015667514875531197,
-0.0005126590258441865,
0.040033210068941116,
-0.014888118021190166,
-0.03096025250852108,
0.022387979552149773,
-0.010596922598779202,
-0.010366654954850674,
-0.0345795601606369,
0.0049941567704081535,
0.04566527530550957,
-0.0013921742793172598,
-0.012768924236297607,
-0.0015948996879160404,
-0.010976593941450119,
-0.03003520518541336,
-0.01870501972734928,
-0.01929624378681183,
0.03112327679991722,
-0.02685132808983326,
0.04781566187739372,
0.04145496338605881,
-0.038562096655368805,
-0.010816886089742184,
-0.06696871668100357,
-0.028881419450044632,
0.023614289239048958,
-0.009704631753265858,
0.046789802610874176,
-0.006879889871925116,
-0.0030413137283176184,
0.07925035804510117,
0.004570718389004469,
-0.04870694875717163,
-0.01118635293096304,
-0.008420136757194996,
0.017728755250573158,
0.011401365511119366,
0.013044058345258236,
0.03658834472298622,
-0.014034525491297245,
0.028749536722898483,
0.012113782577216625,
0.03588319942355156,
0.02755456604063511,
-0.00034586977562867105,
-0.0121436333283782,
0.02807660773396492,
0.004520273767411709,
0.03496965020895004,
0.0282457135617733,
-0.013800015673041344,
-0.01401352696120739,
0.030761873349547386,
-0.009254985488951206,
0.046858593821525574,
0.025588778778910637,
-0.034250300377607346,
0.07356484979391098,
0.002548235934227705,
0.043633412569761276,
-0.010573195293545723,
0.04741957411170006,
0.030223535373806953,
0.013796218670904636,
-0.01257132925093174,
0.03652675077319145,
0.05015560984611511,
-0.0384831465780735,
0.030439332127571106,
0.021503297612071037,
0.012509265914559364,
-0.03081158548593521,
-0.002405450213700533,
0.024619078263640404,
-0.0014963721623644233,
0.005842913407832384,
-0.011755063198506832,
-0.056339796632528305,
0.022466255351901054,
0.02723846398293972,
0.04020467773079872,
-0.0372009202837944,
-0.03664611652493477,
0.03223820775747299,
-0.06612240523099899,
-0.03146297484636307,
-0.01997924968600273,
0.05710862949490547,
-0.014682838693261147,
0.04550635814666748,
-0.016953403130173683,
0.019011056050658226,
0.0038825813680887222,
0.007867216132581234,
-0.059405066072940826,
0.000840010994579643,
-0.035888347774744034,
-0.0018439720151945949,
0.007212826982140541,
0.0051955003291368484,
-0.0035435925237834454,
-0.036080002784729004,
-0.00207910081371665,
-0.004439784213900566,
0.02425655908882618,
-0.026505088433623314,
-0.015845412388443947,
-0.05553529039025307,
0.009023158811032772,
-0.028473306447267532,
0.014541659504175186,
-0.006224820390343666,
-0.017511213198304176,
0.021045738831162453,
0.02388758957386017,
-0.051973942667245865,
-0.010012323036789894,
-0.019388096407055855,
0.041169796139001846,
-0.0007575370254926383,
0.03816018998622894,
0.045827895402908325,
0.027300449088215828,
-0.004901490174233913,
-0.025507567450404167,
0.005160223692655563,
0.051003728061914444,
0.026537775993347168,
-0.012315467931330204,
0.023372991010546684,
-0.03422537073493004,
-0.012741249054670334,
-0.010852138511836529,
0.09194901585578918,
-0.021015014499425888,
0.018331734463572502,
0.0063868253491818905,
-0.013868843205273151,
-0.04821878671646118,
0.017602086067199707,
0.0313342921435833,
0.01570628210902214,
-0.03254522755742073,
-0.05271466448903084,
0.01672610081732273,
-0.026260124519467354,
0.008970441296696663,
-0.04811156168580055,
-0.01794407144188881,
-0.032540202140808105,
-0.009904075413942337,
0.021412396803498268,
0.03883686661720276,
-0.008630610071122646,
-0.027315838262438774,
0.02835349552333355,
0.031901780515909195,
-0.005992118269205093,
0.013422440737485886,
0.007369399536401033,
-0.016877470538020134,
0.03657989948987961,
-0.013226225972175598,
0.013354945927858353,
-0.05764196068048477,
-0.030912211164832115,
0.035615578293800354,
0.02819063700735569,
-0.015135694295167923,
0.009658636525273323,
-0.03306044265627861,
-0.025384869426488876,
0.07398251444101334,
-0.0049172574654221535,
0.017403485253453255,
-0.0048736389726400375,
-0.028385695070028305,
-0.02615431137382984,
-0.04145059362053871,
0.0027220388874411583,
0.02236604504287243,
-0.00027300568763166666,
0.028765862807631493,
-0.025958621874451637,
-0.0004284885653760284,
-0.027184244245290756,
0.032295841723680496,
0.028807122260332108,
0.08414439111948013,
-0.0006761795957572758,
-0.024252096191048622,
-0.0010184167185798287,
0.02874867059290409,
0.0043799662962555885,
-0.08723976463079453,
0.001927260309457779,
0.01662578247487545,
-0.00989550817757845,
0.0047454750165343285,
-0.025569822639226913,
-0.03479098528623581,
0.06111687049269676,
0.01473076269030571,
-0.036793939769268036,
-0.00105905847158283,
-0.017551114782691002,
0.04905730113387108,
0.040950845927000046,
-0.006466669030487537,
0.047527212649583817,
0.08454318344593048,
-0.007289373781532049,
0.0009651448344811797,
-0.024066977202892303,
0.02392026223242283,
-0.050426069647073746,
-0.00394463911652565,
-0.02197347767651081,
0.005778685212135315,
0.024705670773983,
0.02820989117026329,
-0.02735123224556446,
0.029139705002307892,
0.033673033118247986,
-0.020016076043248177,
-0.02710253931581974,
0.008745064027607441,
-0.002477188128978014,
-0.007231466937810183,
0.014237937517464161,
0.028495438396930695,
0.002046420006081462,
-0.016754373908042908,
0.013802073895931244,
-0.0019026563968509436,
0.006166194565594196,
0.05177358537912369,
-0.026770634576678276,
0.007521022576838732,
-0.07168217748403549,
-0.006327357143163681,
-0.004277955275028944,
-0.07387600839138031,
0.054981034249067307,
-0.002182325813919306,
0.017322847619652748,
-0.010583106428384781,
-0.03713212162256241,
-0.014516029506921768,
0.02202826738357544,
-0.02941587008535862,
0.0010761982994154096,
-0.006256407592445612,
0.020401550456881523,
0.022356877103447914,
-0.00738499965518713,
-0.08910686522722244,
-0.005587995983660221,
0.0011644845362752676,
0.009546068497002125,
0.010323457419872284,
-0.029052212834358215,
-0.02079862728714943,
-0.03469174727797508,
0.011044064536690712,
0.005617204587906599,
0.015611985698342323,
-0.014102909713983536,
0.012241270393133163,
0.014585441909730434,
0.008228600956499577,
0.04051237180829048,
0.009716600179672241,
-0.022747421637177467,
0.02638213336467743,
-0.024100646376609802,
-0.005613825749605894,
0.0007872983696870506,
0.08860728144645691,
-0.019364414736628532,
-0.003971780184656382,
-0.006063849199563265,
0.01043995562940836,
0.03417108952999115,
-0.02903676964342594,
-0.009557717479765415,
0.057985033839941025,
0.024510562419891357,
0.0596611313521862,
0.010239687748253345,
-0.005740330088883638,
-0.01844538189470768,
0.011687416583299637,
0.026320382952690125,
-0.0036061301361769438,
-0.024083146825432777,
-0.0714469850063324,
0.00002778769157885108,
0.0073483530431985855,
-0.029215369373559952,
0.0316324457526207,
0.09105155616998672,
0.020467210561037064,
-0.047046441584825516,
0.007769378833472729,
-0.027997691184282303,
0.001804985455237329,
-0.006899857893586159,
0.02467254363000393,
-0.0005100014386698604,
0.018654966726899147,
-0.02354384772479534,
-0.07506808638572693,
-0.03454618155956268,
0.012475578114390373,
0.030268466100096703,
0.016959013417363167,
0.04302074387669563,
-7.050286967569264e-7,
0.004148494452238083,
-0.014294324442744255,
-0.026654968038201332,
-0.02484670653939247,
-0.00033061616704799235,
-0.026935942471027374,
0.05031365901231766,
-0.02596290037035942,
-0.027596252039074898,
0.03552873432636261,
0.05967698618769646,
-0.017886251211166382,
0.027256514877080917,
0.026741407811641693,
0.014934142120182514,
0.04002179205417633,
-0.011274084448814392,
-0.052732110023498535,
0.03739973530173302,
-0.03883041441440582,
0.039660267531871796,
-0.0005596565315499902,
-0.031031634658575058,
0.04168834537267685,
0.01162963267415762,
0.0484444759786129,
-0.023487446829676628,
-0.023060103878378868,
-0.02411709353327751,
0.041957296431064606,
-0.028446581214666367,
0.006992235314100981,
0.0024370169267058372,
0.03332067281007767,
0.0060163456946611404,
0.03617269918322563,
0.021767614409327507,
0.002815679647028446,
-0.060220569372177124,
-0.02129986323416233,
-0.012748616747558117,
-0.04193078354001045,
0.00692620687186718,
0.030190611258149147,
-0.03706579655408859,
0.040034495294094086,
-0.033855825662612915,
0.016607075929641724,
-0.008937717415392399,
0.006258110050112009,
0.007006900385022163,
0.03415660560131073,
0.03545099124312401,
0.021845411509275436,
0.04181075468659401,
0.005885341204702854,
0.11709035187959671,
0.07128828018903732,
0.01769746094942093,
-0.030145986005663872,
-0.0004661987186409533,
-0.006792821921408176,
-0.0392872579395771,
-0.025096973404288292,
0.02277071587741375,
-0.0017422252567484975,
0.004195523913949728,
-0.04213676601648331,
0.049944255501031876,
-0.010761835612356663,
0.007619823794811964,
0.028477169573307037,
-0.027754439041018486,
-0.021745778620243073,
0.028841791674494743,
0.013720930553972721,
0.010338516905903816,
0.00803950522094965,
-0.015706660225987434,
-0.0018850854830816388,
-0.050335612148046494,
0.01665353588759899,
-0.007894313894212246,
-0.023439113050699234,
0.03688778355717659,
-0.02980276569724083,
-0.031976740807294846,
-0.01614493504166603,
0.007133559789508581,
-0.015218718908727169,
-0.049764618277549744,
0.03762023523449898,
0.026977920904755592,
0.026650898158550262,
0.030697811394929886,
0.02520536072552204,
-0.021306680515408516,
0.018205635249614716,
0.009551852010190487,
-0.02018062397837639,
-0.009195650927722454,
-0.03454039990901947,
-0.03058970719575882,
0.03549455478787422,
-0.007507511880248785,
0.026187453418970108,
0.014813597314059734,
-0.01557548251003027,
0.014241027645766735,
-0.03904171288013458,
-0.008680548518896103,
-0.015868080779910088,
0.03643251955509186,
-0.008395004086196423,
-0.009593261405825615,
0.00004420917321112938,
0.012548157013952732,
0.0013900762423872948,
0.009760173037648201,
-0.008572706952691078,
-0.04427728429436684,
0.004863422363996506,
-0.00411638431251049,
0.028397532179951668,
-0.001996902748942375,
-0.019945185631513596,
0.039903901517391205,
-0.026398515328764915,
-0.0295833982527256,
-0.06982520967721939,
0.02838457189500332,
0.0036125669721513987,
0.05194621533155441,
0.010353008285164833,
0.005338321439921856,
-0.020066002383828163,
-0.1125694066286087,
0.012652416713535786,
0.0005146998446434736,
-0.021809902042150497,
-0.00938238762319088,
-0.02778565138578415,
0.027226410806179047,
0.06290870904922485,
-0.02509278804063797,
0.03232070431113243,
-0.02227005735039711,
0.005841043312102556,
0.018692325800657272,
-0.009466318413615227,
-0.033989399671554565,
-0.0017938880482688546,
-0.04750872030854225,
0.040298815816640854,
-0.009605473838746548,
0.004583367612212896,
-0.016827957704663277,
-0.005241318140178919,
-0.014996537938714027,
0.0809939056634903,
-0.03625290095806122,
-0.004326923750340939,
-0.027717290446162224,
-0.041398435831069946,
0.01858249492943287,
0.02394649013876915,
0.007744545582681894,
-0.05245830863714218,
-0.0473812073469162,
-0.024958791211247444,
-0.00893013458698988,
-0.005490398034453392,
0.025059295818209648,
-0.0010406851070001721,
0.008317796513438225,
-0.05486706271767616,
0.0021609116811305285,
-0.030117332935333252,
-0.030147289857268333,
-0.038662999868392944,
0.013420023955404758,
0.0181000716984272,
-0.021125486120581627,
-0.01777614653110504,
-0.0013829955132678151,
0.029339829459786415,
-0.03041299618780613,
0.041203223168849945,
0.031287502497434616,
-0.023238470777869225,
-0.03990375995635986,
0.01818939857184887,
-0.013723068870604038,
0.0474897101521492,
-0.0190606527030468,
-0.03400811925530434,
0.03111637569963932,
-0.08201643079519272,
-0.049653828144073486,
0.010755081661045551,
-0.0054322052747011185,
0.025100983679294586,
0.026439351961016655,
-0.001298548188060522,
-0.027902472764253616,
0.04942575842142105,
-0.030788572505116463,
-0.009552078321576118,
0.010993028990924358,
0.007304737810045481,
-0.01887054741382599,
0.00788111612200737,
-0.0014007427962496877,
0.005327388644218445,
0.008335447870194912,
0.024584071710705757,
0.029647791758179665,
-0.0003469902148935944,
-0.026284607127308846,
0.02853219397366047,
-0.016124699264764786,
0.050944507122039795,
0.02637460082769394,
-0.0006225709803402424,
0.006783171556890011,
0.04341700300574303,
-0.02358601801097393,
0.040789440274238586,
0.059249427169561386,
0.03287626430392265,
-0.10000858455896378,
-0.01839705929160118,
-0.0119809964671731,
0.013111029751598835,
0.02906278893351555,
-0.03683684021234512,
0.05946236476302147,
0.031002193689346313,
-0.04876372963190079,
0.042789217084646225,
-0.007116084918379784,
0.02708754688501358,
-0.03425508365035057,
0.007907032035291195,
-0.06120271980762482,
0.016130896285176277,
0.04958707094192505,
0.05037974193692207,
0.021932095289230347,
0.0010864816140383482,
-0.02866187132894993,
-0.005262246821075678,
-0.014098329469561577,
0.037433549761772156,
-0.012352966703474522,
-0.020497092977166176,
0.035281211137771606,
-0.051561884582042694,
-0.06092241406440735,
-0.007516901940107346,
0.006840643938630819,
-0.026233023032546043,
-0.04148440808057785,
0.0016041093040257692,
0.004793606698513031,
0.034193623811006546,
0.01999787613749504,
-0.02386985719203949,
-0.006335754878818989,
0.02040286548435688,
0.0017132405191659927,
-0.014898181892931461,
-0.021560920402407646,
0.019026223570108414,
0.029498441144824028,
-0.027094265446066856,
-0.06715521961450577,
0.03154793009161949,
-0.010831758379936218,
-0.008560415357351303,
-0.0012725512497127056,
-0.01629537343978882,
-0.0011282982304692268,
-0.012397537007927895,
0.009801915846765041,
-0.05191151797771454,
-0.05235311761498451,
-0.017492420971393585,
0.03379354998469353,
0.008284108713269234,
0.04138018563389778,
-0.0041534630581736565,
-0.036012955009937286,
0.005991711281239986,
0.01715141348540783,
-0.02121361531317234,
-0.0865364670753479,
-0.004418305121362209,
-0.01008943747729063,
-0.02008742094039917,
-0.03565794229507446,
-0.03365389257669449,
-0.05398115888237953,
0.017666183412075043,
-0.010247309692203999,
0.02007853426039219,
0.002513551153242588,
-0.05455898493528366,
-0.04708316922187805,
-0.05318909510970116,
0.02677183598279953,
-0.008615324273705482,
0.012182233855128288,
-0.012967401184141636,
0.006340675055980682,
-0.003601954784244299,
0.005982459057122469,
0.04618743062019348,
-0.025691021233797073,
-0.017140069976449013,
0.008155732415616512,
0.014948660507798195,
0.027048572897911072,
0.0075993589125573635,
0.013931534253060818,
-0.020972056314349174,
-0.017046231776475906,
-0.026564138010144234,
0.011882198043167591,
-0.028072459623217583,
0.004450100939720869,
-0.019117292016744614,
-0.013677367940545082,
-0.028440622612833977,
-0.024859027937054634,
-0.038815081119537354,
0.10712739825248718,
0.033838093280792236,
-0.023813053965568542,
0.06413017958402634,
-0.008395062759518623,
0.020255735144019127,
0.00049591064453125,
-0.025459671393036842,
-0.037821993231773376,
0.014140435494482517,
-0.008977226912975311,
-0.020707104355096817,
0.006585812196135521,
-0.0038838849868625402,
0.02221071720123291,
-0.017900628969073296,
0.018854929134249687,
0.043412402272224426,
-0.013316513039171696,
-0.018764786422252655,
0.011820563115179539,
0.040476907044649124,
0.022321417927742004,
-0.008126002736389637,
0.0018849297193810344,
0.03565667197108269,
0.034740012139081955,
0.04030224308371544,
0.041117582470178604,
-0.016429439187049866,
-0.012183748185634613,
0.034283317625522614,
-0.008579791523516178,
-0.040786366909742355,
0.02322988212108612,
0.011257410049438477,
0.006944375112652779,
-0.033584535121917725,
-0.017074229195713997,
0.08222508430480957,
0.017990466207265854,
-0.037515558302402496,
-0.010383601300418377,
-0.040300656110048294,
0.04718244448304176,
-0.025931334123015404,
0.0006939916638657451,
-0.05274251103401184,
0.01765330322086811,
0.045596830546855927,
-0.0020861406810581684,
0.007577672600746155,
0.029434101656079292,
-0.018858829513192177,
0.009764106012880802,
-0.022158212959766388,
0.025998950004577637,
0.015859637409448624,
-0.0878332331776619,
0.014060419984161854,
0.003449865151196718,
-0.007247347850352526,
-0.04057270288467407,
0.03230311721563339,
-0.026355059817433357,
-0.011572256684303284,
-0.002229055855423212,
0.07734149694442749,
0.05218755826354027,
0.02488751709461212,
-0.028703438118100166,
-0.02648855932056904,
0.02663862705230713,
-0.034002821892499924,
-0.03275560960173607,
-0.0281569492071867,
-0.0014003550168126822,
-0.01063096895813942,
-0.010376148857176304
] |
<p>It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state.</p>
<p>Does this claim specifically mean that the entropy of the initial universe was zero?</p>
<p>Is zero-entropy state unique for given physical laws?</p>
<p>Is it possible that entropy was growing always so that only difference in entropy has physical meaning rather than absolute value? Was there ever negative entropy state?</p>
| 10,799 |
[
-0.02040230669081211,
-0.03506605327129364,
0.023014934733510017,
-0.015709733590483665,
0.047083381563425064,
0.020930618047714233,
-0.030768804252147675,
0.0022758133709430695,
-0.02617817185819149,
-0.05560796707868576,
-0.005555793642997742,
0.00934092327952385,
-0.0020230456721037626,
0.021464431658387184,
0.03178556635975838,
-0.020832395181059837,
-0.01047979760915041,
0.006827057804912329,
-0.02013748325407505,
-0.006790209095925093,
0.009325413964688778,
0.022501088678836823,
0.01058713998645544,
0.048038989305496216,
-0.03503529727458954,
0.046269118785858154,
0.029494093731045723,
0.01604389399290085,
0.046863578259944916,
0.04809857904911041,
0.005722050555050373,
-0.0044222380965948105,
-0.020300496369600296,
0.03839016333222389,
0.02813810110092163,
-0.03382955491542816,
-0.015238547697663307,
-0.058969177305698395,
-0.0086338110268116,
0.004887138959020376,
-0.04765339568257332,
-0.028438739478588104,
-0.02974332496523857,
0.031939879059791565,
-0.04535296931862831,
0.0055613708682358265,
0.0010922437068074942,
0.008999424055218697,
0.028721986338496208,
-0.023521380499005318,
0.013700699433684349,
-0.0177821833640337,
0.051387183368206024,
0.014894326217472553,
-0.014522258192300797,
-0.01292379479855299,
0.07588250935077667,
0.06234745681285858,
-0.012164677493274212,
-0.03057141974568367,
-0.02663462795317173,
-0.02134300395846367,
0.032468900084495544,
-0.006421718746423721,
-0.016839180141687393,
0.05888974666595459,
0.0145676014944911,
-0.017380204051733017,
0.02700405940413475,
0.012281324714422226,
0.02607065998017788,
0.02327827177941799,
0.003162899985909462,
0.006587165407836437,
0.03746047988533974,
-0.011233873665332794,
0.0036085513420403004,
-0.016798924654722214,
0.028938062489032745,
0.08246909081935883,
0.01323353685438633,
-0.015146922320127487,
0.03949863836169243,
0.03939219191670418,
0.007016109302639961,
0.02109111100435257,
0.0701749250292778,
-0.02406437322497368,
0.02552100643515587,
0.0628928691148758,
0.009784886613488197,
0.023941179737448692,
0.01742362417280674,
-0.032537586987018585,
-0.037165723741054535,
0.06686217337846756,
-0.021601123735308647,
0.0338895209133625,
-0.009964135475456715,
-0.04078812897205353,
0.01161834318190813,
-0.03009907156229019,
0.04789631813764572,
0.04493319243192673,
0.013071807101368904,
-0.003916762303560972,
-0.07746997475624084,
0.031693365424871445,
-0.04104628041386604,
-0.030529340729117393,
-0.006069280207157135,
0.0026400936767458916,
0.00689454423263669,
-0.024060823023319244,
-0.004405367188155651,
-0.027077963575720787,
0.0064887055195868015,
-0.057328399270772934,
0.051760461181402206,
0.04881129786372185,
0.03935647010803223,
0.006912109442055225,
0.005078156478703022,
-0.016707463189959526,
-0.04289594292640686,
-0.009899977594614029,
0.016847193241119385,
-0.005493667908012867,
-0.032890260219573975,
0.053856831043958664,
-0.030041592195630074,
0.005466765258461237,
-0.008639081381261349,
-0.0034822982270270586,
0.04364236444234848,
0.009747753851115704,
-0.07439972460269928,
-0.0713045671582222,
0.06072692573070526,
-0.007219035644084215,
-0.0393475703895092,
-0.034098900854587555,
0.009881101548671722,
-0.0042681582272052765,
0.05490673705935478,
-0.023101652041077614,
0.01435033604502678,
-0.006448101252317429,
0.02137087658047676,
0.0042182267643511295,
-0.007730227895081043,
-0.015775375068187714,
-0.002826821757480502,
-0.03369034081697464,
-0.005198730621486902,
-0.08575356751680374,
0.03556729108095169,
0.05858834460377693,
-0.03240237757563591,
-0.03072323091328144,
0.0057641793973743916,
-0.04426770657300949,
-0.007785735186189413,
0.003005092730745673,
0.0018240412464365363,
-0.03213435783982277,
0.07715270668268204,
0.03575273975729942,
0.00028300529811531305,
0.046082958579063416,
0.009107274934649467,
0.033202797174453735,
0.009491818025708199,
0.02176615037024021,
0.02237790636718273,
-0.02581295743584633,
-0.003341516712680459,
-0.0023082273546606302,
0.0236982349306345,
0.0028998281341046095,
-0.01657870225608349,
0.011855942197144032,
-0.006540677510201931,
0.006901901680976152,
0.02476434037089348,
0.021361010149121284,
0.0035990681499242783,
-0.017408093437552452,
0.025668971240520477,
-0.04399335756897926,
-0.022322412580251694,
-0.08395423740148544,
-0.00039950365317054093,
0.022501053288578987,
-0.003977611660957336,
0.01603037491440773,
0.018816091120243073,
0.07177432626485825,
-0.04364820942282677,
0.0032628357876092196,
0.012522555887699127,
0.016865160316228867,
-0.004054661374539137,
-0.026796923950314522,
0.028747135773301125,
0.04689580574631691,
0.052137672901153564,
-0.03923950344324112,
-0.0027107270434498787,
0.010722205974161625,
-0.07677061855792999,
0.013750414364039898,
0.006186599377542734,
0.04161616414785385,
-0.016258327290415764,
0.024710070341825485,
0.018940694630146027,
0.007002128288149834,
0.007418917957693338,
0.021584024652838707,
-0.0327376164495945,
0.0477447509765625,
0.023198239505290985,
0.007982365787029266,
-0.033971887081861496,
0.01904892362654209,
0.017250003293156624,
-0.017328517511487007,
-0.013877194374799728,
-0.027613190934062004,
-0.07788065075874329,
-0.009346251375973225,
0.04471918195486069,
0.05552120506763458,
-0.02289118617773056,
-0.00365461315959692,
0.01946078985929489,
0.015777232125401497,
-0.010242072865366936,
-0.011344303376972675,
-0.01777736097574234,
-0.06413957476615906,
0.010311642661690712,
-0.014810807071626186,
0.041315674781799316,
0.02929348684847355,
0.04096745699644089,
-0.009425336495041847,
0.03086904063820839,
-0.01392865739762783,
-0.010913331992924213,
0.025022905319929123,
0.006924613378942013,
-0.0010752814123407006,
0.014909818768501282,
-0.04989025741815567,
0.0024167646188288927,
-0.025773663073778152,
0.010128600522875786,
0.00957225076854229,
0.013670587912201881,
0.02550036646425724,
-0.04179826378822327,
-0.007990018464624882,
-0.029414895921945572,
0.018125656992197037,
0.011085591278970242,
-0.01913568191230297,
0.025533271953463554,
-0.026669500395655632,
-0.001539558987133205,
0.009002822451293468,
-0.004955102223902941,
-0.050220806151628494,
-0.01795336976647377,
0.028877301141619682,
-0.015188184566795826,
-0.012488962151110172,
-0.07319417595863342,
-0.005188691429793835,
0.01941680535674095,
0.0032214035745710135,
-0.009318969212472439,
0.05440772324800491,
-0.042593151330947876,
0.028115250170230865,
-0.015938203781843185,
-0.003083593677729368,
0.013055715709924698,
-0.012760571204125881,
0.0477745495736599,
0.014007216319441795,
-0.035179827362298965,
-0.038259245455265045,
0.02054084651172161,
-0.026628566905856133,
0.029674261808395386,
-0.01181556936353445,
-0.010504358448088169,
0.06693298369646072,
-0.03233172371983528,
-0.053924281150102615,
-0.008264869451522827,
-0.0725974515080452,
-0.04771283641457558,
-0.001507133012637496,
0.00581709947437048,
0.011721095070242882,
-0.008458890952169895,
0.05035218223929405,
0.03843430057168007,
-0.053041812032461166,
-0.05343209207057953,
-0.04129669815301895,
-0.06110532954335213,
0.023979993537068367,
-0.05562342330813408,
0.02913961559534073,
-0.04471972584724426,
-0.04437543451786041,
0.06363745778799057,
0.04856085404753685,
0.013115988112986088,
-0.02039938233792782,
-0.023689081892371178,
-0.0033133134711533785,
0.003484877059236169,
-0.01710614189505577,
-0.004036490805447102,
0.009717782959342003,
0.019292056560516357,
0.03651725500822067,
0.06784429401159286,
-0.0014655896229669452,
0.0015360568650066853,
-0.029918840155005455,
0.023619091138243675,
-0.01601669192314148,
0.017866576090455055,
0.006383656524121761,
0.02825029194355011,
0.010051178745925426,
0.01800188422203064,
0.014394891448318958,
0.02765696868300438,
0.010799659416079521,
-0.04822724685072899,
0.0702999159693718,
0.021142782643437386,
0.012648901902139187,
-0.06632248312234879,
0.04452044144272804,
-0.04249146580696106,
0.02320403791964054,
-0.019434086978435516,
-0.0018573362613096833,
-0.006175156217068434,
0.020567169412970543,
0.014071532525122166,
-0.013422288000583649,
-0.007234261836856604,
-0.015264231711626053,
0.0036650407128036022,
-0.009354552254080772,
-0.004962871316820383,
0.04781755059957504,
-0.008679497987031937,
0.016907624900341034,
0.025565385818481445,
0.0390634760260582,
0.03582528606057167,
-0.004365372937172651,
-0.04119567945599556,
0.007713754661381245,
-0.04535028338432312,
-0.010346056893467903,
-0.0032284690532833338,
0.01640978641808033,
0.023630235344171524,
0.07358485460281372,
0.007156746927648783,
-0.0003731221950147301,
-0.012592877261340618,
-0.03641274943947792,
-0.0933304950594902,
0.002030640374869108,
-0.08946623653173447,
0.00756444875150919,
0.013723650015890598,
0.01173414010554552,
-0.011295954696834087,
-0.03558150306344032,
-0.016449201852083206,
-0.019043801352381706,
0.023846281692385674,
-0.04900847002863884,
-0.012711716815829277,
-0.04504561796784401,
-0.02592029795050621,
-0.003848020453006029,
0.008187252096831799,
0.04889445751905441,
-0.023532308638095856,
0.026024911552667618,
0.026789119467139244,
0.007464076858013868,
0.030306536704301834,
-0.01173360925167799,
0.0014400763902813196,
0.025433065369725227,
0.028716959059238434,
0.01683049090206623,
0.013080018572509289,
0.014321665279567242,
0.01339886337518692,
0.019675906747579575,
0.04158325493335724,
0.025683214887976646,
-0.037170179188251495,
-0.01214337907731533,
-0.020981399342417717,
-0.018358588218688965,
-0.006172151304781437,
0.032301247119903564,
0.0017223207978531718,
0.033626489341259,
0.010100794024765491,
0.029441341757774353,
-0.012659280560910702,
0.0340656153857708,
0.08199732005596161,
-0.012205875478684902,
-0.01610199548304081,
-0.005252371542155743,
-0.012524996884167194,
-0.043564774096012115,
-0.008512705564498901,
0.010575484484434128,
-0.0022842504549771547,
-0.02496158331632614,
-0.005033038556575775,
-0.00460465345531702,
0.03033166006207466,
-0.03882680460810661,
-0.0332336463034153,
0.0023641909938305616,
0.04671650379896164,
-0.02212398685514927,
0.02028014324605465,
0.023010805249214172,
0.02553710527718067,
0.030981354415416718,
0.029397832229733467,
-0.029112916439771652,
-0.031828489154577255,
-0.0198806319385767,
0.013221584260463715,
0.02851564809679985,
0.03727024793624878,
-0.000010465657396707684,
-0.07023660093545914,
-0.05804458633065224,
0.05583615601062775,
-0.009523624554276466,
0.028055058792233467,
-0.011112954467535019,
0.013823732733726501,
0.004299963358789682,
-0.040999412536621094,
-0.0059327417984604836,
0.02937893196940422,
-0.007109333295375109,
0.021586919203400612,
0.005188329610973597,
0.0013428840320557356,
-0.022586597129702568,
0.010481864213943481,
-0.008272767998278141,
0.010308458469808102,
-0.04225291684269905,
0.03385673463344574,
0.0007250545895658433,
0.014174782671034336,
-0.0009012498194351792,
-0.07068793475627899,
0.01932835392653942,
-0.005727676209062338,
-0.016734858974814415,
0.006010935641825199,
-0.007552077062427998,
-0.006166425533592701,
0.00720935920253396,
-0.007203314919024706,
-0.02844909206032753,
0.020198702812194824,
-0.046106014400720596,
0.028014272451400757,
0.004248821642249823,
-0.02145843766629696,
0.05007877200841904,
0.042066723108291626,
0.019770318642258644,
0.018768297508358955,
-0.036299530416727066,
0.029720010235905647,
-0.03197845444083214,
0.013884855434298515,
-0.04542872682213783,
0.01941986009478569,
-0.022281259298324585,
0.05453865975141525,
0.0023296205326914787,
0.022140193730592728,
0.01116186287254095,
-0.025018107146024704,
-0.006552845239639282,
0.0034675539936870337,
0.015608576126396656,
0.0010366111528128386,
-0.0102084344252944,
0.03195132315158844,
-0.008089909330010414,
-0.011381718330085278,
0.028553621843457222,
0.012754400260746479,
0.031085960566997528,
0.02186654321849346,
-0.02617090567946434,
0.06404383480548859,
-0.01107256393879652,
-0.03711261600255966,
0.017550621181726456,
-0.03673283010721207,
0.05024838075041771,
0.003293863497674465,
-0.011729507707059383,
0.022614195942878723,
-0.06419084221124649,
-0.010170362889766693,
0.016290104016661644,
-0.004609687719494104,
0.021466434001922607,
-0.048469413071870804,
0.034870319068431854,
0.00037477342993952334,
-0.004141401499509811,
-0.08242470026016235,
-0.03416362404823303,
0.024662431329488754,
0.010287727229297161,
-0.011693179607391357,
-0.017207784578204155,
0.009172002784907818,
-0.020854277536273003,
0.01322393398731947,
-0.010103129781782627,
0.05810568854212761,
0.011361083947122097,
0.008533835411071777,
0.00987139344215393,
0.015231292694807053,
0.035475507378578186,
-0.0035841006319969893,
-0.0678374320268631,
0.022234207019209862,
-0.020716939121484756,
-0.004904831759631634,
0.008944046683609486,
0.05240849778056145,
-0.008291167207062244,
-0.04243138059973717,
0.02360766939818859,
0.0039231982082128525,
0.021822744980454445,
-0.020378194749355316,
-0.023276325315237045,
0.03303832188248634,
-0.012903256341814995,
-0.019855763763189316,
0.005845219828188419,
0.027127349749207497,
-0.012432471849024296,
0.0008966129389591515,
-0.016418803483247757,
-0.01315539050847292,
0.005213526543229818,
-0.06673045456409454,
0.03271534666419029,
-0.011359700001776218,
-0.00005708480966859497,
0.003048533806577325,
0.07134588807821274,
0.03909637778997421,
-0.051160793751478195,
-0.0008715539006516337,
-0.059890229254961014,
-0.008681883104145527,
-0.0034580696374177933,
0.011370684951543808,
-0.004554275423288345,
0.012924326583743095,
-0.0385327972471714,
-0.020152240991592407,
-0.02930876426398754,
-0.030754754319787025,
0.03795711323618889,
0.016647372394800186,
0.04774271324276924,
0.041746459901332855,
-0.009504041634500027,
-0.01902513951063156,
-0.03675831854343414,
-0.000024811715775285847,
0.023273466154932976,
-0.014189312234520912,
0.0301594790071249,
-0.025444163009524345,
-0.018867887556552887,
0.023820828646421432,
0.031652115285396576,
-0.019710982218384743,
0.028222214430570602,
0.035430315881967545,
-0.0031484009232372046,
0.025991739705204964,
-0.03132271021604538,
-0.06432368606328964,
0.05687839165329933,
-0.03412993252277374,
0.052246131002902985,
0.009092218242585659,
-0.03755640238523483,
0.04060453176498413,
-0.02495349571108818,
0.026897402480244637,
-0.05205924063920975,
0.0029561349656432867,
-0.060797229409217834,
0.001803755760192871,
0.011601123958826065,
0.03355956822633743,
0.01592594012618065,
-0.008630745112895966,
-0.0075346496887505054,
-0.0004854838771279901,
0.010261033661663532,
0.0245575662702322,
-0.0620136633515358,
-0.005421220324933529,
-0.01420689933001995,
-0.0574948750436306,
0.021212562918663025,
-0.020273691043257713,
-0.007194662932306528,
0.008296187035739422,
-0.03279753029346466,
0.027402503415942192,
0.024555865675210953,
0.0006775170913897455,
-0.013445643708109856,
0.03734586015343666,
-0.020346932113170624,
0.02727620117366314,
-0.026774350553750992,
0.01984071359038353,
0.14686602354049683,
0.07550960779190063,
0.00517310993745923,
-0.05152427777647972,
0.011748332530260086,
-0.011553547345101833,
-0.006106616463512182,
-0.017321495339274406,
0.03634970635175705,
-0.016928652301430702,
0.034897755831480026,
0.016563288867473602,
0.0348394550383091,
0.0013229947071522474,
-0.030206268653273582,
0.03177296742796898,
-0.06069780886173248,
-0.02225746214389801,
0.001228749635629356,
0.037382107228040695,
0.007909298874437809,
0.021341072395443916,
-0.03387364745140076,
0.0023743656929582357,
0.02317509800195694,
0.009952584281563759,
-0.025640608742833138,
-0.061194974929094315,
-0.008447343483567238,
-0.02424025349318981,
-0.01452555600553751,
0.042444609105587006,
0.024716584011912346,
-0.01761607825756073,
-0.04499441012740135,
-0.019749395549297333,
0.015252020210027695,
0.003781616687774658,
0.004657968413084745,
0.005869464483112097,
0.0254302229732275,
-0.009173243306577206,
-0.008697707206010818,
-0.002122896257787943,
-0.05731223523616791,
0.00024845407460816205,
0.004290055949240923,
0.042187705636024475,
-0.03907041624188423,
0.01710009202361107,
-0.035495467483997345,
0.002524883020669222,
-0.002186583587899804,
-0.04116445407271385,
-0.021328747272491455,
0.007898141629993916,
0.047587085515260696,
-0.024791181087493896,
-0.06298333406448364,
0.005670410580933094,
-0.00850850623100996,
-0.02671319991350174,
0.04404876008629799,
-0.043353427201509476,
0.009594975039362907,
0.02095613069832325,
0.010530924424529076,
0.0163625068962574,
-0.014634680934250355,
0.015817079693078995,
-0.010131917893886566,
0.002931978553533554,
-0.0702168196439743,
-0.005147943273186684,
-0.013219138607382774,
-0.008513666689395905,
0.05595504865050316,
0.05011564865708351,
0.0036152182146906853,
-0.029317375272512436,
-0.0431036539375782,
0.012141070328652859,
-0.01864430494606495,
0.012705499306321144,
-0.017593277618288994,
0.013797663152217865,
0.0218491330742836,
0.04968583211302757,
-0.012306120246648788,
-0.0006102293264120817,
0.0351162888109684,
0.027350209653377533,
0.029647326096892357,
0.014570038765668869,
0.023290034383535385,
0.021147100254893303,
-0.045866288244724274,
-0.01396978460252285,
-0.016620328649878502,
0.01379950437694788,
0.02560628391802311,
0.014670389704406261,
0.0016957143088802695,
0.03595028817653656,
0.004052257630974054,
0.017955107614398003,
0.013993341475725174,
-0.029592834413051605,
-0.023869255557656288,
0.021672053262591362,
0.02850874699652195,
-0.021307621151208878,
-0.05089971423149109,
-0.02338319830596447,
0.012880115769803524,
0.005003250204026699,
0.020129969343543053,
-0.041736356914043427,
-0.01870873011648655,
-0.03328518196940422,
0.011719809845089912,
-0.05523986369371414,
-0.05069860443472862,
-0.019384464249014854,
0.0058966223150491714,
0.014537970535457134,
0.029823733493685722,
-0.005988490302115679,
0.04631371423602104,
0.0015454287640750408,
-0.05254954844713211,
0.03311612457036972,
0.005698331631720066,
-0.027949772775173187,
-0.0064324550330638885,
0.036551736295223236,
-0.01659301109611988,
0.048811350017786026,
-0.01028309017419815,
-0.03401153162121773,
0.014560929499566555,
-0.039697568863630295,
-0.08356121927499771,
0.02995464578270912,
0.003564185928553343,
0.020375072956085205,
0.04009666293859482,
-0.029954377561807632,
-0.034406792372465134,
0.03838611766695976,
-0.015555260702967644,
0.0025152896996587515,
0.0018744729459285736,
-0.0025976947508752346,
0.005127307027578354,
-0.012467371299862862,
0.012690898962318897,
0.002412809059023857,
-0.014825561083853245,
0.039914652705192566,
0.008009593933820724,
0.01386001892387867,
-0.028049223124980927,
-0.010089926421642303,
-0.03496332839131355,
0.00583915039896965,
0.01734994351863861,
0.013293808326125145,
0.03628478944301605,
0.04173289239406586,
-0.03361682966351509,
0.03800031170248985,
0.027895698323845863,
0.0001436400052625686,
-0.09322492778301239,
0.012000268325209618,
-0.006831429898738861,
0.0046806312166154385,
0.03398074954748154,
-0.02619798295199871,
0.04869970306754112,
0.017139310017228127,
-0.05104798078536987,
0.01613643392920494,
-0.011810023337602615,
-0.02684757299721241,
-0.0046891141682863235,
0.00312154833227396,
-0.028438957408070564,
0.07275606691837311,
0.05493897944688797,
0.06438682228326797,
0.02492799237370491,
0.03041340969502926,
-0.030120713636279106,
0.00006805734301451594,
-0.01402762159705162,
0.01601923443377018,
-0.02182554267346859,
0.008092046715319157,
0.03811243548989296,
-0.025593874976038933,
-0.026483098044991493,
0.03713249787688255,
-0.04045277088880539,
-0.007227263413369656,
0.006410690955817699,
0.04412025958299637,
0.0395490936934948,
0.026168160140514374,
0.03327719122171402,
0.00017470386228524148,
-0.023652058094739914,
0.03812414035201073,
0.005936616566032171,
0.007351725362241268,
0.009584028273820877,
-0.020168261602520943,
-0.004422944039106369,
-0.029255080968141556,
-0.013888992369174957,
0.012818495742976665,
-0.01860978454351425,
0.01008697785437107,
0.014543529599905014,
0.01864149607717991,
-0.018460627645254135,
0.025895744562149048,
0.014981585554778576,
-0.034731797873973846,
-0.01701187528669834,
0.02402305230498314,
-0.011347489431500435,
-0.052712369710206985,
-0.013445709832012653,
0.020784959197044373,
-0.028215697035193443,
0.027299432083964348,
-0.00725272111594677,
0.0025523463264107704,
-0.06383758038282394,
-0.014671246521174908,
-0.008423694409430027,
0.010112106800079346,
-0.01641874946653843,
-0.06357057392597198,
-0.05355198681354523,
0.03278419002890587,
0.004829783923923969,
0.0344904325902462,
0.004182520788162947,
-0.07537944614887238,
-0.0445072203874588,
-0.08474498242139816,
0.012286563403904438,
-0.008937706239521503,
0.023919526487588882,
-0.028423501178622246,
-0.019709857180714607,
-0.021568458527326584,
-0.020464040338993073,
0.0446346215903759,
0.02139742486178875,
-0.009338422678411007,
0.012432957999408245,
0.04415230453014374,
0.051864225417375565,
-0.00550680560991168,
0.02045205608010292,
-0.012482990510761738,
-0.0535491518676281,
0.019716210663318634,
-0.003984759096056223,
-0.017877383157610893,
0.002324607688933611,
0.008859515190124512,
-0.05514632165431976,
-0.002643205225467682,
-0.014075307175517082,
-0.02003972977399826,
0.09609571844339371,
0.0036073317751288414,
-0.039351705461740494,
0.06051260605454445,
-0.05262695252895355,
0.04489448666572571,
0.04252573475241661,
0.03646314516663551,
-0.04701852798461914,
0.026801476255059242,
-0.002801177790388465,
-0.04973422735929489,
0.02107364684343338,
0.0007359191658906639,
0.007617316208779812,
-0.004530799109488726,
-0.026246841996908188,
0.0432291254401207,
-0.040200404822826385,
0.03724512457847595,
0.031352151185274124,
-0.012939232401549816,
0.09581978619098663,
-0.0030241564381867647,
-0.038053736090660095,
0.012642105109989643,
0.0368359349668026,
-0.01949688419699669,
0.057957492768764496,
0.06420482695102692,
-0.0022582444362342358,
0.01638125814497471,
0.010665472596883774,
-0.0298788882791996,
0.021998031064867973,
0.013075783848762512,
0.019678235054016113,
-0.05240253359079361,
-0.04563672095537186,
0.026320572942495346,
-0.024015842005610466,
0.022558370605111122,
0.017457490786910057,
-0.012213174253702164,
0.08411534130573273,
0.0039102863520383835,
0.013717332854866982,
-0.024434709921479225,
-0.014674209989607334,
-0.039920635521411896,
0.01267261803150177,
-0.015124666504561901,
0.04097693786025047,
-0.008654761128127575,
-0.039411261677742004,
-0.037383005023002625,
0.01706523634493351,
0.02689911611378193,
-0.07077601552009583,
-0.01373268198221922,
0.006416584365069866,
0.026299389079213142,
-0.015027460642158985,
0.028435558080673218,
-0.029797416180372238,
-0.03196272999048233,
0.04215158894658089,
0.0186000969260931,
0.040467269718647,
-0.013855678960680962,
-0.012397355400025845,
-0.0392804890871048,
0.04310685768723488,
-0.009456231258809566,
0.0014663683250546455,
-0.02200702577829361,
0.04136885702610016,
-0.04531464725732803,
-0.04004838690161705
] |
<p>Let's have minimally extended gauge invariant lagrangian (with free kinetic term of EM field):
$$
\tag 1 L (\Psi , \partial_{\mu} \Psi) \to L (\Psi , D_{\mu}\Psi ) - \frac{1}{4}F^{\mu \nu}F_{\mu \nu}, \quad D_{\mu} = \partial_{\mu} - iQA_{\mu}.
$$
Here $A_{\mu}$ is given by $F_{\mu \nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}$ .</p>
<p>It is well-known result that for an arbitrary amplitude of EM process (I have cut here photon propagators and polarization vectors; all of operators here is given in Heisenberg picture)
$$
\tag 2 M^{\mu_{1}...\mu_{n}}(q_{1}, ..., q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{iq_{1}x_{1} + ...+iq_{n}x_{n}} \langle | \hat{T}\left( \hat{J}^{\mu_{1}}(x_{1})...\hat{J}^{\mu_{n}}(x_{n}) \right)|\rangle ,
$$
$$
\hat{J}^{\mu} = \hat{\bar{\Psi}}\gamma^{\mu}\hat{\Psi}, \quad \partial_{\mu}\hat{J}^{\mu} = 0,
$$
we have identity
$$
\tag 3 q_{\mu_{i}}M^{...\mu_{i}...} = 0.
$$
Let's have than non-zero photon mass. Then we will get modified photon propagators (so the new force law) and non-invariance of lagrangian, but $\hat{J}_{\mu}$ is still conserved, so it seems that $(2)$ still satisfies identity $(3)$. I have checked this statement for processes $WW^{+} \to \gamma \gamma$ and $e e^{+} \to \gamma \gamma$ at the lowest order.</p>
<p>But is this statement true in general? If yes, why we usually say that photon must have strictly zero mass (nonzero but very small mass doesn't contradict the experimental data)? I'm not interested in Higgs mechanism, because I'm not interested in exactly gauge invariance.</p>
| 10,800 |
[
0.011441197246313095,
0.00847105123102665,
0.01105295680463314,
-0.02644605003297329,
0.04373105987906456,
0.03592822700738907,
-0.027017490938305855,
-0.041668035089969635,
-0.0015888243215158582,
-0.03536912053823471,
0.06027674674987793,
-0.0030598361045122147,
0.07181850075721741,
0.008417680859565735,
-0.007608292158693075,
0.021962186321616173,
0.011383775621652603,
0.014021048322319984,
-0.01600688323378563,
-0.03449033573269844,
-0.017935650423169136,
0.07919488102197647,
-0.012390241958200932,
0.015238963067531586,
-0.04181014746427536,
0.03289366140961647,
0.023352866992354393,
0.01684928685426712,
-0.00583899300545454,
0.06441237032413483,
-0.007301703095436096,
-0.01457227487117052,
0.004003334790468216,
0.003982681781053543,
-0.017489464953541756,
0.018640141934156418,
0.000499874004162848,
-0.055628977715969086,
0.04338134452700615,
0.010974769480526447,
-0.046554677188396454,
-0.029144184663891792,
-0.045606646686792374,
0.008852861821651459,
-0.04221821948885918,
0.009021530859172344,
0.008760597556829453,
0.017427820712327957,
0.09166937321424484,
-0.034420400857925415,
0.08320798724889755,
0.003984890878200531,
0.030827559530735016,
-0.01319517008960247,
-0.013670695014297962,
-0.06665998697280884,
0.05899859219789505,
0.04482949897646904,
0.0368557870388031,
-0.06729447841644287,
-0.026833977550268173,
-0.03925320878624916,
0.006055811420083046,
-0.053265295922756195,
0.014838344417512417,
0.03972450643777847,
-0.0027979821898043156,
0.021769586950540543,
0.007267398294061422,
-0.0067373402416706085,
0.02327486127614975,
-0.014908305369317532,
0.044214703142642975,
0.004438160918653011,
-0.0010326061164960265,
0.018414968624711037,
-0.0014802493387833238,
0.010705473832786083,
0.01603972166776657,
0.005143261980265379,
0.007234332151710987,
0.02492561936378479,
0.029895324259996414,
0.010756234638392925,
-0.026726936921477318,
-0.02772425301373005,
0.052418164908885956,
-0.012079190462827682,
0.007848182693123817,
0.03783038258552551,
-0.010215641930699348,
0.015902020037174225,
0.06366976350545883,
-0.03357028588652611,
-0.016252340748906136,
0.013197658583521843,
0.02142595686018467,
0.03682190552353859,
-0.020518047735095024,
-0.029376139864325523,
-0.021605366840958595,
0.0024402805138379335,
-0.029156045988202095,
0.07452967762947083,
0.035724155604839325,
-0.01822132058441639,
-0.03623875975608826,
0.005094224587082863,
-0.050652313977479935,
-0.017506398260593414,
-0.030105479061603546,
0.01172433141618967,
-0.04515906050801277,
-0.021103274077177048,
-0.01854170300066471,
-0.04567389190196991,
0.016221346333622932,
-0.037751562893390656,
0.08971121907234192,
0.07375916838645935,
0.003748701186850667,
-0.03426525741815567,
-0.00038071483140811324,
-0.019496139138936996,
-0.05701165273785591,
-0.003581285709515214,
0.058883871883153915,
-0.0019312679069116712,
-0.030834631994366646,
0.007344874087721109,
0.027724428102374077,
-0.009469401091337204,
0.0010367014911025763,
0.013932502828538418,
-0.0008466188446618617,
-0.04008900001645088,
-0.09573514759540558,
-0.01859673298895359,
0.05185401067137718,
-0.021896865218877792,
0.009649673476815224,
-0.06305395066738129,
-0.033065877854824066,
0.04836060479283333,
0.108177550137043,
-0.006981926504522562,
0.03668184205889702,
0.006905929185450077,
0.02168383076786995,
-0.00030548032373189926,
0.02439967170357704,
-0.0028153788298368454,
-0.02497974969446659,
-0.022433152422308922,
-0.046395525336265564,
-0.05634354427456856,
0.02992929331958294,
0.04472825676202774,
-0.020354952663183212,
0.010251245461404324,
0.0842347964644432,
-0.020456930622458458,
0.03454479202628136,
-0.009601914323866367,
-0.014536065049469471,
-0.0379832461476326,
0.041874583810567856,
0.0007010670378804207,
-0.0110517842695117,
0.023523373529314995,
-0.012631499208509922,
0.01483274344354868,
-0.017758110538125038,
0.01858401484787464,
0.005452136509120464,
-0.04596440866589546,
-0.03192219138145447,
-0.028089234605431557,
0.005884746089577675,
-0.017388245090842247,
-0.011695493012666702,
-0.02323186583817005,
-0.07585166394710541,
0.01676253415644169,
0.004009352531284094,
-0.0011070814216509461,
-0.009687702171504498,
0.0075538866221904755,
-0.007193933241069317,
-0.046368926763534546,
-0.016460642218589783,
-0.0671464055776596,
0.029525674879550934,
0.02906462363898754,
-0.036011356860399246,
0.043497178703546524,
-0.021931301802396774,
-0.010850588791072369,
0.008564016781747341,
-0.03776225447654724,
0.00021085455955471843,
0.023237237706780434,
0.007920571602880955,
0.012198829092085361,
0.04086543992161751,
0.028659570962190628,
0.005461885593831539,
0.031279388815164566,
0.048391275107860565,
-0.03757162019610405,
-0.023408329114317894,
0.014845176599919796,
-0.01297851838171482,
0.02247580513358116,
0.00344568258151412,
0.02024856023490429,
0.00846593827009201,
-0.013637056574225426,
-0.029861975461244583,
0.009335387498140335,
-0.039928123354911804,
0.04795847088098526,
0.02413463592529297,
-0.03374076262116432,
0.019354598596692085,
0.039791934192180634,
-0.008440634235739708,
0.048448845744132996,
-0.010453972965478897,
-0.028723279014229774,
-0.03403131291270256,
-0.02483251877129078,
0.014650733210146427,
0.044669121503829956,
-0.032933663576841354,
0.03263690695166588,
0.011850131675601006,
0.03549189865589142,
0.015210617333650589,
-0.003322686767205596,
-0.02027702145278454,
-0.06623724102973938,
0.047345396131277084,
0.04122796654701233,
-0.018941879272460938,
-0.015412447974085808,
0.012412075884640217,
-0.018906401470303535,
0.006083603948354721,
-0.0027144523337483406,
-0.035422418266534805,
-0.0047923494130373,
-0.02329203300178051,
-0.038053009659051895,
-0.019922086969017982,
-0.028905881568789482,
0.03210948035120964,
-0.0149497389793396,
0.04435988515615463,
0.02923264168202877,
-0.019387366250157356,
-0.004444919992238283,
-0.03625226393342018,
-0.04696828871965408,
0.011009059846401215,
-0.02549065090715885,
0.0060925912111997604,
-0.013925006613135338,
-0.005303964950144291,
-0.03334769234061241,
0.01596745103597641,
-0.021459290757775307,
-0.028884943574666977,
-0.01042343582957983,
-0.019657865166664124,
0.03540138155221939,
0.06302709132432938,
0.00429152324795723,
-0.028418604284524918,
-0.008573684841394424,
0.040491100400686264,
0.0047186268493533134,
0.05881940573453903,
0.02711661159992218,
-0.019640257582068443,
-0.045999202877283096,
-0.054295800626277924,
-0.02429843693971634,
0.03073558211326599,
-0.004471614025533199,
0.022053701803088188,
0.022210456430912018,
0.0062085650861263275,
-0.05080278590321541,
-0.030088555067777634,
0.003746399423107505,
-0.01801539771258831,
-0.020679466426372528,
-0.019765561446547508,
0.05718136206269264,
0.026229238137602806,
-0.040646303445100784,
-0.024140765890479088,
-0.0073125711642205715,
-0.037784233689308167,
-0.03169091045856476,
0.011603017337620258,
0.006624680012464523,
-0.04409204423427582,
0.0732654333114624,
0.04408073052763939,
-0.019326776266098022,
0.004625878296792507,
-0.048519037663936615,
-0.004146446939557791,
0.03147347643971443,
0.000498035573400557,
0.016093235462903976,
0.012033933773636818,
-0.04469899460673332,
0.07553745061159134,
0.04686998203396797,
-0.01567857339978218,
-0.04173034057021141,
0.0022448673844337463,
-0.018795551732182503,
-0.05153988301753998,
-0.007833322510123253,
0.005539019126445055,
-0.007845794782042503,
0.00840035267174244,
0.039115555584430695,
0.01872434839606285,
-0.0036139576695859432,
0.004873216617852449,
0.00832129642367363,
0.03031659498810768,
-0.013119475916028023,
0.003293524030596018,
0.06493949145078659,
0.0011304091894999146,
0.005798173137009144,
-0.0022458937019109726,
0.033393606543540955,
0.004760006442666054,
-0.02128325030207634,
-0.036353375762701035,
0.06622491776943207,
0.038001567125320435,
0.01931862346827984,
-0.03478486090898514,
0.024731900542974472,
-0.01696411333978176,
-0.045965805649757385,
-0.02335166372358799,
0.030841849744319916,
-0.002798608038574457,
-0.03186928853392601,
0.022522099316120148,
0.03582703694701195,
0.01809023693203926,
-0.01355790439993143,
-0.025840505957603455,
-0.005106670316308737,
-0.0540895015001297,
0.02667986787855625,
-0.0401664674282074,
-0.023913517594337463,
0.02127748914062977,
0.022152477875351906,
0.002394428476691246,
-0.009310146793723106,
-0.005250494461506605,
-0.03177695721387863,
-0.02436644956469536,
0.023460105061531067,
0.005234427750110626,
0.034823227673769,
0.01886999048292637,
0.05154476314783096,
0.003916495945304632,
0.00010228560131508857,
-0.028602875769138336,
0.02601582370698452,
-0.08448541164398193,
0.01582317054271698,
-0.008032754994928837,
0.00797177478671074,
0.017145883291959763,
-0.03230056166648865,
0.004889948293566704,
-0.016905782744288445,
-0.016637464985251427,
-0.030548730865120888,
-0.022507114335894585,
-0.02089572325348854,
0.01473266165703535,
-0.05272580310702324,
-0.02339266985654831,
-0.01447659358382225,
0.05940483137965202,
0.017085343599319458,
-0.013892949558794498,
-0.04221257194876671,
0.017742687836289406,
-0.025715317577123642,
-0.009698223322629929,
-0.010106927715241909,
0.024464605376124382,
0.05741304159164429,
0.02427208051085472,
0.036522503942251205,
0.0022182371467351913,
-0.04218859598040581,
-0.015044430270791054,
0.05356728658080101,
0.03521304205060005,
0.03461861237883568,
0.0016377896536141634,
-0.004794504959136248,
-0.052455827593803406,
-0.010821796022355556,
0.008837329223752022,
0.07035433501005173,
0.0390908382833004,
-0.019576692953705788,
0.031144173815846443,
-0.008970986120402813,
-0.010241392068564892,
0.02753933146595955,
0.034668322652578354,
0.023413514718413353,
-0.02042762190103531,
-0.06032629683613777,
0.03473139554262161,
0.002254754537716508,
-0.009691505692899227,
-0.0027729510329663754,
-0.00008059231913648546,
-0.01286687795072794,
-0.004266684874892235,
0.008450695313513279,
0.046553246676921844,
-0.005716983694583178,
-0.01522084791213274,
0.003633455839008093,
-0.009174128994345665,
0.020033637061715126,
-0.0021555228158831596,
0.022557323798537254,
0.03934234380722046,
0.013735899701714516,
0.004915919154882431,
0.025502506643533707,
-0.06703921407461166,
0.006967827212065458,
0.030922213569283485,
0.041994135826826096,
0.0014700553147122264,
-0.01175760943442583,
-0.014180595986545086,
0.010281701572239399,
0.010707949288189411,
0.0005684272618964314,
0.047452639788389206,
0.028959767892956734,
-0.017117226496338844,
-0.014781502075493336,
-0.02113226242363453,
-0.05247827619314194,
0.03626462072134018,
-0.007173670455813408,
-0.028438221663236618,
-0.026958085596561432,
0.011712901294231415,
0.018171971663832664,
0.018167275935411453,
-0.015961142256855965,
0.03134358301758766,
0.009421475231647491,
0.004814342129975557,
0.008958944119513035,
0.023969613015651703,
-0.005519095342606306,
-0.11929058283567429,
0.006347069516777992,
0.006808529142290354,
-0.04260002076625824,
0.04055525362491608,
-0.020598215982317924,
-0.04743330180644989,
0.015064713545143604,
0.017344363033771515,
0.021072305738925934,
0.006853941362351179,
-0.06980239599943161,
0.03195246681571007,
-0.013364911079406738,
-0.05195442959666252,
0.052370790392160416,
0.053525760769844055,
-0.0340876467525959,
0.00688296789303422,
-0.026156071573495865,
0.040071550756692886,
-0.027514640241861343,
0.007241846993565559,
-0.03434803709387779,
0.01278986968100071,
0.0043868618085980415,
0.04427047818899155,
-0.038571082055568695,
0.023882301524281502,
0.002097456017509103,
-0.0032903256360441446,
-0.0003841678553726524,
0.018568847328424454,
-0.028784766793251038,
-0.019596029072999954,
-0.016178973019123077,
0.010828999802470207,
-0.006198779679834843,
-0.01444296445697546,
0.005044518504291773,
0.008551734499633312,
0.009002523496747017,
0.03170767053961754,
-0.004410420544445515,
-0.020485959947109222,
-0.018622545525431633,
-0.028669903054833412,
-0.004382343031466007,
-0.012565000914037228,
0.030442511662840843,
0.011390583589673042,
0.013030586764216423,
0.003887823550030589,
0.00147711590398103,
-0.04608874395489693,
0.010129053145647049,
-0.04297434911131859,
0.03137580677866936,
-0.01222932804375887,
0.007283322047442198,
0.0032349317334592342,
0.016848983243107796,
-0.08936446905136108,
-0.015472968108952045,
-0.00994475930929184,
-0.046200815588235855,
0.009613378904759884,
-0.025286436080932617,
-0.00329040689393878,
-0.026030130684375763,
-0.050190094858407974,
-0.0008362941443920135,
0.06509275734424591,
-0.036157816648483276,
0.013975483365356922,
0.009887895546853542,
0.020814618095755577,
0.013087047263979912,
-0.029033808037638664,
-0.03682120144367218,
-0.005680907983332872,
0.0012111472897231579,
-0.013291954062879086,
0.011113615706562996,
0.035121504217386246,
0.0071264514699578285,
-0.04514157027006149,
-0.014963495545089245,
-0.028189120814204216,
-0.0037022288888692856,
-0.014218687079846859,
-0.014498686417937279,
0.03561927750706673,
0.04140337556600571,
0.01266702450811863,
-0.030031844973564148,
-0.03568347916007042,
0.007445988245308399,
0.02998838759958744,
0.012528900057077408,
-0.020718950778245926,
0.014742247760295868,
-0.04347226396203041,
0.04489999637007713,
-0.022554179653525352,
0.01782863587141037,
0.004735535942018032,
0.05328245460987091,
0.0025461260229349136,
-0.016315296292304993,
0.015879688784480095,
-0.02295161783695221,
-0.00676828995347023,
-0.038919877260923386,
0.02910350076854229,
-0.0037585548125207424,
0.009007523767650127,
-0.01707381382584572,
-0.018516024574637413,
-0.04911418631672859,
0.011998468078672886,
0.053544528782367706,
0.029613427817821503,
0.02466263435781002,
0.00017696490976959467,
-0.0014130211202427745,
-0.015994008630514145,
-0.026062753051519394,
-0.014719107188284397,
0.02850186452269554,
-0.01324370689690113,
0.03954261913895607,
-0.026658035814762115,
0.008224003948271275,
0.049704987555742264,
0.0229104645550251,
-0.05828644335269928,
0.00021876847313251346,
0.012400257401168346,
0.03771505132317543,
-0.006077094003558159,
-0.010362645611166954,
-0.049456942826509476,
0.04866722598671913,
-0.05022205039858818,
0.014621846377849579,
0.03496844321489334,
-0.005645631812512875,
0.013942033983767033,
0.037053730338811874,
0.023450162261724472,
0.0026855268515646458,
-0.005644067190587521,
-0.04316044598817825,
0.04672187939286232,
0.030141420662403107,
-0.015406434424221516,
0.01037217490375042,
0.013614732772111893,
0.040657322853803635,
-0.01395094208419323,
0.019311128184199333,
0.021468814462423325,
-0.035788122564554214,
-0.028493201360106468,
-0.027227871119976044,
-0.039725225418806076,
0.08971966803073883,
-0.042921535670757294,
-0.014980700798332691,
-0.014012813568115234,
-0.0023941854014992714,
0.05290299281477928,
0.02320035547018051,
0.020050859078764915,
-0.01728670671582222,
0.043883804231882095,
-0.009937853552401066,
0.008014251478016376,
-0.007042806129902601,
0.014057549647986889,
0.1378677934408188,
0.03844431787729263,
0.007682417519390583,
-0.053649600595235825,
-0.00765259237959981,
-0.009085457772016525,
0.01661219447851181,
-0.025036798790097237,
0.01969301700592041,
-0.015861889347434044,
-0.04447777941823006,
-0.037060994654893875,
0.04392335191369057,
-0.007433359511196613,
-0.002265972550958395,
0.05365530028939247,
-0.01399526558816433,
-0.06913616508245468,
0.012385215610265732,
0.03378984332084656,
-0.016961203888058662,
0.008853974752128124,
-0.06297187507152557,
0.020873602479696274,
-0.028003646060824394,
0.02287987805902958,
-0.007423515431582928,
-0.0201373603194952,
-0.01147471833974123,
-0.02593976818025112,
-0.04903458058834076,
-0.041572537273168564,
-0.039548635482788086,
-0.010203074663877487,
-0.03748272731900215,
0.004978379234671593,
-0.0011474894126877189,
-0.04469602555036545,
0.04081941395998001,
0.0380823127925396,
0.014020842500030994,
0.01192384772002697,
0.04415911063551903,
-0.008733248338103294,
-0.018389156088232994,
0.030169617384672165,
-0.012178231030702591,
0.0828632265329361,
0.0023433028254657984,
0.019753260537981987,
0.02075785957276821,
-0.02610900066792965,
-0.0048384577967226505,
-0.013225268572568893,
-0.004488340578973293,
0.008398743346333504,
0.02823972888290882,
-0.017517725005745888,
0.019953109323978424,
0.01600160077214241,
0.024998359382152557,
0.04658760502934456,
0.026422062888741493,
-0.043504200875759125,
0.002623239066451788,
-0.019467491656541824,
0.0001904286618810147,
0.021230734884738922,
-0.000741082476451993,
-0.03208991140127182,
-0.0022458077874034643,
-0.038722481578588486,
-0.009117855690419674,
-0.059832148253917694,
0.03465091809630394,
0.011492992751300335,
0.04843137040734291,
0.002500722883269191,
0.010418523102998734,
-0.030693816021084785,
-0.06162232533097267,
0.008394473232328892,
-0.012744585983455181,
-0.009068700484931469,
0.014639956876635551,
-0.011597405187785625,
-0.003050359897315502,
0.052341971546411514,
0.0028941440396010876,
0.00048597820568829775,
0.03736855089664459,
0.041509274393320084,
0.03685874864459038,
-0.028103169053792953,
-0.02095792628824711,
0.01949545368552208,
0.023750241845846176,
0.006117569282650948,
-0.045908018946647644,
0.0013223994756117463,
0.01989576779305935,
0.016256282106041908,
-0.005033427383750677,
0.05073172599077225,
-0.015153237618505955,
-0.050002291798591614,
-0.02136141061782837,
0.0168890580534935,
0.02498180791735649,
0.03471997007727623,
0.03192809969186783,
-0.06201766058802605,
-0.03689693287014961,
-0.005730133969336748,
0.008264156058430672,
-0.0030667854007333517,
-0.013660045340657234,
-0.049634408205747604,
-0.019745640456676483,
-0.024035165086388588,
0.030342301353812218,
0.005035311449319124,
-0.03842784836888313,
-0.024341367185115814,
0.0004879315383732319,
-0.046078335493803024,
-0.009735927917063236,
-0.006334912963211536,
0.015744399279356003,
0.005469831638038158,
-0.02479630708694458,
-0.006799030117690563,
0.06169528886675835,
-0.01493464782834053,
-0.020360272377729416,
0.002347384113818407,
0.003491370938718319,
0.0009413579828105867,
0.02805834636092186,
-0.039605483412742615,
0.014627550728619099,
-0.025176269933581352,
-0.03342464938759804,
0.06947001069784164,
0.020479245111346245,
0.047634199261665344,
0.04164445027709007,
-0.0261661559343338,
-0.02319205179810524,
0.04683148115873337,
-0.016690507531166077,
-0.008700896985828876,
-0.031243499368429184,
-0.05059337243437767,
-0.012194579467177391,
-0.03225024417042732,
0.005061368923634291,
0.015614191070199013,
-0.028989890590310097,
0.007777167484164238,
0.016452718526124954,
-0.004075055010616779,
-0.024904396384954453,
0.017575977370142937,
-0.010609381832182407,
0.01843419298529625,
0.01138328667730093,
0.009009987115859985,
0.012119574472308159,
0.04705870896577835,
0.008040745742619038,
0.0006917144637554884,
-0.026198113337159157,
0.0380123108625412,
-0.11829780787229538,
-0.04236747324466705,
0.005284150131046772,
0.06439725309610367,
0.10288086533546448,
-0.05073597654700279,
0.035568755120038986,
0.026230724528431892,
-0.06904236972332001,
0.03288443386554718,
-0.009965218603610992,
0.007097078021615744,
0.004318132996559143,
0.014108428731560707,
-0.010370361618697643,
0.06520874053239822,
0.014605829492211342,
0.04069240391254425,
0.006558232009410858,
0.03575655445456505,
0.0031157031189650297,
-0.00013232330093160272,
-0.05209735780954361,
0.024952679872512817,
0.0474335141479969,
-0.021542755886912346,
0.08419440686702728,
-0.013469493947923183,
-0.015949977561831474,
0.014667147770524025,
0.01919679157435894,
-0.00427674874663353,
-0.012687142938375473,
0.048276711255311966,
0.02572050504386425,
0.02215353585779667,
-0.0017725289799273014,
-0.02477785013616085,
0.031162496656179428,
-0.015100705437362194,
0.04555510729551315,
0.04595474153757095,
-0.014474958181381226,
0.011344988830387592,
0.02035146951675415,
-0.03503597527742386,
-0.043382205069065094,
0.03740789368748665,
-0.002455515554174781,
-0.04645587503910065,
0.015086478553712368,
-0.0051467204466462135,
-0.012387342751026154,
-0.00918339192867279,
0.03850919380784035,
-0.055138684809207916,
-0.01675749383866787,
0.011861574836075306,
0.018614348024129868,
0.031010767444968224,
0.02162403240799904,
0.004433604422956705,
-0.013458238914608955,
0.027058349922299385,
0.011842397041618824,
-0.01478596031665802,
-0.04846833273768425,
0.005730681587010622,
-0.008383238688111305,
-0.005926916375756264,
0.00878422986716032,
-0.025444598868489265,
-0.07427205890417099,
-0.009815629571676254,
0.001602108241058886,
0.006232954561710358,
-0.024993818253278732,
0.0040259272791445255,
0.009688334539532661,
-0.0690871849656105,
0.03795132040977478,
0.003236643970012665,
-0.014998157508671284,
-0.021531298756599426,
0.004632113967090845,
0.010403376072645187,
0.009445885196328163,
0.07057179510593414,
0.0017367120599374175,
-0.045351482927799225,
0.018791131675243378,
-0.0010791688691824675,
-0.010433492250740528,
-0.01598549447953701,
-0.011534499004483223,
-0.01363329403102398,
0.04611074924468994,
-0.012489558197557926,
0.03864966705441475,
-0.02990603819489479,
0.05315534025430679,
-0.020533738657832146,
-0.0028484463691711426,
0.022910568863153458,
0.02434505894780159,
-0.04272894933819771,
0.0396532267332077,
-0.018033910542726517,
-0.0422728955745697,
0.018855633214116096,
-0.007520583458244801,
0.02307431399822235,
0.021405279636383057,
-0.049716267734766006,
-0.06337465345859528,
0.00014965601440053433,
-0.0014550855848938227,
0.00015535637794528157,
-0.017672454938292503,
0.019436819478869438,
0.0254230834543705,
-0.015880903229117393,
0.014640302397310734,
0.04241802543401718,
-0.01710977591574192,
-0.021714527159929276,
0.04582953453063965,
0.022656382992863655,
0.04264957830309868,
0.04387596622109413,
0.03871852532029152,
-0.007151709403842688,
-0.004562445916235447,
0.04554570093750954,
0.02261815406382084,
0.00037287655868567526,
-0.02024225890636444,
0.008750306442379951,
0.009244559332728386,
-0.015171226114034653,
0.006250094156712294,
0.02409129962325096,
0.011039524339139462,
-0.02629939280450344,
0.013025185093283653,
0.0445021390914917,
0.0011669042287394404,
0.04634924605488777,
0.0007915371097624302,
-0.011052960529923439,
0.06905421614646912,
-0.04217546060681343,
0.006772039923816919,
-0.00958670862019062,
0.02036285027861595,
0.007316182367503643,
0.039004962891340256,
-0.004348378628492355,
0.09679510444402695,
-0.012257865630090237,
-0.03442633897066116,
-0.02157200686633587,
-0.024855496361851692,
-0.013699456118047237,
-0.04574369266629219,
-0.009371775202453136,
0.023940613493323326,
-0.0051329066045582294,
0.01991795189678669,
-0.05587121844291687,
-0.0044604153372347355,
-0.01792135275900364,
0.002902693348005414,
0.01631675474345684,
0.023530058562755585,
0.02514072321355343,
-0.011938318610191345,
-0.04413484036922455,
0.055889587849378586,
0.005788175389170647,
-0.028660768643021584,
-0.01388847827911377,
-0.0005328953266143799,
0.003845586907118559,
-0.004696318879723549
] |
<p>In Peskin and Schroeder p. 669 it is argued that the axial current can be parametrized between the vacuum and an on-shell pion state as:</p>
<p>$$<0|j^{\mu 5}(x)|\pi^b(p)>=-ip^\mu f_\pi \delta^{ab}e^{-ipx}$$</p>
<p>This is then described as a parametrization of the amplitude for the axial current to create a pion state from the vacuum. This interpretation puzzles me: isn't it the role of the creation operators of a given theory to do this? Does the above expression correspond to an actual physical process or is it just part of an amplitude in a Feynman diagram for an actual process?</p>
| 10,801 |
[
0.04520553722977638,
-0.0031630799639970064,
0.015019566752016544,
-0.00079199334140867,
-0.003488589311018586,
0.013179421424865723,
-0.00680969376116991,
0.00019168101425748318,
-0.010058180429041386,
0.03274364396929741,
0.023991886526346207,
0.0027511329390108585,
0.05165627598762512,
-0.0065119341015815735,
-0.0029249368235468864,
0.05764445289969444,
0.027504701167345047,
-0.01635146141052246,
-0.009459152817726135,
-0.02365654706954956,
-0.0003580096527002752,
0.06848423928022385,
0.0036049899645149708,
0.0029317326843738556,
-0.02253129333257675,
0.024115221574902534,
0.020039169117808342,
0.04859465733170509,
-0.022547967731952667,
0.048667896538972855,
0.024023622274398804,
-0.020858673378825188,
-0.007106180302798748,
0.026325318962335587,
0.006767152342945337,
0.00981360673904419,
-0.025547312572598457,
-0.051851771771907806,
0.0044004530645906925,
0.033851221203804016,
-0.0302661694586277,
-0.023754499852657318,
-0.02066056802868843,
0.028596822172403336,
-0.017493000254034996,
-0.001244247774593532,
-0.009160438552498817,
-0.01147185917943716,
0.04023096337914467,
-0.044615283608436584,
0.041539669036865234,
0.04683572053909302,
0.01591779664158821,
-0.008288698270916939,
0.01108874287456274,
-0.00019911011622752994,
0.08838912099599838,
0.028841668739914894,
0.013868642970919609,
-0.06637797504663467,
-0.029700595885515213,
-0.02395498938858509,
-0.035109467804431915,
-0.009467720985412598,
-0.007174176629632711,
-0.007700481452047825,
0.036935076117515564,
-0.005730533041059971,
-0.01338957343250513,
0.009062022902071476,
0.025556985288858414,
0.022615447640419006,
0.015073093585669994,
-0.014222190715372562,
0.021437667310237885,
0.009185501374304295,
-0.005630842875689268,
-0.01808835193514824,
0.02537815272808075,
0.04399658739566803,
-0.02735336497426033,
-0.008549965918064117,
0.007399383001029491,
0.05194916948676109,
-0.011406498961150646,
0.0024897432886064053,
0.07723738253116608,
-0.04338713735342026,
0.00525593850761652,
-0.011513757519423962,
-0.03166649118065834,
0.002722334349527955,
0.034156013280153275,
0.011288568377494812,
-0.029508201405405998,
0.028016790747642517,
-0.015373505651950836,
0.06740479171276093,
0.014663809910416603,
0.014991287142038345,
-0.0035844685044139624,
0.0018964034970849752,
-0.014144187793135643,
0.032835204154253006,
-0.02801229991018772,
0.012181663885712624,
-0.010744634084403515,
0.015521424822509289,
-0.010490033775568008,
-0.01610465720295906,
-0.09970341622829437,
0.0013152064057067037,
-0.052557069808244705,
0.03840416669845581,
0.0075032878667116165,
-0.04416453093290329,
0.01351760234683752,
-0.020464908331632614,
0.051089443266391754,
-0.0014892370672896504,
0.036519285291433334,
-0.012818598188459873,
0.07524518668651581,
-0.028229832649230957,
-0.07037729769945145,
-0.025268957018852234,
0.004280288238078356,
-0.010236892849206924,
-0.044501516968011856,
0.029589185491204262,
0.005854135844856501,
0.015994999557733536,
-0.003228431101888418,
-0.00958284828811884,
0.007190155331045389,
-0.043584614992141724,
-0.06978978216648102,
-0.048240482807159424,
0.012300144881010056,
0.006741884630173445,
-0.027040783315896988,
-0.0849006399512291,
-0.027006028220057487,
0.04536737501621246,
0.06747820973396301,
-0.019397446885704994,
-0.030177267268300056,
0.00534037034958601,
0.013969913125038147,
0.010220267809927464,
-0.05611640587449074,
-0.04114324226975441,
-0.0258173868060112,
-0.057171259075403214,
-0.016858771443367004,
-0.040226925164461136,
0.03653820976614952,
0.05102024972438812,
0.008861085399985313,
-0.01102657150477171,
0.03843758627772331,
-0.03780437260866165,
0.02618952840566635,
0.02409915067255497,
0.00809810683131218,
0.00997564010322094,
0.050605658441782,
0.04714434593915939,
-0.027045534923672676,
0.06865976005792618,
0.004591310862451792,
0.04588798061013222,
0.013594048097729683,
0.026415038853883743,
0.04475623369216919,
-0.07027391344308853,
-0.02843543328344822,
-0.03293853998184204,
0.04333037510514259,
-0.0057001542299985886,
-0.007487896829843521,
-0.010521460324525833,
-0.019277459010481834,
-0.009461385197937489,
-0.021602896973490715,
0.008607953786849976,
-0.020662477239966393,
0.0035089366137981415,
0.0010881932685151696,
-0.07086510211229324,
-0.005693249870091677,
-0.04551396518945694,
-0.007969717495143414,
0.03724479302763939,
-0.013232538476586342,
0.04548583924770355,
-0.02201235108077526,
0.0181119441986084,
-0.01793750748038292,
-0.07416409254074097,
0.0027121850289404392,
0.016689805313944817,
0.029528385028243065,
0.009143507108092308,
-0.012293958105146885,
0.016786975786089897,
0.006211603991687298,
0.01304448302835226,
0.03650403395295143,
-0.02371940016746521,
-0.024031100794672966,
-0.04385272040963173,
0.021500414237380028,
0.03881720080971718,
-0.007099596783518791,
0.017091892659664154,
0.011489995755255222,
-0.02145475707948208,
-0.004469872917979956,
0.012369242496788502,
-0.05382771044969559,
0.057652007788419724,
0.056615639477968216,
0.02928924188017845,
-0.01001797802746296,
0.0062159947119653225,
0.004641175735741854,
0.033943597227334976,
0.005440463777631521,
-0.027564095333218575,
-0.04751205071806908,
-0.0224357470870018,
0.03302326798439026,
0.02741861157119274,
-0.013911846093833447,
0.049918945878744125,
0.0443449504673481,
0.012411999516189098,
0.024149704724550247,
0.032193418592214584,
-0.01483491063117981,
0.012419736944139004,
0.06299515813589096,
0.03452565521001816,
-0.0011014945339411497,
0.0038949651643633842,
0.05536958947777748,
0.0038043493404984474,
0.023693138733506203,
-0.02384561114013195,
-0.03884320333600044,
0.018101373687386513,
-0.06176740676164627,
0.013349202461540699,
-0.020907852798700333,
-0.033242449164390564,
0.02365637756884098,
-0.027126559987664223,
0.06773784756660461,
0.025996720418334007,
-0.010150137357413769,
-0.007272640243172646,
-0.03531436622142792,
0.0013593174517154694,
0.020027130842208862,
-0.04344683513045311,
-0.010165801271796227,
-0.008021448738873005,
0.017350265756249428,
-0.014849985018372536,
0.032472867518663406,
0.015371344983577728,
0.019347023218870163,
-0.012182323262095451,
0.017195535823702812,
0.03612535819411278,
0.006140954326838255,
0.05577322840690613,
-0.03281697258353233,
-0.030635373666882515,
0.0082987817004323,
-0.003644354408606887,
0.04401452839374542,
0.05169112607836723,
-0.042578257620334625,
0.002176612848415971,
-0.04622843861579895,
-0.017794551327824593,
0.021965624764561653,
-0.027669142931699753,
0.002332738833501935,
-0.017275210469961166,
-0.029081666842103004,
-0.03294019028544426,
0.0013110541040077806,
-0.0031023845076560974,
-0.0020575851667672396,
0.025350693613290787,
0.012172305025160313,
-0.004252158105373383,
0.04154134914278984,
-0.04232494905591011,
0.02384101413190365,
-0.016239933669567108,
-0.06592778116464615,
0.0009520044550299644,
-0.003120663808658719,
0.01876780018210411,
-0.049231287091970444,
0.04231495410203934,
0.026690172031521797,
-0.03155898302793503,
0.021160129457712173,
-0.008636541664600372,
-0.004169274587184191,
0.011839625425636768,
-0.01645093970000744,
-0.01620136946439743,
0.0009053782559931278,
-0.04163520038127899,
0.10774505138397217,
0.026940256357192993,
-0.051273930817842484,
-0.01227656565606594,
0.01627309061586857,
-0.02376171201467514,
-0.01598401926457882,
-0.04433145001530647,
0.07179749757051468,
0.00595856225118041,
0.03918450325727463,
0.005621748510748148,
0.026392430067062378,
0.014234366826713085,
-0.0034746122546494007,
-0.04436580836772919,
0.03856133669614792,
-0.013081810437142849,
-0.004819080233573914,
0.01271242555230856,
-0.025700490921735764,
-0.014523184858262539,
-0.035852786153554916,
0.0244845412671566,
0.015996811911463737,
-0.015423689968883991,
-0.029286038130521774,
0.06683854013681412,
0.001257741474546492,
0.0032034635078161955,
-0.017500758171081543,
0.022366605699062347,
-0.04823432117700577,
-0.029325492680072784,
-0.011577943339943886,
0.015303254127502441,
-0.005673587322235107,
-0.03367694094777107,
-0.026828572154045105,
0.03408142179250717,
-0.004542720038443804,
-0.024516865611076355,
-0.0026754646096378565,
-0.006249517668038607,
-0.005552786402404308,
0.02310754731297493,
-0.010165940038859844,
-0.026715675368905067,
-0.0032351037953048944,
0.015715787187218666,
-0.011557687073946,
0.008448782376945019,
-0.0518752746284008,
-0.004011635668575764,
-0.058804914355278015,
-0.03404802829027176,
-0.010337939485907555,
0.030615175142884254,
0.03794104605913162,
0.06373690813779831,
0.0019317514961585402,
-0.009904932230710983,
-0.0000304695622617146,
-0.024005429819226265,
-0.06250787526369095,
0.0032207705080509186,
-0.036984868347644806,
0.006537832319736481,
-0.0419556200504303,
-0.02591870166361332,
0.0036470836494117975,
-0.017883818596601486,
-0.04758785292506218,
-0.011795474216341972,
-0.02656257338821888,
-0.04214184358716011,
0.0008288153912872076,
-0.009062067605555058,
0.0009431016515009105,
-0.03288320451974869,
0.00036073141382075846,
0.08290471136569977,
-0.005135538522154093,
0.042630068957805634,
-0.007412394043058157,
-0.034303367137908936,
-0.013325875625014305,
-0.003955794032663107,
0.02879265509545803,
0.04024237021803856,
-0.00845411978662014,
0.057876165956258774,
0.050337787717580795,
-0.01865028403699398,
-0.006887279916554689,
0.05327952653169632,
0.05666336044669151,
0.053055401891469955,
-0.052477892488241196,
0.010068174451589584,
-0.0402984619140625,
-0.020344574004411697,
0.029578080400824547,
0.057501841336488724,
0.0154429841786623,
0.04281560704112053,
0.02320391684770584,
0.007044666912406683,
0.010947351343929768,
0.01259569637477398,
0.08444327116012573,
0.0202068742364645,
-0.04234057292342186,
-0.04673582315444946,
0.04283517971634865,
-0.013624124228954315,
-0.009913460351526737,
-0.02422082982957363,
0.009556382894515991,
-0.011271351017057896,
-0.01722981221973896,
-0.00285980012267828,
-0.0006637479527853429,
-0.02474311925470829,
0.0012821982381865382,
0.004623538814485073,
-0.028373761102557182,
0.009473931044340134,
0.0016860106261447072,
0.06782201677560806,
0.05427602678537369,
0.026601940393447876,
0.049439914524555206,
-0.030314020812511444,
-0.048357367515563965,
-0.006316335406154394,
0.009573395363986492,
0.04255339875817299,
0.005419979803264141,
-0.009140550158917904,
-0.07117608934640884,
-0.00850207544863224,
0.03039454109966755,
-0.007920944131910801,
0.012470387853682041,
-0.029710475355386734,
0.015788113698363304,
0.016736026853322983,
-0.01039830967783928,
-0.025938527658581734,
0.04759681597352028,
0.00032168705365620553,
-0.005409225355833769,
-0.069624163210392,
-0.021565977483987808,
0.025049975141882896,
0.06143263727426529,
-0.010652578435838223,
-0.0007585030398331583,
0.011958751827478409,
0.0263158418238163,
0.023046260699629784,
0.025421226397156715,
0.004192910622805357,
-0.07098990678787231,
-0.01820049062371254,
-0.00792776606976986,
0.015138288959860802,
0.06261797249317169,
-0.019379086792469025,
-0.022069552913308144,
0.0024065631441771984,
0.016835201531648636,
0.017400428652763367,
0.005870169959962368,
-0.07148099690675735,
0.06875210255384445,
-0.004475427325814962,
-0.0045085083693265915,
0.051701620221138,
0.04066573455929756,
-0.05341232568025589,
-0.004149417392909527,
-0.022599348798394203,
0.03995509445667267,
0.013318058103322983,
0.013809173367917538,
-0.03861846402287483,
0.01917278580367565,
0.013772806152701378,
0.06217857077717781,
-0.013080415315926075,
0.008730348199605942,
0.0061760409735143185,
-0.03693767264485359,
-0.0025731953792274,
0.006218695547431707,
-0.05790966749191284,
-0.0304173044860363,
-0.03636997193098068,
0.03867226094007492,
0.02797519415616989,
-0.04683750122785568,
-0.018039178103208542,
-0.000970211171079427,
0.04160037264227867,
-0.009589738212525845,
-0.00375309307128191,
0.035220641642808914,
0.01954324170947075,
-0.050631165504455566,
0.04383854940533638,
-0.034135788679122925,
0.028228573501110077,
0.004518355708569288,
0.004273953847587109,
-0.01833384670317173,
-0.0462561696767807,
-0.026546351611614227,
0.0037136240862309933,
-0.025790970772504807,
-0.002367463195696473,
-0.0471268929541111,
-0.00009423288429388776,
0.0353819876909256,
0.0011545434826985002,
-0.06722337007522583,
-0.03414341062307358,
0.027817796915769577,
-0.012674838304519653,
-0.03338431194424629,
-0.013387491926550865,
-0.03470388427376747,
-0.01089585479348898,
-0.032317228615283966,
0.006980627775192261,
0.06407901644706726,
-0.0315404087305069,
-0.004824726842343807,
0.0004538353532552719,
0.03768962621688843,
0.03948487713932991,
-0.018580710515379906,
0.004860452376306057,
0.034459859132766724,
-0.010818389244377613,
0.006398414261639118,
0.05301837623119354,
0.039615027606487274,
0.0019334672251716256,
-0.0318341888487339,
-0.0037501573096960783,
0.024212924763560295,
0.029253922402858734,
-0.011178713291883469,
-0.017208727076649666,
0.01511420775204897,
0.007906612940132618,
0.037471842020750046,
0.016886014491319656,
-0.0311548113822937,
-0.030848640948534012,
0.018070999532938004,
0.05674971267580986,
-0.010539928451180458,
0.00443310709670186,
-0.006572817452251911,
0.051792990416288376,
-0.005856835283339024,
-0.0033596111461520195,
0.016680311411619186,
0.040578100830316544,
-0.0018642214126884937,
0.01284215971827507,
0.017457755282521248,
0.011507023125886917,
-0.002516743028536439,
-0.005788535811007023,
0.04573120176792145,
0.017725780606269836,
0.009071859531104565,
-0.02727346308529377,
0.009673187509179115,
-0.05346221849322319,
0.034355491399765015,
0.004571101162582636,
-0.014121832326054573,
0.02082153595983982,
0.012271963991224766,
0.010838878341019154,
-0.016770169138908386,
-0.006013480946421623,
0.010251110419631004,
0.033595237880945206,
-0.0427069328725338,
0.032739605754613876,
-0.08083721250295639,
-0.02025633119046688,
0.016322163864970207,
0.03460993617773056,
-0.035305049270391464,
-0.0022080179769545794,
0.05121345445513725,
0.02290179394185543,
0.01422382052987814,
0.02008877694606781,
-0.03616505488753319,
0.026351923123002052,
-0.0038215124513953924,
0.04032467305660248,
-0.004083615727722645,
-0.014969184063374996,
0.02587900497019291,
-0.0009954760316759348,
0.03442461043596268,
-0.02375013381242752,
-0.011989496648311615,
-0.06790880113840103,
-0.003140439046546817,
0.03188930079340935,
0.004463858902454376,
0.024536749348044395,
0.029244376346468925,
-0.013612915761768818,
0.0017216159030795097,
0.04589097201824188,
0.03264378756284714,
-0.05247499793767929,
-0.0038416613824665546,
-0.06044815480709076,
-0.041058849543333054,
0.07943059504032135,
-0.03333771601319313,
-0.03614267334342003,
0.049848079681396484,
-0.021457809954881668,
0.025810034945607185,
0.005447231698781252,
0.052584003657102585,
-0.02225583791732788,
0.05034944415092468,
-0.04017249494791031,
-0.025445833802223206,
-0.03693489730358124,
0.027402270585298538,
0.13482420146465302,
0.07534855604171753,
-0.0010444594081491232,
-0.08241970837116241,
0.0040186429396271706,
-0.02825235016644001,
-0.009280429221689701,
-0.011608539149165154,
0.05312551558017731,
-0.01475999504327774,
-0.02854917384684086,
-0.008889301680028439,
0.07948700338602066,
0.020961817353963852,
0.03584682568907738,
0.047471992671489716,
-0.04692382737994194,
-0.05681657791137695,
0.035065021365880966,
0.011325382627546787,
-0.0011615017428994179,
-0.029573477804660797,
-0.07681430131196976,
0.020757600665092468,
0.016613246873021126,
0.027193475514650345,
0.01090011466294527,
-0.03469144180417061,
0.024559348821640015,
-0.01268542930483818,
-0.040345799177885056,
0.001662466092966497,
-0.0044591412879526615,
0.014928681775927544,
0.0037753318902105093,
-0.035484571009874344,
-0.01326722465455532,
-0.013917476870119572,
0.03367634117603302,
0.03441397100687027,
0.024963650852441788,
-0.03418518230319023,
-0.0007614466594532132,
0.011579866521060467,
-0.029374102130532265,
-0.01883930340409279,
-0.02468002960085869,
0.05259950831532478,
-0.023409012705087662,
-0.024416694417595863,
0.001874757930636406,
0.009387265890836716,
0.011163915507495403,
-0.023561077192425728,
-0.036103181540966034,
-0.024509387090802193,
0.02538459189236164,
-0.020082248374819756,
0.03302869573235512,
-0.028079062700271606,
0.03348985314369202,
0.0336347296833992,
0.028238704428076744,
0.0289106834679842,
-0.03444606438279152,
0.00418842164799571,
0.011953138746321201,
0.036552101373672485,
0.0035798116587102413,
-0.020499147474765778,
-0.027160771191120148,
-0.004138101823627949,
-0.04830588400363922,
-0.03232359141111374,
0.015014288946986198,
-0.012228394858539104,
0.05795407295227051,
-0.0272408127784729,
-0.004146875347942114,
-0.0133577361702919,
-0.06877955049276352,
0.02650972083210945,
-0.03836898133158684,
-0.017173802480101585,
-0.030755406245589256,
0.0004813385021407157,
0.04671202972531319,
0.055225927382707596,
-0.006729209329932928,
-0.00864400528371334,
-0.010634669102728367,
0.03961513191461563,
0.01377913635224104,
-0.014446655288338661,
-0.004907248541712761,
0.018995419144630432,
-0.015580554492771626,
-0.005265847779810429,
-0.010516262613236904,
0.007520653307437897,
0.0006161951459944248,
-0.02025512047111988,
0.00727660208940506,
0.032967835664749146,
-0.0000942937404033728,
-0.005770453251898289,
0.014394113793969154,
-0.0404408723115921,
0.0021356770303100348,
0.022749723866581917,
-0.0021398733370006084,
-0.05816422775387764,
-0.013179123401641846,
-0.02914191223680973,
0.02890246920287609,
0.01735972799360752,
0.007433097343891859,
-0.03358905389904976,
-0.006138072814792395,
-0.019343901425600052,
-0.02094379812479019,
0.0008317650645039976,
-0.003424396039918065,
-0.04189225286245346,
0.021969718858599663,
-0.01205174159258604,
0.012241381220519543,
-0.005661299452185631,
0.027311041951179504,
-0.011745007708668709,
-0.014490224421024323,
-0.009270203299820423,
-0.021196046844124794,
-0.018781863152980804,
-0.024579519405961037,
-0.0031043814960867167,
0.0007954558823257685,
0.02347635291516781,
-0.005166962277144194,
-0.013566650450229645,
0.017799749970436096,
-0.034108854830265045,
-0.04673771187663078,
0.06584052741527557,
0.028810927644371986,
0.010337729007005692,
0.03627792373299599,
-0.019021809101104736,
-0.03086598962545395,
0.016321726143360138,
-0.04802703857421875,
0.02312573231756687,
0.0024335922207683325,
-0.0043541183695197105,
0.020062362775206566,
-0.011081366799771786,
-0.020120615139603615,
0.019444681704044342,
0.0026978806126862764,
0.02205122634768486,
0.003581840544939041,
-0.003166689770296216,
-0.0007220362313091755,
0.016071727499365807,
-0.006997544784098864,
0.030724771320819855,
0.016397906467318535,
0.013892759568989277,
-0.03184401988983154,
0.0040134768933057785,
0.0013277576072141528,
0.006173457484692335,
0.030160391703248024,
0.006034969352185726,
-0.061441123485565186,
0.002819343004375696,
-0.03513728082180023,
0.018008315935730934,
0.001709543983452022,
-0.06774016469717026,
0.024041559547185898,
0.0009722556569613516,
-0.06470401585102081,
-0.005193920340389013,
-0.030082188546657562,
-0.03544287383556366,
-0.03834585100412369,
-0.02934780903160572,
-0.015417676419019699,
0.04632330313324928,
0.03417142853140831,
-0.00041399599285796285,
-0.005768130533397198,
-0.026257265359163284,
-0.01892303116619587,
-0.01146983727812767,
0.003114973660558462,
0.038489412516355515,
0.005511178635060787,
-0.032681457698345184,
0.08579346537590027,
-0.007197159342467785,
-0.041886504739522934,
0.01802087388932705,
0.01424332708120346,
-0.01999027281999588,
-0.029969992116093636,
0.02857859618961811,
0.05698953941464424,
0.048298511654138565,
0.01455234456807375,
0.005925252567976713,
-0.014857846312224865,
0.0052814665250480175,
0.03429479897022247,
0.00633649155497551,
-0.02618938684463501,
0.0013640393735840917,
-0.02050088904798031,
-0.030074477195739746,
-0.0559675432741642,
0.027515843510627747,
-0.04019717127084732,
-0.050019945949316025,
-0.027065157890319824,
0.007436305750161409,
0.00424185860902071,
0.015828650444746017,
0.010557963512837887,
-0.03309285268187523,
0.007768124341964722,
-0.019522175192832947,
0.03696105629205704,
-0.01354663074016571,
-0.03729370981454849,
-0.012061743065714836,
-0.031215693801641464,
0.042424216866493225,
0.05664324760437012,
-0.028283139690756798,
-0.036444291472435,
-0.0014833378372713923,
0.0003581774653866887,
-0.004583199508488178,
0.055523212999105453,
-0.038436081260442734,
-0.03366230055689812,
0.0061387489549815655,
-0.00005449569653137587,
0.03608514368534088,
-0.02515581250190735,
-0.05337830260396004,
0.020241491496562958,
-0.010683846659958363,
0.07451354712247849,
0.008924472145736217,
-0.00044435638119466603,
0.007149918936192989,
-0.013916244730353355,
0.017149850726127625,
0.02067573182284832,
0.010202944278717041,
-0.00957551784813404,
-0.0723184198141098,
0.036674775183200836,
-0.0008820794755592942,
0.041806966066360474,
-0.00487205944955349,
0.026705877855420113,
-0.000583021785132587,
-0.0171954408288002,
-0.026448965072631836,
0.008736878633499146,
-0.01333577185869217,
0.06240076944231987,
0.02571776881814003,
0.016290104016661644,
-0.01207723468542099,
-0.022592194378376007,
-0.06918418407440186,
0.04663020372390747,
0.011301246471703053,
-0.000046110577386571094,
0.0762164369225502,
-0.000359299941919744,
0.033447884023189545,
0.04752770811319351,
-0.017858605831861496,
-0.045565225183963776,
0.03896130993962288,
0.0007435636944137514,
-0.047257598489522934,
0.019161241129040718,
-0.000018200287740910426,
-0.011767924763262272,
-0.01198215689510107,
-0.0039336360059678555,
0.03953438997268677,
-0.02404373325407505,
-0.03912711143493652,
0.02677532471716404,
0.010945248417556286,
0.02045728825032711,
0.013667267747223377,
0.01563558354973793,
-0.006124440580606461,
0.02482593059539795,
-0.003959487657994032,
0.014850698411464691,
0.06109517067670822,
0.01890958473086357,
0.027975717559456825,
-0.012563291005790234,
-0.03823358938097954,
0.03716659173369408,
-0.009491737931966782,
0.023506999015808105,
-0.010196240618824959,
-0.0034738373942673206,
0.04451390728354454,
-0.03357945755124092,
-0.009862600825726986,
0.012981032021343708,
-0.018819686025381088,
0.06620851159095764,
-0.05096449330449104,
0.0014164210297167301,
-0.026746202260255814,
-0.009950077161192894,
0.016649000346660614,
0.018212417140603065,
0.02884237840771675,
0.019216392189264297,
-0.007204444147646427,
-0.030237389728426933,
-0.03344113007187843,
-0.0131076630204916,
0.022325100377202034,
-0.07660999149084091,
-0.07313902676105499,
0.013022556900978088,
-0.032087989151477814,
0.0022788478527218103,
-0.01089322566986084,
-0.026796111837029457,
-0.0004832390695810318,
0.029370782896876335,
0.04425138980150223,
0.005046663340181112,
-0.011199560947716236,
-0.05026378855109215,
-0.031401023268699646,
0.06592297554016113,
-0.0010894517181441188,
-0.0032976996153593063,
0.019052792340517044,
0.000581316533498466,
0.020718460902571678,
0.03246092423796654
] |
<p>I am trying to understand what a term like $$ \mathcal{L}_{int} = (\partial^{\mu}A )^2 B^2 $$ with $A$ and $B$ being scalar fields for instance means. I understand how to draw an interaction term in Feynman diagrams without the derivative and how to interpret it (connecting external lines, find the correct value for the interaction coupling constant and so on).</p>
<p>But if I have a derivative in front of one of the fields, how do I interpret it ? Is it still two $A$ scalar particles interacting with two $B$ scalar particles ? How the derivative changes the interaction ?</p>
<p>I search a bit on Internet about that and found some resources : <a href="http://www.theory.caltech.edu/~preskill/ph205/205Chapter4-Page1-63.pdf">Preskill Notes</a> (see p. 4.33) or <a href="http://www.maths.tcd.ie/~cblair/notes/list.pdf">Useful Formulae and Feynman Rules</a> (see p. 20) but still... Don't understand. </p>
| 10,802 |
[
0.033095456659793854,
0.007931690663099289,
-0.02512544021010399,
0.0006122156628407538,
0.018687840551137924,
0.05497826635837555,
-0.011194893158972263,
-0.054887089878320694,
-0.0013451320119202137,
-0.031157657504081726,
0.03015720658004284,
0.012257102876901627,
0.07236563414335251,
-0.016984954476356506,
0.03373285382986069,
0.009527367539703846,
-0.0007907056715339422,
-0.02484842948615551,
0.01642061211168766,
-0.017894821241497993,
-0.02614891156554222,
0.02686995454132557,
0.01934197172522545,
0.007731668651103973,
-0.0064279455691576,
0.039066165685653687,
0.004009306896477938,
0.014766726642847061,
-0.002533760154619813,
0.058506473898887634,
0.010009320452809334,
-0.074444979429245,
0.013839387334883213,
-0.017220299690961838,
0.010946734808385372,
0.005450966767966747,
-0.010537609457969666,
-0.042923394590616226,
0.008458361960947514,
0.026733487844467163,
-0.047204043716192245,
-0.004941517021507025,
0.00014970630581956357,
0.06677751988172531,
-0.04061255604028702,
-0.00666824821382761,
-0.0018763677217066288,
-0.025492364540696144,
0.06482221931219101,
-0.050529319792985916,
0.04404960572719574,
0.06923965364694595,
0.05424553155899048,
0.03312890604138374,
-0.024064231663942337,
-0.012225047685205936,
0.02288084290921688,
0.08082588016986847,
0.027789605781435966,
-0.0778825655579567,
-0.022916965186595917,
-0.014189822599291801,
-0.01413366012275219,
-0.017988160252571106,
-0.026224253699183464,
0.04239083454012871,
-0.004212632775306702,
0.0066266548819839954,
0.0299664456397295,
-0.01250535249710083,
0.0018493318930268288,
0.02672005444765091,
0.03878012299537659,
-0.02148241549730301,
0.0055931913666427135,
-0.001652191043831408,
-0.002408571308478713,
-0.01716683991253376,
0.02291671745479107,
0.03844510763883591,
-0.01435886137187481,
0.03759637847542763,
0.02186126448214054,
0.02954285219311714,
0.028523992747068405,
-0.02591375634074211,
0.061839595437049866,
0.028052305802702904,
0.002594641176983714,
-0.006315988022834063,
-0.026460062712430954,
0.027996033430099487,
0.05661575123667717,
-0.03289410471916199,
-0.044223129749298096,
0.04260982200503349,
-0.00900328904390335,
0.016929978504776955,
0.00302674388512969,
-0.03214032202959061,
-0.031190503388643265,
-0.01573130302131176,
0.012193695642054081,
0.08560498058795929,
0.007893049158155918,
-0.03115268237888813,
-0.047832898795604706,
0.009049379266798496,
0.00977673102170229,
-0.00933577585965395,
-0.020060548558831215,
0.026371818035840988,
-0.015614143572747707,
0.0337771512567997,
-0.00024469243362545967,
-0.03901480510830879,
-0.00860284361988306,
0.02766946516931057,
0.04086920991539955,
0.026529328897595406,
0.06444902718067169,
-0.05670439079403877,
0.026565464213490486,
-0.010480399243533611,
-0.08305326104164124,
0.004042530432343483,
0.03383857011795044,
0.023006947711110115,
-0.0557832196354866,
0.03981368988752365,
0.012636011466383934,
0.00931947585195303,
-0.004032389260828495,
0.04457483068108559,
0.018464742228388786,
-0.02437327802181244,
-0.07423896342515945,
-0.07299886643886566,
0.035807639360427856,
-0.0030762862879782915,
-0.012021348811686039,
-0.06840895116329193,
-0.04486880823969841,
0.04188280552625656,
0.10889145731925964,
-0.007609162013977766,
-0.015654515475034714,
-0.013300548307597637,
0.030663415789604187,
-0.009072981774806976,
-0.015782861039042473,
-0.021597135812044144,
-0.00491713173687458,
-0.015681935474276543,
0.0031267297454178333,
-0.0543333925306797,
0.014517723582684994,
0.051506612449884415,
-0.02037825807929039,
-0.013642378151416779,
0.11490977555513382,
-0.022828394547104836,
0.03520119562745094,
0.025434322655200958,
-0.02056117355823517,
0.00018948965589515865,
0.0450005829334259,
0.0014732445124536753,
0.02435114048421383,
0.046569857746362686,
0.014877917245030403,
0.027964336797595024,
-0.017952313646674156,
0.04659554734826088,
0.058851029723882675,
0.002876270329579711,
-0.007038117852061987,
-0.0250235702842474,
-0.00265414803288877,
-0.025996489450335503,
-0.044292155653238297,
-0.062288086861371994,
-0.032049648463726044,
0.01839834451675415,
-0.023647109046578407,
-0.003334948094561696,
0.020178714767098427,
0.01274596806615591,
-0.0037729889154434204,
-0.06315429508686066,
-0.04661804437637329,
-0.1059558093547821,
0.0017680184682831168,
0.001431843964383006,
-0.04428684711456299,
0.03394323214888573,
-0.01572025939822197,
0.005186981055885553,
-0.020434536039829254,
-0.031251460313797,
0.012185451574623585,
0.04230791702866554,
0.016885578632354736,
0.007126733660697937,
0.02155367098748684,
0.02133900485932827,
0.04391050338745117,
-0.009934848174452782,
0.03563190996646881,
-0.03955144062638283,
-0.031710993498563766,
0.02586599439382553,
-0.005748116411268711,
0.014456269331276417,
-0.011275473050773144,
-0.02729662135243416,
-0.016700981184840202,
0.006367589812725782,
-0.022183330729603767,
0.02602452039718628,
-0.07027141749858856,
0.05425911024212837,
0.04581360146403313,
0.042925845831632614,
0.0045847161673009396,
0.06167367845773697,
0.010495651513338089,
0.03459002450108528,
-0.027308017015457153,
-0.021548034623265266,
-0.030567973852157593,
-0.026634465903043747,
0.03744228929281235,
0.02378736063838005,
-0.010393679141998291,
0.004866478964686394,
0.024210793897509575,
0.0032531809993088245,
0.034396953880786896,
0.0338330939412117,
-0.027754778042435646,
-0.05021630972623825,
0.0015755373751744628,
0.02317173406481743,
-0.017789319157600403,
0.015814349055290222,
0.00002588650386314839,
0.012584442272782326,
0.037293076515197754,
-0.012983822263777256,
-0.026981765404343605,
0.0190713033080101,
-0.03460698202252388,
-0.007404823787510395,
-0.0046724583953619,
0.00622303131967783,
0.0341474823653698,
0.006018255837261677,
0.05740519240498543,
0.033372461795806885,
-0.0143241286277771,
-0.02568422444164753,
-0.017432082444429398,
-0.03405318036675453,
0.019534971565008163,
-0.031524550169706345,
-0.027203215286135674,
-0.0430893637239933,
0.011072051711380482,
-0.028389157727360725,
0.013751834630966187,
0.020494909957051277,
-0.012760014273226261,
-0.031355664134025574,
-0.021851615980267525,
0.013342765159904957,
0.042024414986371994,
0.03597743809223175,
-0.018253177404403687,
-0.04467972368001938,
0.012753610499203205,
-0.023373493924736977,
0.025230882689356804,
0.008334056474268436,
-0.039218537509441376,
0.018198255449533463,
-0.05351787060499191,
-0.017136547714471817,
0.03391466662287712,
0.00019846686336677521,
0.03804413601756096,
0.009503894485533237,
-0.0058886525221168995,
-0.0551767461001873,
-0.058775149285793304,
0.011815554462373257,
0.01625300571322441,
-0.0007774923578836024,
-0.0003642591182142496,
0.017107613384723663,
0.006773379631340504,
-0.02351965755224228,
0.021148158237338066,
-0.01916017010807991,
-0.047388672828674316,
-0.029434990137815475,
0.017627477645874023,
0.021926438435912132,
0.0042244973592460155,
0.006157110445201397,
0.013993422500789165,
-0.027264898642897606,
-0.031943999230861664,
-0.029671965166926384,
-0.027644746005535126,
-0.005632502026855946,
-0.002553721657022834,
0.004872740712016821,
-0.00801768433302641,
-0.05372709780931473,
0.06623835116624832,
0.031221112236380577,
-0.028291815891861916,
-0.022860215976834297,
-0.00034493787097744644,
-0.0033169016242027283,
-0.034756701439619064,
0.01911797747015953,
0.017776090651750565,
-0.01619228720664978,
0.029217619448900223,
0.020340019837021828,
0.0358840636909008,
0.03648613393306732,
0.014933147467672825,
-0.015314105898141861,
0.0002802333328872919,
-0.025087645277380943,
-0.01894766092300415,
0.05507940798997879,
-0.007680462673306465,
0.003629944985732436,
-0.002839196240529418,
0.010737220756709576,
0.02826016955077648,
0.051812611520290375,
-0.005251293536275625,
0.0673186257481575,
0.03469480574131012,
0.010638361796736717,
-0.03141266480088234,
0.01369203720241785,
-0.0031452758703380823,
-0.024790912866592407,
0.02908320538699627,
-0.02927221730351448,
0.007172230631113052,
-0.03424840047955513,
-0.01683606021106243,
0.00916704535484314,
0.0285667572170496,
-0.04073223099112511,
-0.029239578172564507,
0.00030522557790391147,
-0.01716858334839344,
0.004725102335214615,
-0.022170880809426308,
-0.005276097450405359,
0.033209871500730515,
0.04023479297757149,
-0.029223067685961723,
-0.04233013466000557,
-0.05956818908452988,
-0.020923998206853867,
-0.04763971269130707,
-0.006669146940112114,
-0.0033480492420494556,
0.03398033604025841,
0.013816500082612038,
0.0623592771589756,
-0.0208605770021677,
-0.004233337473124266,
0.03458991274237633,
-0.006638592109084129,
-0.06663653999567032,
0.0763387605547905,
-0.01649228297173977,
-0.030178934335708618,
-0.024366986006498337,
-0.03914328292012215,
0.027613705024123192,
-0.008135502226650715,
-0.03007548861205578,
-0.027653615921735764,
-0.011843721382319927,
-0.05466568470001221,
0.005763460416346788,
-0.06779489666223526,
-0.029220523312687874,
-0.04806361719965935,
0.042036402970552444,
0.021796410903334618,
-0.01877211593091488,
0.014835676178336143,
0.06393354386091232,
-0.024302463978528976,
-0.05475294589996338,
-0.014518152922391891,
-0.013285168446600437,
0.03805592283606529,
0.021597784012556076,
0.035522282123565674,
-0.016502177342772484,
-0.04631400108337402,
0.03923247009515762,
0.04491330683231354,
0.09522552788257599,
0.022355569526553154,
-0.0001267249317606911,
-0.002760975854471326,
-0.0423770435154438,
-0.018803363665938377,
-0.008997947908937931,
0.07478974759578705,
-0.011210815981030464,
-0.008956147357821465,
0.046073053032159805,
0.031704191118478775,
-0.012166709639132023,
0.04709553346037865,
0.015553496778011322,
0.01239277608692646,
-0.030651669949293137,
-0.058075301349163055,
0.018893055617809296,
-0.006727435626089573,
-0.009221353568136692,
-0.012512286193668842,
-0.0051197935827076435,
-0.020790111273527145,
0.002730674808844924,
0.021694248542189598,
0.008463138714432716,
-0.02903800457715988,
-0.002995465649291873,
0.007729213219136,
-0.007600908633321524,
0.004248457495123148,
-0.03745931759476662,
-0.012125100940465927,
0.06514836847782135,
0.04817981645464897,
0.0015572125557810068,
0.015975164249539375,
-0.05596490949392319,
-0.025135578587651253,
0.03477336838841438,
0.06122073158621788,
0.0002934618678409606,
-0.01734313927590847,
-0.01274359691888094,
-0.00867636501789093,
0.06807544082403183,
-0.005172742065042257,
0.001425952068530023,
-0.021895378828048706,
-0.00012063906615367159,
-0.03522147983312607,
-0.025903280824422836,
-0.03874288499355316,
0.05099065601825714,
-0.007786919828504324,
0.012497573159635067,
-0.04588104784488678,
-0.00893434789031744,
-0.011688271537423134,
0.03851604461669922,
-0.010773039422929287,
0.04423486441373825,
-0.005724567454308271,
-0.004013890866190195,
0.028039928525686264,
-0.0011817177291959524,
0.010508723556995392,
-0.07215403020381927,
0.00911618396639824,
-0.010430722497403622,
-0.0288509801030159,
0.05766654759645462,
0.00521400012075901,
-0.020483259111642838,
0.024217091500759125,
0.03513616696000099,
-0.009570921771228313,
-0.011987029574811459,
-0.0291281770914793,
0.06574204564094543,
0.03982271999120712,
0.005913372151553631,
0.06786583364009857,
0.0392770878970623,
-0.01811150461435318,
-0.02033108100295067,
-0.014737872406840324,
0.0468595027923584,
0.02567359060049057,
0.03777863830327988,
-0.04765957593917847,
-0.028950946405529976,
-0.05233655497431755,
0.04043589159846306,
-0.03695696219801903,
0.01290823146700859,
-0.011665505357086658,
-0.03448909893631935,
-0.020138684660196304,
0.0440407395362854,
-0.003250821027904749,
-0.021842215210199356,
0.007401713170111179,
-0.002402818761765957,
0.005950376391410828,
-0.011135261505842209,
0.02763146534562111,
0.007410064339637756,
-0.01538757886737585,
0.024301061406731606,
0.033685002475976944,
0.024575144052505493,
0.006823492702096701,
-0.012825846672058105,
0.0020871979650110006,
-0.044836267828941345,
0.03329910337924957,
0.021704401820898056,
-0.028700165450572968,
0.01908525824546814,
-0.029444867745041847,
-0.037422068417072296,
-0.015166031196713448,
-0.019973790273070335,
0.005218978971242905,
-0.06194089353084564,
0.02415620908141136,
0.011943893507122993,
0.007041313219815493,
-0.05841067433357239,
-0.02442697435617447,
0.0089457668364048,
-0.04539721459150314,
-0.03240231052041054,
-0.011074974201619625,
-0.030764058232307434,
-0.018488803878426552,
-0.03387029096484184,
0.018615275621414185,
0.06716117262840271,
-0.03748031705617905,
-0.022617630660533905,
-0.012759602628648281,
0.02507154271006584,
0.0433741956949234,
0.014521442353725433,
0.006803213153034449,
0.022240279242396355,
-0.00169685750734061,
0.009849906899034977,
0.024365907534956932,
0.060153380036354065,
-0.015415403060615063,
0.0075684902258217335,
0.010601138696074486,
-0.01203024573624134,
0.04561051353812218,
0.0015708658611401916,
-0.012537699192762375,
0.004243721719831228,
0.052029967308044434,
0.012228352017700672,
0.013028828427195549,
0.005385272670537233,
-0.006892327219247818,
0.04548605903983116,
0.002988944761455059,
0.019399596378207207,
0.01680545136332512,
-0.031250953674316406,
0.02572299726307392,
-0.0036996558774262667,
0.021413471549749374,
-0.008031168021261692,
0.03137822449207306,
-0.023591801524162292,
0.01292103435844183,
0.018066439777612686,
-0.00368451327085495,
0.042448993772268295,
-0.0348716638982296,
0.02200193516910076,
0.012187151238322258,
0.02059631608426571,
-0.022967038676142693,
-0.00871401745826006,
-0.05117380991578102,
-0.007497816346585751,
0.04582906886935234,
-0.04553082585334778,
0.02630799077451229,
0.020262517035007477,
-0.019840866327285767,
0.010336985811591148,
-0.04016012325882912,
-0.04158056527376175,
-0.007029606029391289,
-0.011077220551669598,
0.05080747976899147,
-0.061720531433820724,
-0.03564564138650894,
0.03888242691755295,
0.026935601606965065,
-0.03797074034810066,
0.0072244624607264996,
0.030999023467302322,
0.03453100845217705,
0.01785123161971569,
-0.021557096391916275,
-0.03750087693333626,
0.06443867087364197,
-0.004437784198671579,
0.011030832305550575,
0.02097681723535061,
-0.008439713157713413,
0.05467740818858147,
0.032281000167131424,
0.005171252880245447,
-0.0010862096678465605,
-0.01317098829895258,
-0.0266435444355011,
0.011540808714926243,
0.04557100683450699,
-0.02399999089539051,
0.01980287954211235,
0.006121035199612379,
0.04155271500349045,
-0.012390545569360256,
0.011197705753147602,
0.005912945605814457,
-0.06190996989607811,
-0.020881205797195435,
-0.046683475375175476,
-0.04002677649259567,
0.053479570895433426,
-0.0254156906157732,
-0.05810684338212013,
-0.0010536584304645658,
-0.03081166371703148,
0.022796766832470894,
-0.0013679342810064554,
-0.00030895567033439875,
-0.01781831681728363,
0.06505884975194931,
-0.015447724610567093,
0.008283048868179321,
-0.008336499333381653,
-0.034620095044374466,
0.1124456450343132,
0.03157156705856323,
-0.03239261358976364,
-0.07308362424373627,
0.021251264959573746,
-0.030528001487255096,
0.0037769146729260683,
-0.0581924244761467,
0.03573431074619293,
-0.009220479987561703,
-0.017824821174144745,
-0.024147294461727142,
0.041588280349969864,
-0.010543138720095158,
0.0005934046930633485,
0.04926253855228424,
-0.031086696311831474,
-0.08411473780870438,
-0.01531018316745758,
0.033767081797122955,
-0.03021210804581642,
-0.005506932735443115,
-0.060613248497247696,
-0.012379521504044533,
0.00827330257743597,
0.04712739214301109,
-0.00572098046541214,
-0.03164207190275192,
0.03125607222318649,
-0.02336217649281025,
-0.032570838928222656,
-0.002340268110856414,
0.024418724700808525,
0.015421963296830654,
-0.0253453329205513,
0.005063519347459078,
0.03137711435556412,
-0.015102406032383442,
0.008347269147634506,
0.03498990088701248,
0.009717283770442009,
-0.0005518092075362802,
0.010835117660462856,
0.030863100662827492,
-0.008225223049521446,
-0.02251509018242359,
-0.04428452253341675,
0.07817938178777695,
0.022098304703831673,
-0.024485336616635323,
0.0013293158262968063,
0.015661068260669708,
0.019252650439739227,
-0.02228330820798874,
-0.028574805706739426,
0.01572166010737419,
0.022055217996239662,
-0.024405114352703094,
0.02821914665400982,
-0.0040030586533248425,
0.038427356630563736,
-0.010541103780269623,
0.001826105173677206,
0.010130454786121845,
-0.033117007464170456,
0.010648200288414955,
-0.029166406020522118,
0.028669990599155426,
-0.017878033220767975,
-0.012783019803464413,
-0.04117617756128311,
-0.007204830646514893,
-0.020527346059679985,
-0.0006346884765662253,
0.01264150533825159,
0.017790276557207108,
0.036376986652612686,
-0.022442013025283813,
-0.009989369660615921,
-0.009835298173129559,
-0.06514684855937958,
0.040669865906238556,
-0.01816246658563614,
-0.00012877705739811063,
-0.009145110845565796,
-0.0026906533166766167,
0.02221522107720375,
0.027882959693670273,
-0.0009527040529064834,
-0.029906125739216805,
0.006745942402631044,
0.02871055342257023,
0.017657216638326645,
-0.022401679307222366,
-0.044938355684280396,
0.025079336017370224,
-0.013537995517253876,
0.004321742337197065,
-0.0010465303203091025,
0.004631258547306061,
-0.026878122240304947,
0.005422815680503845,
-0.013412922620773315,
0.03793513774871826,
-0.02229396440088749,
0.02632204070687294,
0.04377280920743942,
-0.014473188668489456,
-0.001993657788261771,
0.03878752142190933,
0.014690594747662544,
-0.011108197271823883,
-0.028792621567845345,
-0.014822294004261494,
-0.002777597401291132,
0.013680781237781048,
0.020003436133265495,
-0.04478633403778076,
-0.029139067977666855,
-0.014700425788760185,
0.0036637845914810896,
-0.01808544620871544,
0.0043942308984696865,
-0.06204737350344658,
0.01508998591452837,
0.006954261101782322,
-0.012323477305471897,
-0.004449525848031044,
0.03634819760918617,
-0.019141696393489838,
-0.004067865666002035,
-0.006419259589165449,
0.004669680260121822,
-0.00892693642526865,
-0.01862633228302002,
0.010910866782069206,
-0.014566637575626373,
0.016063716262578964,
0.005868028849363327,
-0.047287069261074066,
0.036943137645721436,
-0.018207972869277,
-0.058714888989925385,
0.029315359890460968,
0.03814943879842758,
0.032644033432006836,
0.031874485313892365,
-0.011301923543214798,
-0.047101572155952454,
0.05003175139427185,
-0.001233255839906633,
0.017890850082039833,
-0.019249461591243744,
-0.0780409425497055,
-0.016814634203910828,
-0.0485989972949028,
0.0169223602861166,
0.012328163720667362,
0.010592926293611526,
-0.023158224299550056,
0.010019443929195404,
-0.03923545777797699,
-0.024727266281843185,
0.004858839325606823,
-0.003511476796120405,
0.06322169303894043,
-0.02429676428437233,
-0.009714232757687569,
0.03187604621052742,
0.04270521178841591,
-0.00182917935308069,
0.009372447617352009,
0.014362997375428677,
0.017903586849570274,
-0.09742938727140427,
-0.021669961512088776,
0.010439724661409855,
0.037252020090818405,
0.02449234202504158,
-0.07000137120485306,
0.012880837544798851,
0.008337166160345078,
-0.012768667191267014,
-0.007524717599153519,
-0.0016522217774763703,
0.002933708019554615,
-0.0015945031773298979,
0.01277301274240017,
-0.015814892947673798,
0.07101336866617203,
0.015931250527501106,
0.004975299816578627,
0.0053291916847229,
-0.001343900221399963,
-0.01124669797718525,
-0.02020406536757946,
0.005954618565738201,
0.029201403260231018,
0.003283132566139102,
-0.042214490473270416,
0.06406677514314651,
0.012946723029017448,
-0.03570054844021797,
0.02402755431830883,
-0.0020833814051002264,
-0.010342911817133427,
-0.01439586654305458,
0.0051238806918263435,
0.01661003567278385,
0.03845144063234329,
0.036378163844347,
0.0010868401732295752,
-0.00907773058861494,
0.020911145955324173,
0.050256215035915375,
0.01607000268995762,
-0.00872037373483181,
-0.0156787671148777,
-0.00388998631387949,
-0.0021611598785966635,
-0.019224239513278008,
0.04366729408502579,
-0.027585197240114212,
-0.04839701950550079,
-0.026092402637004852,
-0.0264341589063406,
0.04101383686065674,
-0.018886102363467216,
0.04805651679635048,
-0.016815422102808952,
-0.0165554266422987,
0.023320063948631287,
0.020969105884432793,
-0.01810862310230732,
0.020336857065558434,
-0.0062676770612597466,
-0.011401825584471226,
0.03341711312532425,
0.03473547846078873,
0.0046996260061860085,
-0.06021922826766968,
0.005551592446863651,
-0.0014635842526331544,
-0.0176323801279068,
-0.015381584875285625,
-0.027350986376404762,
-0.052306223660707474,
-0.0011912278132513165,
0.0223463736474514,
0.03545541316270828,
-0.015190831385552883,
-0.03719576820731163,
0.02466728538274765,
-0.06618490815162659,
0.036596350371837616,
0.009222691878676414,
-0.018385853618383408,
-0.060524389147758484,
-0.010425220243632793,
-0.006236607208848,
0.0038546756841242313,
0.05812349170446396,
0.012436325661838055,
-0.003735916456207633,
0.03700945898890495,
0.01603715494275093,
0.01042547170072794,
-0.03207726031541824,
-0.00756000867113471,
0.01206403598189354,
0.010671422816812992,
-0.023351484909653664,
0.03948794677853584,
0.0045153857208788395,
0.058132756501436234,
0.01652143895626068,
0.023893771693110466,
0.006346565205603838,
0.010347790084779263,
-0.042266473174095154,
0.050201572477817535,
0.00832798145711422,
-0.027066821232438087,
0.03787987679243088,
0.004488965962082148,
0.03389643877744675,
0.026166025549173355,
-0.037858668714761734,
-0.01586412638425827,
0.01366768404841423,
-0.050461046397686005,
-0.011272274889051914,
-0.018447401002049446,
-0.012130008079111576,
-0.009849566966295242,
-0.08598195016384125,
-0.00624077906832099,
0.015458776615560055,
-0.03333910182118416,
-0.0017044681590050459,
0.047526080161333084,
0.027357198297977448,
0.03990333899855614,
0.04738835245370865,
0.01181862223893404,
-0.005383210256695747,
0.015539556741714478,
-0.020608050748705864,
0.012105370871722698,
0.028226682916283607,
0.013096163049340248,
-0.016095848754048347,
0.05086999386548996,
-0.011207175441086292,
0.0003398889093659818,
-0.006273843813687563,
0.022731328383088112,
-0.013660520315170288,
0.01224032323807478,
-0.015406850725412369,
-0.026296863332390785,
0.028456522151827812,
0.0007281283615157008,
-0.005085902288556099,
0.08691699057817459,
-0.05306209996342659,
0.010224469006061554,
-0.012712731957435608,
0.007797899655997753,
0.00462381960824132,
0.026093650609254837,
0.0564635805785656,
0.028511855751276016,
-0.006208619102835655,
-0.01619037799537182,
-0.03674469143152237,
-0.01907670497894287,
0.017214661464095116,
-0.06339853256940842,
0.026225585490465164,
0.0128292515873909,
-0.012251247651875019,
0.005863129161298275,
-0.024391569197177887,
-0.003823864972218871,
-0.044209592044353485,
0.05773310735821724,
0.04303959384560585,
0.013932918198406696,
-0.022380992770195007,
0.014307014644145966,
-0.03018205240368843,
0.07424630969762802,
-0.055473461747169495,
-0.002531586214900017,
-0.024773500859737396,
0.01659468375146389,
-0.023882323876023293,
-0.00601152703166008
] |
<p>I am learning about waves (intro course) and as I was studying Wave Functions, I got a little confused.</p>
<p>The book claims that the wave function of a sinusoidal wave moving in the $+x$ direction is $y(x,t) = A\cos(kx - wt)$.</p>
<p>However, I see a drawing of the wave and they always seem to be $\cos$ graphs. Are sinusoidal waves always cosine graphs? Or can they be sine? If I ever see a sine wave, then does that mean that this is merely a pulse/wave travelling once and not oscillating in a periodic motion?</p>
<p>Sorry for the basic beginners question.</p>
| 10,803 |
[
0.005655332934111357,
-0.010135551914572716,
-0.023288387805223465,
-0.05589082092046738,
0.07949195802211761,
0.019105033949017525,
-0.0315147303044796,
-0.04831361398100853,
0.02328210510313511,
-0.026743516325950623,
0.03244040161371231,
0.03020666167140007,
0.06078743934631348,
0.012303724884986877,
0.03857230395078659,
0.028089111670851707,
-0.049649205058813095,
-0.010202030651271343,
-0.03374509885907173,
0.0028023889753967524,
-0.008328759111464024,
-0.003305376973003149,
0.01587059162557125,
0.002217621076852083,
-0.005873986054211855,
0.028051631525158882,
0.04267645627260208,
0.032292284071445465,
0.030074745416641235,
0.012353586032986641,
0.007129989564418793,
-0.031466975808143616,
-0.011754630133509636,
0.048461347818374634,
0.030622068792581558,
-0.029471611604094505,
-0.02141958847641945,
-0.041149623692035675,
-0.023486370220780373,
0.01601976901292801,
-0.010449289344251156,
-0.002076026750728488,
0.007993588224053383,
0.032339826226234436,
-0.03936576098203659,
0.006656675133854151,
0.030164750292897224,
-0.014810134656727314,
0.03444253280758858,
-0.062384773045778275,
0.07449612766504288,
-0.01857014000415802,
0.07185487449169159,
0.013576149009168148,
0.007287244312465191,
0.02802382968366146,
0.0760330781340599,
0.05027587339282036,
-0.06199207156896591,
-0.030010009184479713,
-0.0018094301922246814,
-0.044467367231845856,
-0.00794400554150343,
-0.013726013712584972,
-0.04444761574268341,
0.02211582288146019,
0.0014448171714320779,
-0.03626913204789162,
0.011712050065398216,
-0.01096745952963829,
-0.025513816624879837,
0.020664019510149956,
0.02510533481836319,
-0.0501176081597805,
-0.01875941827893257,
-0.020196251571178436,
0.001595641952008009,
0.018547791987657547,
0.03138763830065727,
0.025708651170134544,
-0.01141098327934742,
0.020350556820631027,
0.00699643325060606,
0.006954775657504797,
-0.004870590288192034,
-0.011106548830866814,
0.0938679426908493,
0.018890082836151123,
-0.012664852663874626,
-0.00609430018812418,
-0.011258847080171108,
0.005416413303464651,
0.024825135245919228,
-0.048910148441791534,
0.0006243274547159672,
0.03433174639940262,
-0.003932273015379906,
0.03079981356859207,
0.022560032084584236,
-0.04503750428557396,
0.027007589116692543,
-0.029131973162293434,
0.0523701086640358,
0.07569511234760284,
0.0007919515483081341,
0.000008429447916569188,
-0.03216427564620972,
0.03651341050863266,
-0.019071092829108238,
-0.03350815176963806,
-0.0147501016035676,
0.03305859491229057,
0.023704152554273605,
0.050386153161525726,
0.0018692038720473647,
-0.00014908952289260924,
0.028738493099808693,
0.0029501186218112707,
0.011325505562126637,
0.07811535894870758,
0.0571657195687294,
-0.04620778560638428,
0.07140245288610458,
0.007898113690316677,
-0.05982798710465431,
-0.0011742286151275039,
-0.006039236672222614,
-0.003863581921905279,
-0.027035877108573914,
0.041044093668460846,
0.03107529878616333,
-0.014070766977965832,
0.03719395771622658,
-0.026313090696930885,
0.06843870878219604,
-0.031153183430433273,
-0.10596436262130737,
-0.037298399955034256,
0.015054972842335701,
-0.019164355471730232,
-0.021722890436649323,
-0.064127117395401,
-0.009187044575810432,
0.014869274571537971,
0.07620186358690262,
-0.04027491807937622,
-0.0006452126544900239,
-0.018758729100227356,
0.024802319705486298,
-0.0049569206312298775,
-0.012804553844034672,
-0.006017009261995554,
-0.017521463334560394,
-0.07869289815425873,
0.00705631822347641,
-0.02584063448011875,
-0.00026222364977002144,
0.009974065236747265,
0.04947512596845627,
-0.05495616793632507,
0.04804521054029465,
-0.027064194902777672,
-0.007793523371219635,
0.031166382133960724,
0.011052248068153858,
-0.057146914303302765,
0.10924667865037918,
0.024176986888051033,
-0.00794255267828703,
0.0362907275557518,
0.011736600659787655,
0.021368596702814102,
0.02036377042531967,
0.03916877880692482,
0.007320080883800983,
-0.05449599400162697,
-0.026898598298430443,
-0.018418719992041588,
0.0152602419257164,
-0.005637769121676683,
-0.013345208950340748,
-0.04413452744483948,
0.012120245955884457,
0.03989491984248161,
0.014502405188977718,
0.05695042759180069,
-0.014971937984228134,
-0.00451692147180438,
0.004201863426715136,
-0.04656725749373436,
0.022693881765007973,
-0.03674158453941345,
0.03895176574587822,
-0.033602211624383926,
0.011565081775188446,
0.03860866278409958,
0.04428095370531082,
0.027631226927042007,
-0.020400196313858032,
-0.02401667833328247,
0.001064663752913475,
0.07026345282793045,
-0.018674340099096298,
-0.04177113622426987,
0.034891728311777115,
0.03414008766412735,
-0.0062283058650791645,
0.03855021670460701,
0.017401469871401787,
-0.02810087613761425,
0.011964035220444202,
0.004986991174519062,
-0.048891905695199966,
-0.008631845004856586,
0.0023651323281228542,
-0.01328928954899311,
-0.015177165158092976,
-0.01095101609826088,
-0.023521050810813904,
0.05197405442595482,
-0.023417877033352852,
0.04176759719848633,
0.07529880851507187,
0.00014562915021087974,
-0.011553701013326645,
0.03333592414855957,
0.016013318672776222,
0.0244497898966074,
0.012354552745819092,
-0.05144114047288895,
-0.03510037064552307,
0.025236938148736954,
0.05107533186674118,
0.000697659095749259,
-0.0018622525967657566,
-0.0027564330957829952,
0.013394342735409737,
0.04359593614935875,
0.06383471190929413,
0.030398549512028694,
0.002595140365883708,
-0.031314678490161896,
-0.0012107760412618518,
0.02727077342569828,
-0.0010281678987666965,
0.00464659696444869,
0.04591909795999527,
0.01197944488376379,
0.01072563137859106,
0.0014772110152989626,
-0.03484698757529259,
0.04285130277276039,
-0.06892115622758865,
0.028488416224718094,
0.010874707251787186,
-0.002726319245994091,
0.012794594280421734,
-0.02935970015823841,
-0.015538839623332024,
-0.01364944875240326,
-0.005963347386568785,
-0.04039031267166138,
-0.011375928297638893,
0.007708292454481125,
0.00985762383788824,
-0.027199316769838333,
-0.014379619620740414,
-0.027030054479837418,
0.02308785542845726,
-0.028801629319787025,
0.0159288477152586,
-0.026530666276812553,
-0.012245036661624908,
-0.017450636252760887,
-0.01487899012863636,
0.04717973619699478,
0.0077761998400092125,
0.058067772537469864,
-0.05585969612002373,
-0.056991782039403915,
-0.005780341103672981,
-0.037292711436748505,
0.003989315126091242,
-5.836021088612142e-8,
-0.02555774711072445,
0.02113865688443184,
-0.06187465786933899,
-0.014711163938045502,
0.022406700998544693,
-0.024827105924487114,
0.020366689190268517,
-0.029070941731333733,
-0.02168363705277443,
-0.05749918520450592,
-0.009467686526477337,
-0.059455323964357376,
0.07132293283939362,
-0.026385480538010597,
0.00731909042224288,
0.03463996201753616,
-0.008237375877797604,
-0.027510207146406174,
0.03015739470720291,
-0.007104524876922369,
-0.034913454204797745,
0.003453981364145875,
-0.02127387560904026,
0.029999693855643272,
-0.038532108068466187,
0.02687191776931286,
0.015286114066839218,
-0.07747943699359894,
-0.01418017316609621,
-0.03576013445854187,
-0.027386236935853958,
0.009415020234882832,
-0.0260870773345232,
0.005646802950650454,
0.027104636654257774,
-0.029780803248286247,
0.055643778294324875,
0.033313751220703125,
-0.029525678604841232,
0.015459421090781689,
0.0017865763511508703,
-0.020633351057767868,
-0.037226032465696335,
-0.000014895098502165638,
0.04805619642138481,
-0.007166869007050991,
0.02210227958858013,
0.016943199560046196,
-0.01660297065973282,
0.07222269475460052,
-0.00201201974414289,
-0.005006836727261543,
0.028823520988225937,
0.00913142692297697,
0.028808696195483208,
0.04013952240347862,
0.022655216977000237,
-0.045871175825595856,
0.039569031447172165,
-0.0029564255382865667,
0.011589165776968002,
0.018861860036849976,
-0.003675245214253664,
0.0451110377907753,
-0.02336188778281212,
-0.0007259051199071109,
-0.05304619297385216,
0.05123298242688179,
0.04263000935316086,
0.027644600719213486,
-0.015863120555877686,
0.030874507501721382,
0.026768919080495834,
0.01042444072663784,
0.02764272689819336,
0.006280158180743456,
-0.018884941935539246,
-0.03224526345729828,
-0.022207366302609444,
-0.020929571241140366,
0.014298707246780396,
0.025313451886177063,
0.00110140151809901,
-0.03859000280499458,
0.046662602573633194,
0.0013181836111471057,
0.002121053636074066,
-0.0022705390583723783,
-0.019416699185967445,
-0.013235473074018955,
-0.048295069485902786,
-0.03807281702756882,
-0.00009953186236089095,
0.023555267602205276,
0.015914596617221832,
0.07737863063812256,
0.014722838066518307,
0.04083842411637306,
-0.0018745462875813246,
0.0077337464317679405,
-0.05870397016406059,
0.02607061341404915,
-0.059225235134363174,
0.0035349824465811253,
-0.012742817401885986,
-0.01258429791778326,
0.006990235298871994,
-0.0029747996013611555,
-0.020396096631884575,
0.0007653860957361758,
-0.04424736276268959,
-0.042019594460725784,
0.00667529134079814,
0.0015402431599795818,
0.001586920116096735,
-0.03378856182098389,
0.01841958425939083,
0.03090241365134716,
-0.05560345575213432,
0.012868823483586311,
0.036645062267780304,
-0.010288076475262642,
0.008788134902715683,
-0.01411793939769268,
-0.006466343998908997,
0.018811769783496857,
0.011567275039851665,
0.04227114096283913,
-0.0010492688743397593,
0.006256576627492905,
-0.002176689449697733,
0.015062023885548115,
0.0720183327794075,
-0.0016855124849826097,
0.0041336556896567345,
-0.025793205946683884,
-0.04756229743361473,
0.0035520149394869804,
-0.010491807945072651,
0.0427480973303318,
0.03443494066596031,
-0.012061764486134052,
0.012325276620686054,
-0.0014264208730310202,
0.003132229670882225,
0.06784983724355698,
0.0210195854306221,
0.007606996223330498,
-0.010370546951889992,
-0.0099156079813838,
0.013130612671375275,
-0.04173740744590759,
-0.014421794563531876,
0.02884821593761444,
-0.015252136625349522,
-0.0009095052373595536,
0.035150546580553055,
0.03781730681657791,
0.00791503768414259,
0.01264906395226717,
0.0077049811370670795,
0.0045080967247486115,
0.025549598038196564,
0.004158209078013897,
-0.032262932509183884,
0.02435494214296341,
0.02649226225912571,
0.024484826251864433,
0.01351411733776331,
-0.023930134251713753,
-0.05857757478952408,
0.0009711912134662271,
0.015247007831931114,
0.017044885084033012,
-0.0009332986664958298,
-0.004647376015782356,
-0.06828812509775162,
-0.032935261726379395,
0.03327462077140808,
0.0019938875921070576,
0.021285057067871094,
-0.03989807143807411,
0.0031097838655114174,
-0.04866284504532814,
-0.030877644196152687,
0.007504686247557402,
0.0017384071834385395,
0.006270264275372028,
0.005384521558880806,
-0.0031115415040403605,
0.011719747446477413,
0.007969971746206284,
-0.014122772961854935,
0.0024378099478781223,
0.06454402208328247,
-0.005128306802362204,
-0.04563991352915764,
-0.022997058928012848,
0.018879977986216545,
0.005574772600084543,
-0.0647256001830101,
-0.011405269615352154,
0.006872314494103193,
0.004440634045749903,
0.03597264364361763,
0.007245535030961037,
-0.04436951130628586,
-0.0047011226415634155,
0.008325065486133099,
-0.002261515473946929,
0.032248374074697495,
-0.03131891414523125,
0.056408464908599854,
0.031586311757564545,
-0.0078695397824049,
0.028936544433236122,
0.03766138479113579,
-0.02386089228093624,
-0.029132476076483727,
-0.01670008897781372,
0.05146333575248718,
-0.048455990850925446,
0.013877169229090214,
-0.029658501967787743,
-0.008224351331591606,
-0.047307249158620834,
0.033180687576532364,
-0.009222084656357765,
-0.013100049458444118,
-0.033593978732824326,
-0.005410770885646343,
0.009148867800831795,
0.04259632155299187,
-0.005435092840343714,
0.012158897705376148,
0.0005467584705911577,
0.028636377304792404,
-0.01927661895751953,
-0.02153133787214756,
-0.003104632254689932,
-0.03102116286754608,
0.006245287135243416,
0.06436977535486221,
0.017211202532052994,
0.006250783335417509,
-0.05168938636779785,
0.00023890465672593564,
0.00014492054469883442,
-0.05286923795938492,
0.022333113476634026,
-0.019300827756524086,
-0.0066447025164961815,
0.005040386226028204,
-0.06035548076033592,
-0.04608527198433876,
-0.012219258584082127,
0.00947253406047821,
0.03762422129511833,
-0.04766664654016495,
0.022802075371146202,
0.026941699907183647,
-0.006671686191111803,
-0.08132503926753998,
-0.06290022283792496,
0.02513565495610237,
0.00675943773239851,
-0.025680948048830032,
0.006657927762717009,
0.04177645966410637,
-0.03344670683145523,
-0.011505573987960815,
0.0020035267807543278,
0.02316974848508835,
-0.034159183502197266,
-0.002809847705066204,
0.015675535425543785,
0.005453305318951607,
0.08549867570400238,
0.03402402251958847,
-0.032117296010255814,
0.003055900102481246,
-0.034644052386283875,
0.0016182539984583855,
-0.024231260642409325,
0.044501468539237976,
-0.014262898825109005,
0.0028550205752253532,
-0.004382240120321512,
-0.03197045251727104,
0.05606171861290932,
-0.05433981865644455,
-0.02348402328789234,
0.031225332990288734,
0.023522062227129936,
0.003296131966635585,
-0.03445475175976753,
-0.010365553200244904,
-0.0413476824760437,
0.03519522771239281,
0.001884802128188312,
-0.013360615819692612,
-0.035196367651224136,
-0.03641362488269806,
0.005898687057197094,
0.01174064353108406,
0.006799666676670313,
0.041787683963775635,
0.059059079736471176,
-0.016436869278550148,
-0.004022522363811731,
-0.0027530184015631676,
-0.019873524084687233,
-0.008108017966151237,
-0.03807873651385307,
0.003065061289817095,
0.0006573502905666828,
0.0010380744934082031,
-0.03286335617303848,
-0.018989969044923782,
-0.03597574308514595,
0.02220611646771431,
0.06659325957298279,
-0.017426788806915283,
0.027737313881516457,
0.033524855971336365,
0.011872608214616776,
-0.00011604012252064422,
0.010104578919708729,
0.004177694674581289,
-0.015934616327285767,
-0.017359159886837006,
0.012355731800198555,
-0.03779374435544014,
-0.001161562860943377,
0.00959993526339531,
0.010848663747310638,
0.004392304457724094,
-0.003263352671638131,
-0.008416734635829926,
0.019071178510785103,
-0.024016615003347397,
0.03829079121351242,
-0.06271302700042725,
0.005170902702957392,
0.00802860502153635,
0.06241511180996895,
-0.01713193580508232,
-0.03978370502591133,
0.016790539026260376,
0.019029458984732628,
0.014389539137482643,
-0.060103751718997955,
0.011343364603817463,
-0.023802071809768677,
0.00967673771083355,
0.0014537815004587173,
0.04842711612582207,
-0.0013230065815150738,
0.014913545921444893,
0.013718104921281338,
0.009859728626906872,
0.014009987004101276,
-0.001006130944006145,
-0.07246540486812592,
-0.036633070558309555,
-0.022760046645998955,
-0.019151287153363228,
0.01239109132438898,
0.011059610173106194,
-0.030738545581698418,
0.03776862099766731,
-0.035266611725091934,
0.04194338619709015,
0.016412824392318726,
0.015013338066637516,
-0.050827059894800186,
0.0710049718618393,
-0.029178736731410027,
0.008450823836028576,
-0.012624300085008144,
0.007598900236189365,
0.10278646647930145,
0.0697765126824379,
0.021848078817129135,
-0.06513270735740662,
-0.00555617269128561,
-0.019827453419566154,
0.01102093979716301,
-0.04679379612207413,
0.06971936672925949,
0.027811864390969276,
0.011935442686080933,
-0.02443893626332283,
0.06578180193901062,
-0.0203713271766901,
0.027111517265439034,
0.04988671466708183,
-0.04084061086177826,
-0.054890044033527374,
-0.006798679940402508,
-0.007099264767020941,
0.02410283125936985,
0.03757171705365181,
-0.053705137223005295,
-2.532645169139869e-7,
-0.03294318541884422,
-0.024884546175599098,
-0.02395464852452278,
-0.017852427437901497,
0.06157360225915909,
-0.014103519730269909,
-0.044985026121139526,
0.010098441503942013,
0.045417170971632004,
-0.030559249222278595,
-0.028327831998467445,
0.03372157737612724,
0.03240623325109482,
-0.024096932262182236,
0.045272521674633026,
0.00741186086088419,
0.0080966055393219,
-0.0023945763241499662,
0.013693425804376602,
0.007009067106992006,
-0.016587046906352043,
-0.0028252683114260435,
-0.021557217463850975,
0.029919801279902458,
0.001589823979884386,
0.040770530700683594,
-0.0006962857441976666,
0.030611827969551086,
0.004401586018502712,
-0.04500746354460716,
-0.01308579184114933,
-0.039866890758275986,
0.034556031227111816,
-0.02858293056488037,
-0.0271292794495821,
-0.03892660140991211,
-0.002822954673320055,
-0.019985508173704147,
0.04600181803107262,
0.020361851900815964,
-0.020998932421207428,
0.02581898123025894,
0.005262221675366163,
0.01784491539001465,
0.0026927131693810225,
-0.02248874306678772,
0.034169528633356094,
0.004259827546775341,
-0.03673386573791504,
-0.049576204270124435,
0.034790825098752975,
0.021358489990234375,
0.011955217458307743,
0.024954073131084442,
-0.016940001398324966,
-0.00844824593514204,
-0.052545927464962006,
0.004413699731230736,
0.011717310175299644,
-0.03862838074564934,
0.002076481468975544,
-0.012009832076728344,
0.07058168202638626,
0.06165122985839844,
-0.044617027044296265,
0.03660060465335846,
-0.02581677958369255,
0.0075819422490894794,
0.05070558935403824,
-0.03997571021318436,
0.0009147861856035888,
0.03537243232131004,
-0.0015692353481426835,
-0.0036050216294825077,
-0.013391627930104733,
0.050664450973272324,
0.05371057242155075,
0.02624560333788395,
-0.03327251225709915,
0.04349573329091072,
-0.02347744256258011,
-0.022147925570607185,
-0.003648297628387809,
-0.05567547678947449,
0.04650126397609711,
0.016214575618505478,
0.02663830667734146,
-0.02914097160100937,
-0.06811946630477905,
0.00106215535197407,
0.033727843314409256,
0.020839205011725426,
0.0007953023887239397,
-0.02537836693227291,
0.004246503114700317,
0.0013709580525755882,
0.017496485263109207,
-0.034566670656204224,
-0.025991538539528847,
-0.03792708367109299,
0.0024134861305356026,
0.0030862041749060154,
-0.033388204872608185,
-0.0126164760440588,
0.02214287593960762,
-0.025313444435596466,
0.005806928034871817,
0.010329876095056534,
0.06250548362731934,
-0.008013558574020863,
0.0346243716776371,
0.02326543815433979,
-0.020248349756002426,
0.0221684742718935,
-0.01756904646754265,
-0.02647493965923786,
0.037514518946409225,
-0.03725758567452431,
-0.028803687542676926,
0.025192949920892715,
-0.0067866104654967785,
0.025704197585582733,
0.0003018315474037081,
-0.010211756452918053,
0.033663876354694366,
0.016933955252170563,
-0.014071873389184475,
0.02280195616185665,
0.013139245100319386,
-0.02937437780201435,
-0.015852853655815125,
-0.030944259837269783,
-0.010267692618072033,
0.01519693247973919,
0.03194798529148102,
0.04911353439092636,
0.005447786301374435,
0.01664006896317005,
-0.015589103102684021,
-0.008463568985462189,
-0.02250450849533081,
0.02122090756893158,
0.04622495174407959,
-0.007855345495045185,
0.028079193085432053,
0.013037767261266708,
-0.021044885739684105,
0.03959224000573158,
-0.000814493338111788,
0.009556123055517673,
-0.07004700601100922,
0.018494635820388794,
0.03298785910010338,
0.02206871658563614,
0.04476173594594002,
-0.03818472474813461,
-0.0171494223177433,
0.04437684267759323,
-0.057481419295072556,
0.022631026804447174,
-0.02217433974146843,
-0.003067237790673971,
-0.03890532627701759,
-0.010569688864052296,
-0.008953026495873928,
0.039291318506002426,
0.027923470363020897,
0.0524783656001091,
0.008576455526053905,
-0.005925071891397238,
0.0007877661264501512,
0.0007176506333053112,
0.018373820930719376,
0.027974409982562065,
-0.025386923924088478,
-0.026735514402389526,
0.06612283736467361,
-0.026778850704431534,
-0.04195115342736244,
0.029149608686566353,
-0.019223086535930634,
-0.0033219116739928722,
-0.013070402666926384,
0.02575179561972618,
-0.004423898179084063,
0.006535761058330536,
0.02862047217786312,
-0.04478103667497635,
-0.021749822422862053,
0.042246583849191666,
-0.0033464462030678988,
0.02865609899163246,
0.016666026785969734,
-0.009381067007780075,
0.009587225504219532,
-0.0835476741194725,
-0.04619922488927841,
0.005160643253475428,
-0.009137407876551151,
0.0023187845945358276,
-0.01364123448729515,
-0.0407344214618206,
0.03928225859999657,
-0.009102970361709595,
-0.003965691197663546,
-0.02334010973572731,
-0.023427220061421394,
-0.0032901798840612173,
-0.01668906956911087,
0.029152562841773033,
0.004467199556529522,
0.009786355309188366,
-0.07214700430631638,
0.06311880052089691,
-0.007912745699286461,
-0.010367580689489841,
-0.061792198568582535,
-0.0024018993135541677,
0.0073212552815675735,
0.0017155513633042574,
0.003762495703995228,
0.004691204521805048,
0.02053624950349331,
0.0281550120562315,
-0.0033605871722102165,
-0.004972175695002079,
0.002821996808052063,
-0.026392867788672447,
-0.07185990363359451,
-0.040236737579107285,
0.045919012278318405,
0.022485749796032906,
-0.014651782810688019,
-0.05219215154647827,
-0.006762194912880659,
-0.006956997327506542,
0.042737141251564026,
0.0486217737197876,
-0.02807007171213627,
0.007733932696282864,
0.0176544226706028,
-0.020043103024363518,
0.007084953598678112,
-0.04569629952311516,
-0.025089038535952568,
-0.013146228156983852,
-0.030764304101467133,
0.017833704128861427,
0.0011542786378413439,
-0.032404400408267975,
0.04453446716070175,
0.008337747305631638,
-0.011477227322757244,
0.039155904203653336,
-0.017693402245640755,
-0.01853865198791027,
0.011581170372664928,
0.03219696506857872,
-0.023313511162996292,
0.07186834514141083,
-0.02267199382185936,
-0.027562279254198074,
0.023104581981897354,
-0.04006156325340271,
-0.05563415214419365,
0.040113866329193115,
-0.007586479652673006,
0.017012283205986023,
0.00820411741733551,
-0.01716538704931736,
0.023081086575984955,
-0.049654796719551086,
-0.04936496913433075,
0.02446831576526165,
-0.02007230743765831,
-0.017547376453876495,
0.06526932120323181,
0.002106914296746254,
-0.009959246031939983,
-0.000058392623031977564,
-0.009222188033163548,
0.006072754506021738,
0.0018889243947342038,
0.025887880474328995,
0.01645750179886818,
0.02287129871547222,
0.0054091401398181915,
-0.020709825679659843,
-0.00804846826940775,
0.0006305634742602706,
0.021817434579133987,
0.0025397834833711386,
0.05635826662182808,
-0.00993671827018261,
-0.007025799248367548,
0.0038993866182863712,
-0.03987676650285721,
-0.031701989471912384,
0.02988646924495697,
-0.023630328476428986,
0.05764809623360634,
-0.02218315750360489,
0.017430707812309265,
0.024037763476371765,
-0.01155528798699379,
-0.0255901999771595,
0.011787140741944313,
0.028775667771697044,
0.006869675125926733,
-0.03242257609963417,
-0.03818195313215256,
-0.03728969395160675,
-0.02691817469894886,
0.06007448956370354,
-0.062014393508434296,
-0.007253111340105534,
-0.004315560217946768,
-0.0236673466861248,
-0.02193041332066059,
-0.008467508479952812,
-0.02218196913599968,
-0.012564958073198795,
0.006983734667301178,
0.05441718176007271,
-0.014054513536393642,
-0.003999547101557255,
0.009583920240402222,
-0.02826647274196148,
0.04469403252005577,
-0.08235591650009155,
0.02717350795865059,
0.027699967846274376,
0.017399987205863,
0.02605566568672657,
0.020488882437348366
] |
<p>I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I <em>suspect</em> that they are the most fundamentally natural unit for angles. What I want to know is why this is so (or why not).</p>
<p>I understand that using radians is useful in calculus involving trigonometric functions because there are no messy factors like $\pi/180$. I also understand that this is because $\sin(x) / x \rightarrow 1$ as $x \rightarrow 0$ when $x$ is in radians. But why does this mean radians are fundamentally more natural? What is mathematically wrong with these messy factors?</p>
<p>So maybe it's nice and clean to pick a unit which makes $\frac{d}{dx} \sin x = \cos x$. But why not choose to swap it around, by putting the 'nice and clean' bit at the unit of angle measurement itself? Why not define 1 Angle as a full turn, then measure angles as a fraction of this full turn (in a similar way to measuring velocities as a fraction of the speed of light $c = 1$). Sure, you would have messy factors of $2 \pi$ in calculus but what's wrong with this mathematically?</p>
<p>I think part of what I'm looking for is an explanation why the radius is the most important part of a circle. Could you not define another angle unit in a similar way to the radian, but with using the diameter instead of the radius?</p>
<p>Also, if radians are the fundamentally natural unit, does this mean that not only $\pi \,\textrm{rad} = 180 ^\circ$, but also $\pi = 180 ^\circ$, that is $1\,\textrm{rad}=1$?</p>
| 10,804 |
[
0.0023318256717175245,
0.008189134299755096,
-0.006360357161611319,
-0.010446442291140556,
0.040888939052820206,
0.03839073330163956,
-0.021881381049752235,
-0.0398583710193634,
-0.0291912704706192,
-0.005302768666297197,
0.021072780713438988,
0.01816151849925518,
0.06937123835086823,
0.024816198274493217,
0.0355195552110672,
-0.012302298098802567,
-0.022276297211647034,
-0.01279077585786581,
-0.02659250982105732,
-0.042453583329916,
-0.00008127398905344307,
0.009015072137117386,
0.018757333979010582,
-0.00009533195407129824,
-0.014854400418698788,
0.032655782997608185,
0.011575117707252502,
-0.006923214998096228,
0.004292363300919533,
0.0660492405295372,
0.025661403313279152,
-0.001945839379914105,
0.033394135534763336,
0.018426241353154182,
0.012079521082341671,
-0.02369176782667637,
0.0008074739598669112,
0.01805642619729042,
-0.04630409926176071,
0.05759420245885849,
-0.044124629348516464,
-0.017857635393738747,
-0.009727953001856804,
0.0274526234716177,
-0.006174885202199221,
0.04678042232990265,
-0.01984618790447712,
-0.032774653285741806,
0.04936813563108444,
-0.04701926186680794,
0.05595989525318146,
0.008033293299376965,
0.01896228827536106,
0.015388536266982555,
0.008878705091774464,
-0.0151133444160223,
0.07213349640369415,
0.0141020268201828,
-0.017819233238697052,
-0.03844553977251053,
-0.009033908136188984,
-0.032937441021203995,
0.038899656385183334,
0.007013014983385801,
-0.022647777572274208,
0.003097677603363991,
-0.006884627975523472,
0.0027239236515015364,
0.02478068135678768,
-0.036380406469106674,
0.02275233343243599,
0.009162635542452335,
-0.002477246103808284,
-0.024560309946537018,
-0.011065767146646976,
-0.015413972549140453,
0.021854382008314133,
-0.004875966347754002,
0.0782724991440773,
0.045358214527368546,
-0.04292234778404236,
-0.007665105164051056,
0.026157137006521225,
0.02510920725762844,
0.014263947494328022,
-0.014929930679500103,
0.07427790015935898,
0.00874430499970913,
0.01899789273738861,
0.021467175334692,
-0.008608061820268631,
-0.010416194796562195,
0.05220627039670944,
-0.016793470829725266,
-0.0033173460979014635,
0.05081512778997421,
0.00007769359945086762,
0.038097262382507324,
0.028781039640307426,
-0.028263313695788383,
0.00645956676453352,
-0.011592588387429714,
0.0178963802754879,
0.06420585513114929,
-0.02801559865474701,
-0.02307193912565708,
-0.013813340105116367,
0.012878385372459888,
-0.0077738636173307896,
0.00018848163017537445,
-0.019887935370206833,
0.021369192749261856,
-0.022293347865343094,
0.011885188519954681,
0.026668047532439232,
-0.025576388463377953,
0.025102728977799416,
-0.002001548418775201,
0.060994625091552734,
0.06265193223953247,
0.07050938904285431,
-0.047388773411512375,
0.014039993286132812,
-0.02990259975194931,
-0.05819062888622284,
0.018399953842163086,
0.0010809792438521981,
0.03033594973385334,
0.014787597581744194,
-0.004335079342126846,
0.007778715807944536,
-0.013303427025675774,
0.041126903146505356,
0.027548523619771004,
0.013817472383379936,
-0.05610330030322075,
-0.08894915878772736,
-0.06734709441661835,
0.05914926901459694,
0.020515143871307373,
-0.05943820998072624,
-0.10664637386798859,
0.01757279969751835,
0.00104940973687917,
0.07306122779846191,
0.007088550366461277,
0.0012707224814221263,
0.00789776723831892,
0.011459127999842167,
-0.02167479321360588,
-0.046693477779626846,
-0.02405756153166294,
0.0280621275305748,
-0.050620220601558685,
0.01080900989472866,
-0.029377879574894905,
0.010519519448280334,
0.03716683015227318,
0.017890600487589836,
-0.05186917260289192,
0.0464794747531414,
-0.053590327501297,
-0.014733171090483665,
0.07027699798345566,
0.004542037844657898,
-0.05389157310128212,
0.09085418283939362,
0.03755781427025795,
-0.009124642238020897,
0.05376178026199341,
0.03702175244688988,
0.04268153756856918,
0.019793523475527763,
0.012511907145380974,
0.0316934771835804,
-0.019196921959519386,
-0.019131017848849297,
-0.015489106066524982,
0.02866344340145588,
0.016392745077610016,
-0.02022433839738369,
-0.047202400863170624,
0.0029699644073843956,
-0.004581902176141739,
-0.035240087658166885,
0.06935778260231018,
-0.01113838143646717,
0.009465979412198067,
0.019802888855338097,
-0.025033127516508102,
0.01887201890349388,
-0.03787529841065407,
0.01832110807299614,
0.005811701528728008,
-0.014230993576347828,
0.006027013994753361,
0.011917227879166603,
0.008617803454399109,
-0.02018953301012516,
-0.00901824701577425,
-0.017708992585539818,
0.05864671990275383,
0.03601561486721039,
-0.00918465107679367,
0.04176478832960129,
0.04157016798853874,
0.027976512908935547,
0.0046355267986655235,
-0.011691289022564888,
0.004456985741853714,
-0.039703257381916046,
-0.016419226303696632,
-0.04298017919063568,
0.02895035408437252,
-0.017758684232831,
-0.028593478724360466,
0.01576116494834423,
-0.03287820890545845,
-0.03855971619486809,
0.06110749393701553,
-0.010395752266049385,
0.07171928882598877,
-0.0038564212154597044,
-0.011484122835099697,
-0.013356829062104225,
0.06106925755739212,
0.002765391254797578,
-0.016789132729172707,
0.007087657228112221,
-0.03923811390995979,
-0.03633636236190796,
0.01103772222995758,
0.07528281956911087,
0.030596619471907616,
-0.05628475919365883,
0.0063402606174349785,
0.025473125278949738,
0.059560492634773254,
0.019562209025025368,
0.0018549738451838493,
-0.03200190141797066,
-0.03281088173389435,
0.0028309545014053583,
0.01694505847990513,
0.001865458907559514,
-0.005794258322566748,
0.020728824660182,
0.01479110587388277,
0.014440745115280151,
0.0086405910551548,
-0.0009888564236462116,
0.044899437576532364,
-0.0347638800740242,
0.026931704953312874,
0.03603201359510422,
0.0044053359888494015,
0.03321002796292305,
-0.036474574357271194,
-0.0037065758369863033,
0.007109473459422588,
0.0055199358612298965,
-0.034214042127132416,
-0.014549133367836475,
0.01877094805240631,
0.012241056188941002,
-0.015075191855430603,
-0.022027984261512756,
-0.029790420085191727,
0.019987130537629128,
-0.021553272381424904,
-0.003580495249480009,
-0.033321563154459,
-0.02750447392463684,
-0.03829925134778023,
-0.0051194229163229465,
0.014176065102219582,
0.01859712041914463,
0.0013472717255353928,
0.009357437491416931,
-0.02718234620988369,
0.007271989248692989,
-0.016131384298205376,
-0.04288134351372719,
0.009904185310006142,
-0.04591568559408188,
0.008862610906362534,
-0.018538696691393852,
0.009405222721397877,
0.03295845538377762,
-0.012263880111277103,
0.021996458992362022,
-0.0009326683939434588,
-0.03230556845664978,
-0.05790838226675987,
-0.02015593647956848,
-0.0482909120619297,
0.01701142080128193,
-0.009877786040306091,
-0.027076587080955505,
0.05282428860664368,
-0.03987017273902893,
-0.03225488215684891,
0.013175643980503082,
-0.04994218051433563,
-0.028926074504852295,
-0.026597172021865845,
0.00376947526820004,
0.033442314714193344,
-0.0400240458548069,
-0.011618489399552345,
0.0016210568137466908,
-0.0533125102519989,
0.011290724389255047,
-0.03382381424307823,
-0.05470879375934601,
0.02503514476120472,
-0.003130223136395216,
0.051663123071193695,
0.06093450263142586,
0.0009540805476717651,
0.08442994207143784,
0.023541297763586044,
-0.040340665727853775,
-0.007587549742311239,
0.00945240817964077,
-0.0023304938804358244,
-0.03072231449186802,
-0.03089962527155876,
0.043905895203351974,
0.004882963839918375,
0.014779792167246342,
-0.021037811413407326,
-0.002029155381023884,
0.022074049338698387,
0.0207844078540802,
0.012291194871068,
-0.0009416771936230361,
0.004592226352542639,
0.019918082281947136,
0.017917802557349205,
0.05328627675771713,
0.0027796668000519276,
0.026776133105158806,
0.007443432230502367,
0.03312254324555397,
0.014831159263849258,
-0.05718134343624115,
0.03365117311477661,
-0.013783391565084457,
0.009456337429583073,
-0.008902174420654774,
-0.009265860542654991,
-0.011257628910243511,
0.00036642359918914735,
0.0031265714205801487,
0.032002516090869904,
0.014801391400396824,
-0.036528751254081726,
-0.004884528461843729,
0.024909110739827156,
0.05647215247154236,
0.00993629451841116,
0.0017870304873213172,
-0.027021892368793488,
0.018960556015372276,
0.043541692197322845,
-0.008057196624577045,
0.021534282714128494,
0.04599429666996002,
0.04093868285417557,
0.019743947312235832,
-0.029072629287838936,
-0.06937777251005173,
0.0054139066487550735,
-0.05915125459432602,
-0.012424051761627197,
-0.02667551301419735,
0.06264100223779678,
0.009489811025559902,
0.06285730004310608,
0.01872704178094864,
0.005877504125237465,
-0.025696834549307823,
0.0007042487268336117,
-0.06250680238008499,
0.014425624161958694,
-0.04115476831793785,
-0.006079736165702343,
-0.018515365198254585,
0.015127163380384445,
-0.008064277470111847,
-0.03172939643263817,
-0.04361375793814659,
-0.03736081346869469,
-0.05583425983786583,
-0.029889965429902077,
-0.000028271453629713506,
-0.032007813453674316,
-0.03378460183739662,
-0.031258441507816315,
0.06164967641234398,
0.05167172849178314,
-0.016404783353209496,
0.018425146117806435,
0.05169815197587013,
-0.020286886021494865,
-0.015772748738527298,
-0.012199269607663155,
0.003417126601561904,
0.02140973135828972,
0.019172191619873047,
0.02795535884797573,
-0.00875235628336668,
0.03396715968847275,
0.0016563661629334092,
0.020794063806533813,
0.055308327078819275,
0.010620149783790112,
-0.00574388587847352,
-0.010628040879964828,
-0.044274814426898956,
-0.0058618271723389626,
-0.02432951144874096,
0.07149463146924973,
-0.04343245178461075,
-0.00831453688442707,
0.04361985996365547,
-0.010162203572690487,
0.011127892881631851,
0.02940397337079048,
0.014392441138625145,
0.006753635127097368,
-0.0529002919793129,
-0.03240346536040306,
-0.030077727511525154,
-0.023060135543346405,
-0.02479534223675728,
0.003819186007604003,
-0.02712482213973999,
-0.004318016115576029,
-0.03806029260158539,
0.02265511453151703,
-0.00880419835448265,
-0.02692236192524433,
0.021312721073627472,
-0.0029760703910142183,
0.0348738469183445,
0.008407297544181347,
-0.0029550811741501093,
-0.007636752910912037,
0.03595750778913498,
0.044393617659807205,
-0.0003703199326992035,
-0.010687553323805332,
-0.07571117579936981,
0.017398476600646973,
0.00834294967353344,
0.06689730286598206,
-0.014509246684610844,
0.014406085014343262,
-0.00989059079438448,
-0.029310468584299088,
0.03926236182451248,
-0.011812875047326088,
0.0037743966095149517,
-0.08955700695514679,
-0.0072694201953709126,
0.0006408345070667565,
-0.002557089552283287,
-0.026285339146852493,
0.00958324782550335,
0.029706908389925957,
0.01857287622988224,
-0.017750583589076996,
0.012390132062137127,
-0.02811022847890854,
0.003405393799766898,
0.01841656118631363,
0.041219063103199005,
0.028058933094143867,
-0.032116081565618515,
0.03863254189491272,
0.018542082980275154,
0.034600090235471725,
-0.0580783449113369,
0.0048269247636199,
0.021644489839673042,
0.009320962242782116,
0.0035187695175409317,
-0.03542403131723404,
-0.06570308655500412,
0.033740051090717316,
-0.039477501064538956,
0.0021546196658164263,
0.041019145399332047,
-0.04708245396614075,
0.015524360351264477,
0.04347855970263481,
0.014505497179925442,
-0.0009541212930344045,
0.05407937616109848,
0.010440463200211525,
-0.02867279201745987,
-0.017234185710549355,
0.036669082939624786,
-0.031492337584495544,
-0.0371527262032032,
-0.017837483435869217,
-0.009595460258424282,
-0.039524421095848083,
0.03970677778124809,
0.03330829739570618,
0.010960699990391731,
-0.030894676223397255,
-0.052390486001968384,
-0.01151563785970211,
0.034661442041397095,
-0.005998039618134499,
-0.014223474077880383,
-0.01756894960999489,
0.0042607528157532215,
0.01916597969830036,
-0.006842267233878374,
0.01182839646935463,
-0.013026122003793716,
-0.003930927719920874,
0.011516964063048363,
0.015686269849538803,
0.0019056977471336722,
-0.01715666428208351,
0.001917728572152555,
0.02132708579301834,
-0.045701999217271805,
0.03679750859737396,
-0.03041737526655197,
-0.0066629392094910145,
-0.007059256546199322,
-0.058383744210004807,
-0.04481164366006851,
0.0016359471483156085,
0.00990195944905281,
0.04940980300307274,
-0.04801250249147415,
0.006548644043505192,
-0.01057085208594799,
-0.01171704102307558,
-0.05288161709904671,
-0.04006507247686386,
-0.02149096131324768,
-0.014060325920581818,
-0.011211332865059376,
0.015359087847173214,
0.03862099349498749,
-0.009995812550187111,
-0.02313707396388054,
0.007812938652932644,
0.05388375744223595,
-0.019400278106331825,
-0.00467474153265357,
0.005628792103379965,
0.03665561601519585,
0.05130063369870186,
-0.03583456575870514,
-0.0346861258149147,
0.009305278770625591,
0.006320013199001551,
-0.023202694952487946,
0.02019045315682888,
0.05283131077885628,
-0.03500942140817642,
-0.04047301411628723,
-0.00008240259194280952,
-0.04025128856301308,
0.02237262763082981,
-0.02913222461938858,
-0.00010118530917679891,
0.01904565468430519,
-0.013865048997104168,
0.005211250390857458,
0.010341123677790165,
0.04513291269540787,
0.00624488852918148,
0.020735692232847214,
-0.006815160159021616,
0.024877436459064484,
-0.045647282153367996,
-0.06873621046543121,
0.017702586948871613,
-0.00855212938040495,
0.039195332676172256,
-0.010557710193097591,
0.015675432980060577,
-0.044972360134124756,
-0.0183696448802948,
0.00763043574988842,
0.012353361584246159,
0.04329526051878929,
0.033045925199985504,
-0.009182415902614594,
0.01614883542060852,
0.006071567535400391,
-0.027205605059862137,
-0.02565355785191059,
-0.04277969151735306,
-0.0054454077035188675,
0.07542642205953598,
-0.03671499341726303,
0.04204213246703148,
0.006066395901143551,
-0.016227243468165398,
-0.00012320239329710603,
-0.009406913071870804,
-0.02541147917509079,
0.003335270332172513,
-0.02345602586865425,
0.022661013528704643,
-0.04082200676202774,
-0.004664968699216843,
-0.020441366359591484,
0.043904151767492294,
0.026241561397910118,
-0.008947096765041351,
0.00972596462816,
0.03810824826359749,
-0.009412656538188457,
-0.0060681672766804695,
-0.0398610383272171,
0.060621365904808044,
-0.01098614651709795,
0.021432876586914062,
0.007520945277065039,
-0.048395611345767975,
0.04189299792051315,
-0.03996520861983299,
0.004197641275823116,
-0.050487592816352844,
-0.005235779564827681,
-0.015532869845628738,
-0.011967831291258335,
0.02895222418010235,
-0.013869432732462883,
-0.01977095566689968,
-0.03003629483282566,
0.022920288145542145,
-0.03203332796692848,
0.04771040380001068,
0.007209546864032745,
-0.057700008153915405,
-0.015713658183813095,
-0.028966566547751427,
-0.05505504086613655,
0.042224589735269547,
-0.01463564857840538,
-0.012591501697897911,
0.00230267271399498,
-0.0349029004573822,
-0.001803720137104392,
0.02743515372276306,
0.010209438391029835,
-0.045447275042533875,
0.03466365858912468,
0.006137535907328129,
0.003663409035652876,
-0.023551419377326965,
-0.03678250312805176,
0.119249127805233,
-0.00005009043889003806,
-0.010004418902099133,
-0.04312775284051895,
0.04440684616565704,
-0.04018682986497879,
0.02889351174235344,
-0.041020043194293976,
0.022573767229914665,
0.001376585802063346,
0.03801249712705612,
0.0036280544009059668,
0.03699115291237831,
0.017465589568018913,
-0.010886968113481998,
0.03700229898095131,
-0.025165295228362083,
-0.062291134148836136,
-0.0049523646011948586,
0.01619548536837101,
0.023087523877620697,
0.028399281203746796,
-0.027488915249705315,
0.036448027938604355,
-0.037339888513088226,
-0.018115755170583725,
-0.03266245126724243,
-0.02025458589196205,
0.017954953014850616,
-0.006285081617534161,
-0.05239468812942505,
0.011109203100204468,
0.024950338527560234,
-0.04726317897439003,
-0.02691369503736496,
0.023349661380052567,
0.01965981349349022,
0.0094017768278718,
0.004518994130194187,
0.01069075707346201,
0.030946245416998863,
-0.008122843690216541,
-0.0010159669909626245,
0.01807561330497265,
-0.05686376988887787,
-0.03695500269532204,
-0.01211948599666357,
0.031749311834573746,
-0.023164840415120125,
0.020892493426799774,
-0.03778732195496559,
0.023868320509791374,
-0.012603970244526863,
-0.049022406339645386,
-0.014118016697466373,
0.008062738925218582,
0.053222622722387314,
-0.010120255872607231,
-0.039230506867170334,
0.0001296701084356755,
0.05324128270149231,
-0.027268091216683388,
0.06966798007488251,
0.0018796431832015514,
-0.04332931339740753,
-0.016270572319626808,
0.004239528905600309,
0.03226281329989433,
-0.010503840632736683,
-0.019376395270228386,
-0.037893496453762054,
0.018824849277734756,
-0.059056010097265244,
-0.009515916928648949,
0.02399870939552784,
0.023394938558340073,
0.020570481196045876,
-0.01347065344452858,
0.016598928719758987,
-0.026450050994753838,
-0.010399342514574528,
0.03043832816183567,
-0.013705982826650143,
-0.020101362839341164,
-0.06081255152821541,
-0.03038022667169571,
0.022833701223134995,
0.0052777500823140144,
0.010706903412938118,
-0.006882339715957642,
-0.015267779119312763,
0.006902341730892658,
0.023937249556183815,
-0.005089872982352972,
-0.019361462444067,
0.04079859331250191,
-0.022261325269937515,
0.014714527875185013,
-0.00020015904738102108,
0.010720333084464073,
0.04926345497369766,
0.034717511385679245,
-0.004787655547261238,
0.009655623696744442,
0.0003047275240533054,
-0.0007830311078578234,
0.018693668767809868,
-0.06391867250204086,
0.04154440015554428,
0.017447026446461678,
0.01642570085823536,
-0.06859561055898666,
-0.04006386920809746,
-0.020400628447532654,
0.019533181563019753,
-0.03539833799004555,
0.0231886375695467,
-0.022576680406928062,
0.016653520986437798,
-0.027742179110646248,
0.00807497650384903,
-0.049549005925655365,
-0.0059480853378772736,
-0.056184712797403336,
0.005022695753723383,
-0.012352834455668926,
-0.037812575697898865,
-0.011785872280597687,
0.028550513088703156,
0.0148666612803936,
-0.055593814700841904,
0.03845684602856636,
0.019415900111198425,
-0.0017334785079583526,
-0.015896547585725784,
0.009468212723731995,
-0.02079867012798786,
0.036274343729019165,
-0.0777994692325592,
-0.05344076082110405,
0.015574444085359573,
-0.022312501445412636,
-0.059896040707826614,
0.040134496986866,
-0.034978386014699936,
0.007306287530809641,
0.019255196675658226,
0.004832962527871132,
0.0010597652290016413,
0.029295986518263817,
-0.011010894551873207,
0.030108099803328514,
-0.011597178876399994,
0.0000903031905181706,
0.004929815419018269,
-0.019438857212662697,
-0.017582356929779053,
-0.01774691231548786,
0.005183487664908171,
0.07341765612363815,
0.01029849424958229,
0.013639194890856743,
0.01882219687104225,
0.021452877670526505,
-0.016972288489341736,
0.014776195399463177,
0.033587746322155,
0.03769940882921219,
0.01905731111764908,
0.002612825483083725,
-0.053043026477098465,
0.035201944410800934,
0.009575454518198967,
0.02693481184542179,
-0.06109696626663208,
0.0006760428077541292,
0.010524689219892025,
0.015825234353542328,
0.026371676474809647,
-0.04032670706510544,
-0.03272365778684616,
0.024187397211790085,
-0.07506099343299866,
-0.009551283903419971,
-0.046264003962278366,
-0.01691819727420807,
-0.046377863734960556,
-0.041491907089948654,
0.005074955523014069,
0.05606980621814728,
0.014889590442180634,
0.023391468450427055,
0.02798842079937458,
-0.001975579420104623,
-0.0041658757254481316,
-0.054152339696884155,
0.0038838156033307314,
0.0220158901065588,
-0.03112007863819599,
0.005315229296684265,
0.06446052342653275,
0.03291958197951317,
-0.014002853073179722,
0.04208219051361084,
0.00017312369891442358,
0.02431066334247589,
0.018310535699129105,
0.003172915894538164,
0.03805147856473923,
0.034836117178201675,
0.009127006866037846,
-0.034459199756383896,
-0.06201852113008499,
0.012417754158377647,
0.027163641527295113,
0.02529403194785118,
-0.015011603012681007,
-0.01810234598815441,
0.03818577900528908,
-0.046357981860637665,
-0.056456055492162704,
-0.02074340730905533,
-0.016226092353463173,
-0.013037615455687046,
-0.007534403819590807,
0.034300386905670166,
0.002752938773483038,
-0.03888290375471115,
0.008834212087094784,
-0.018400585278868675,
-0.006602726876735687,
0.046837858855724335,
-0.011016354896128178,
0.021121790632605553,
0.02570294588804245,
0.01970812678337097,
-0.009865469299256802,
0.011741222813725471,
0.04692479223012924,
0.015764886513352394,
-0.05321529507637024,
0.003509891452267766,
0.02177457883954048,
-0.03845811262726784,
0.0275608841329813,
-0.003200660925358534,
-0.04888944700360298,
0.015539783984422684,
0.020348209887742996,
0.014067054726183414,
-0.004664203152060509,
-0.038088373839855194,
-0.029659131541848183,
-0.045011647045612335,
0.053929124027490616,
0.02322976663708687,
0.017382953315973282,
-0.02360590547323227,
-0.010844536125659943,
-0.023182276636362076,
0.017099473625421524,
0.06075817346572876,
0.027897488325834274,
-0.005150343757122755,
0.02241423726081848,
0.03719738870859146,
0.012457643635571003,
-0.019584834575653076,
-0.01926586963236332,
-0.021967820823192596,
0.011771304532885551,
-0.004938191268593073,
-0.01460372842848301,
-0.020654866471886635,
0.012026676908135414,
0.014559859409928322,
-0.024761589244008064,
0.028785143047571182,
0.0004990301094949245,
-0.013444258831441402,
0.09589754045009613,
-0.03746606782078743,
-0.009886639192700386,
0.07788868993520737,
0.03823838755488396,
0.006958580110222101,
0.03692842274904251,
-0.03415175899863243,
-0.047473710030317307,
0.021021151915192604,
-0.007217012345790863,
-0.03801582008600235,
-0.023180978372693062,
0.016376834362745285,
0.04089146479964256,
-0.02242281846702099,
-0.009395713917911053,
0.0644989162683487,
-0.05111513286828995,
-0.013506711460649967,
0.032046470791101456,
0.014264109544456005,
0.03263091295957565,
0.013282162137329578,
0.016780022531747818,
0.040396567434072495,
-0.018426962196826935,
0.02540924772620201,
0.010794355534017086,
0.05107899382710457,
0.012704111635684967,
0.008935468271374702,
0.03786635771393776,
-0.004521695431321859,
0.03990296646952629,
-0.016745340079069138,
0.08237778395414352,
-0.012454913929104805,
-0.013570614159107208,
-0.0012142701307311654,
-0.040901023894548416,
-0.016827477142214775,
-0.0014478486264124513,
-0.0124626150354743,
0.09295324236154556,
0.009556169621646404,
0.003973621409386396,
-0.012742440216243267,
-0.01875481940805912,
-0.03891471400856972,
-0.007727252785116434,
0.0269493218511343,
0.0379025936126709,
-0.03463171049952507,
0.0052428594790399075,
-0.019492238759994507,
-0.02102380059659481,
0.057204872369766235,
-0.005417049862444401,
0.02052154205739498,
0.027249522507190704,
-0.00877202209085226,
-0.0038043952081352472,
-0.02109469100832939,
-0.027627302333712578,
-0.03774239867925644,
0.048670943826436996,
0.05016860365867615,
0.06970241665840149,
0.03969460353255272,
-0.014752569608390331,
-0.01203604880720377,
0.051203642040491104,
-0.05546749755740166,
-0.02416893094778061,
0.01742754690349102,
0.033448804169893265,
0.005363856442272663,
-0.01178185734897852
] |
<p>I know it's not possible with Earth today, but With today's level of material science technology, would it be possible to make cable strong and light enough to make a space elevator system connecting a Mars-synchronous satellite to an anchor on Mars' surface, ignoring any load at all by an elevator car? Or can someone say with a high degree of certainty that the level of strength to weight possible in cables today is still far from possible even with Mars' lower mass compared to Earth?</p>
| 10,805 |
[
-0.009789470583200455,
0.0009137549786828458,
-0.039154283702373505,
-0.01309326384216547,
0.05492221564054489,
0.05843956023454666,
-0.034885913133621216,
-0.02287708967924118,
0.004991048015654087,
-0.05619968846440315,
-0.012749278917908669,
0.057863809168338776,
0.024830110371112823,
0.0068769920617341995,
0.04608635976910591,
0.001076419255696237,
0.015813706442713737,
-0.03706815093755722,
-0.005074869841337204,
-0.01563655026257038,
-0.0031421196181327105,
-0.013623226433992386,
0.026313548907637596,
0.043963946402072906,
-0.004224427510052919,
0.0019260775297880173,
0.02402649074792862,
-0.03716623783111572,
0.006479106843471527,
0.048342302441596985,
0.003314798232167959,
-0.007679082918912172,
-0.0005249298992566764,
0.028568154200911522,
0.06273860484361649,
0.021677331998944283,
-0.06268951296806335,
-0.038587361574172974,
0.012277970090508461,
0.054169297218322754,
-0.016157668083906174,
-0.01819515787065029,
-0.012246386148035526,
0.048785436898469925,
-0.03034629486501217,
0.005318674258887768,
0.006370966788381338,
-0.056242965161800385,
0.05945216119289398,
-0.09321475028991699,
0.06488288193941116,
-0.018065866082906723,
0.015254671685397625,
0.034888461232185364,
0.005316955968737602,
-0.030598793178796768,
0.07290662080049515,
0.025671925395727158,
0.03315534442663193,
-0.021767186000943184,
-0.034226492047309875,
-0.008897245861589909,
-0.04006870836019516,
-0.046902235597372055,
-0.024263950064778328,
0.007122621405869722,
-0.05877341330051422,
-0.004338718019425869,
0.06139109656214714,
0.013998564332723618,
0.005514686927199364,
0.027457034215331078,
0.02532179094851017,
-0.0038183340802788734,
-0.027292942628264427,
-0.012903721071779728,
0.015216934494674206,
-0.011287842877209187,
0.029588406905531883,
0.04509222134947777,
-0.03053329326212406,
-0.024048354476690292,
0.04652366042137146,
0.06444302946329117,
0.004163183271884918,
-0.014787571504712105,
0.060419607907533646,
-0.04638249799609184,
0.021790744736790657,
-0.021332425996661186,
0.015308728441596031,
-0.009721740148961544,
-0.008228677324950695,
0.001313888351432979,
0.0004485592362470925,
-0.0003618568880483508,
0.014219598844647408,
0.042414307594299316,
0.005333497188985348,
-0.017217878252267838,
0.009758972562849522,
0.01035144180059433,
0.005677344743162394,
0.07222969084978104,
0.06342169642448425,
-0.030774572864174843,
0.011139286682009697,
0.006566994357854128,
0.010533689521253109,
-0.021293556317687035,
-0.02868708036839962,
-0.025783222168684006,
0.02141582779586315,
-0.04428013041615486,
0.025467107072472572,
-0.02823900245130062,
0.028774723410606384,
-0.03160885348916054,
0.029999421909451485,
0.06965933740139008,
0.03222891688346863,
-0.01287498977035284,
0.08568839728832245,
-0.06034129485487938,
-0.016643095761537552,
0.026330076158046722,
0.02325615845620632,
-0.028811587020754814,
0.00897293258458376,
0.01925010234117508,
0.009335549548268318,
-0.0045072901993989944,
-0.020367948338389397,
-0.03010156750679016,
0.08431713283061981,
-0.000007032030680420576,
-0.061525724828243256,
-0.02722303755581379,
0.0013339048018679023,
-0.019959192723035812,
0.0031537951435893774,
-0.036356933414936066,
0.01281102653592825,
0.009529071860015392,
0.06677120178937912,
0.01734982244670391,
0.04950464144349098,
0.009481117129325867,
0.012578855268657207,
0.007726305164396763,
-0.03315407410264015,
-0.010458077304065228,
-0.0005567219923250377,
-0.08148044347763062,
0.020686130970716476,
-0.06808637827634811,
0.02287248522043228,
0.0022969585843384266,
0.03587330877780914,
-0.048639874905347824,
0.028462233021855354,
-0.01321210153400898,
0.006250846665352583,
0.0138314887881279,
-0.017246603965759277,
-0.005139087326824665,
0.06311941146850586,
0.0090149762108922,
0.010785846970975399,
0.04095712676644325,
0.030231701210141182,
0.0035721256863325834,
0.06281821429729462,
0.03257640451192856,
0.030746636912226677,
-0.06801579147577286,
-0.013193022459745407,
-0.045505590736866,
0.005942231044173241,
0.007486961781978607,
-0.028130769729614258,
-0.046213749796152115,
0.03054426610469818,
0.002835445338860154,
-0.002426553750410676,
0.06553775072097778,
-0.00440939050167799,
-0.03498300164937973,
0.033428143709897995,
-0.013372566550970078,
0.024459021165966988,
-0.0020660862792283297,
0.02462157979607582,
-0.0007876252057030797,
0.020082352682948112,
-0.006461767479777336,
0.027269525453448296,
-0.003111924510449171,
-0.040320735424757004,
-0.02052811160683632,
0.010067294351756573,
0.04625833034515381,
0.003772312542423606,
0.04112055152654648,
0.02500041387975216,
0.050391748547554016,
0.06534586101770401,
0.005047651007771492,
-0.011643461883068085,
-0.0024536349810659885,
-0.04736470803618431,
-0.026206079870462418,
-0.044703807681798935,
0.030917450785636902,
0.029078928753733635,
-0.0017164311138913035,
0.03266236186027527,
-0.0428759939968586,
-0.025420891121029854,
0.023748639971017838,
0.016870766878128052,
0.09206438809633255,
0.009028667584061623,
-0.0036824445705860853,
0.003575157606974244,
0.0017446217825636268,
0.053275398910045624,
0.013580712489783764,
0.006763705052435398,
-0.040935736149549484,
-0.0607072189450264,
-0.005814460571855307,
0.031408607959747314,
0.03528209030628204,
-0.058962929993867874,
0.026307327672839165,
0.020218485966324806,
0.034395258873701096,
0.05264778807759285,
0.0044546592980623245,
-0.039945200085639954,
-0.008783536031842232,
0.027866115793585777,
0.023651478812098503,
0.02288592793047428,
-0.002284507267177105,
0.0030791328754276037,
0.04928114637732506,
-0.021635139361023903,
-0.023487746715545654,
0.033503539860248566,
-0.018694808706641197,
-0.011974306777119637,
0.020868446677923203,
-0.002144220983609557,
-0.03709334135055542,
0.062497302889823914,
-0.05545928329229355,
0.012309277430176735,
0.03353150933980942,
-0.005428213160485029,
0.0052707623690366745,
-0.006881986744701862,
-0.0034645579289644957,
0.026154393330216408,
-0.0004202381824143231,
-0.024010123685002327,
-0.025115398690104485,
0.03869147598743439,
-0.030445115640759468,
0.009524823166429996,
-0.024887969717383385,
0.028546608984470367,
-0.01492062397301197,
0.017932839691638947,
0.005487245507538319,
-0.04510342329740524,
0.04324781894683838,
-0.022759487852454185,
-0.018777994439005852,
-0.01989787630736828,
-0.03467581793665886,
-0.015855295583605766,
0.02216734178364277,
-0.024226481094956398,
-0.004052082076668739,
0.0009996566222980618,
-0.03630601987242699,
0.06218531355261803,
0.03443063050508499,
-0.014693321660161018,
0.01796979084610939,
0.006193792913109064,
-0.019764548167586327,
-0.018646664917469025,
0.0006998194148764014,
0.016437837854027748,
-0.004410328809171915,
0.01732425019145012,
0.010230743326246738,
0.0020260438323020935,
0.0007487911498174071,
0.06747617572546005,
-0.07478389889001846,
-0.03437335044145584,
-0.002431251807138324,
0.006465344224125147,
-0.023371096700429916,
-0.04978300631046295,
0.07150780409574509,
0.04012860730290413,
-0.019571255892515182,
0.007249177899211645,
-0.04053100198507309,
-0.03063017502427101,
0.0324634425342083,
-0.023783724755048752,
0.04987504705786705,
-0.024400806054472923,
-0.03698629140853882,
0.08230174332857132,
0.00907094869762659,
-0.02902272716164589,
-0.01802631840109825,
-0.021230367943644524,
0.006783381570130587,
0.014809840358793736,
0.018383922055363655,
0.006746088620275259,
0.004661858547478914,
0.0015549898380413651,
0.0571705587208271,
-0.013825895264744759,
0.024595271795988083,
0.041795141994953156,
-0.008789187297224998,
-0.018192507326602936,
0.03992137685418129,
-0.01394063513725996,
0.036598291248083115,
0.021400101482868195,
-0.010871530510485172,
0.04439237341284752,
-0.012692861258983612,
0.06478866189718246,
-0.026189114898443222,
-0.036202430725097656,
0.05456482246518135,
0.009480941109359264,
0.04222031310200691,
0.007770612370222807,
0.026229696348309517,
-0.004823510535061359,
-0.0070013003423810005,
0.0023659607395529747,
0.016016654670238495,
0.022629376500844955,
-0.011706517077982426,
-0.038018517196178436,
0.03297370672225952,
0.0897417888045311,
-0.017313044518232346,
-0.032578762620687485,
0.014415387064218521,
0.020086895674467087,
0.022948386147618294,
-0.014459137804806232,
-0.03457897529006004,
0.026800651103258133,
0.02738984487950802,
0.028324943035840988,
0.023644495755434036,
0.012269758619368076,
0.010627061128616333,
-0.04672541841864586,
-0.009963450022041798,
0.0022885219659656286,
0.04604708030819893,
0.007645840290933847,
0.011668943800032139,
0.042569849640131,
0.03795745223760605,
0.029366005212068558,
-0.010601802729070187,
-0.07020334154367447,
-0.011293918825685978,
-0.03778306767344475,
-0.04604637995362282,
0.0013775672996416688,
0.0053146411664783955,
-0.04381152614951134,
-0.04638197273015976,
-0.01708957366645336,
-0.031953997910022736,
0.01573932357132435,
-0.046092770993709564,
0.024377847090363503,
-0.03597765788435936,
-0.007878652773797512,
0.0002997595292981714,
-0.012239404954016209,
0.03599199652671814,
-0.011382353492081165,
-0.01180125493556261,
-0.011916081421077251,
-0.023982839658856392,
-0.01862369477748871,
-0.01625990681350231,
0.027877308428287506,
-0.03621004894375801,
0.00789813231676817,
0.0019624081905931234,
0.028340527787804604,
-0.029477154836058617,
-0.019544504582881927,
0.03790174052119255,
0.035970911383628845,
-0.034439440816640854,
0.025029847398400307,
-0.02951544150710106,
-0.03710450232028961,
-0.02664773538708687,
0.0005121740978211164,
0.005729260388761759,
-0.02001744508743286,
0.010249516926705837,
0.023014800623059273,
-0.010983576066792011,
-0.016650844365358353,
0.029726725071668625,
0.05578886717557907,
0.00609934376552701,
-0.015718216076493263,
-0.06364060193300247,
-0.02307724580168724,
-0.04247249290347099,
-0.05506681650876999,
0.02587483450770378,
0.049577776342630386,
-0.011782814748585224,
0.006684498395770788,
0.03139542415738106,
0.006766472011804581,
-0.006713205948472023,
-0.00456100981682539,
-0.0219905786216259,
0.03885095193982124,
-0.014732466079294682,
0.017998041585087776,
-0.02009677328169346,
0.0067771123722195625,
0.034486643970012665,
0.004652155563235283,
0.002979752840474248,
-0.11843841522932053,
-0.026124149560928345,
0.013273587450385094,
0.04143110662698746,
-0.025246571749448776,
-0.027087213471531868,
-0.03711510822176933,
0.003145623719319701,
0.04903876408934593,
-0.01796465367078781,
0.0326596200466156,
-0.010296895168721676,
0.03083624877035618,
-0.03173395246267319,
0.014198443852365017,
-0.011546820402145386,
0.014834437519311905,
0.01207685936242342,
-0.000304022483760491,
0.027878960594534874,
-0.0017883108230307698,
0.027497148141264915,
0.015699664130806923,
0.04911990091204643,
0.05161835253238678,
0.05857916921377182,
0.014074922539293766,
-0.009256723336875439,
0.006444110535085201,
-0.06325775384902954,
-0.07445584237575531,
-0.008779597468674183,
-0.01179603859782219,
-0.04879786819219589,
0.005154220387339592,
-0.03584242984652519,
-0.03139183670282364,
0.05369054526090622,
0.01044930424541235,
0.010933754034340382,
-0.007190951146185398,
-0.024777427315711975,
-0.012522504664957523,
0.04963706061244011,
0.032952915877103806,
0.047568924725055695,
0.035239461809396744,
-0.020455526188015938,
0.03415602445602417,
-0.0079518873244524,
0.029798556119203568,
-0.04378047585487366,
-0.0023628107737749815,
0.009450376965105534,
0.04090571403503418,
-0.034110624343156815,
0.046643517911434174,
-0.013093600049614906,
0.02412114106118679,
0.011515667662024498,
-0.004346465226262808,
0.007633147295564413,
0.03416344150900841,
0.0036003857385367155,
-0.028625568374991417,
-0.005089995451271534,
0.028391869738698006,
-0.06775210052728653,
-0.03447100892663002,
-0.015367350541055202,
-0.01167064905166626,
-0.027738647535443306,
-0.02697140723466873,
-0.03377741947770119,
-0.01265826728194952,
-0.011966465972363949,
-0.009017332457005978,
-0.006655480712652206,
-0.041262295097112656,
0.06677727401256561,
-0.009959874674677849,
-0.0075180246494710445,
-0.013782146386802197,
-0.06960614770650864,
0.03543002903461456,
0.004255181178450584,
-0.004493349697440863,
0.020224636420607567,
-0.008499158546328545,
0.01815331168472767,
-0.020658202469348907,
-0.010389978997409344,
-0.02851434238255024,
-0.05124793201684952,
0.011401277035474777,
0.0375165231525898,
0.024280810728669167,
-0.028840621933341026,
0.0046994732692837715,
-0.02916024439036846,
-0.03024214692413807,
-0.02102532610297203,
0.06485544890165329,
-0.04055911675095558,
0.02324311062693596,
0.02020913176238537,
0.0076779555529356,
0.030890492722392082,
-0.025595804676413536,
-0.03175809979438782,
-0.0036156524438410997,
-0.01840801164507866,
0.027235159650444984,
-0.054026827216148376,
0.043304719030857086,
-0.03940897062420845,
-0.049548614770174026,
-0.0072539011016488075,
-0.03752836212515831,
0.01624385081231594,
-0.02815055102109909,
-0.018222074955701828,
0.060052771121263504,
0.03035007417201996,
0.012752865441143513,
0.02320355363190174,
0.018339728936553,
0.010611054487526417,
0.012057400308549404,
-0.025430629029870033,
0.012944755144417286,
-0.047257356345653534,
-0.0327368825674057,
0.03517920523881912,
0.013891107402741909,
-0.013715141452848911,
0.02482173591852188,
0.06954996287822723,
0.0027081335429102182,
-0.030940834432840347,
0.012368769384920597,
-0.0015255078906193376,
0.005763679277151823,
-0.027643119916319847,
0.003999002277851105,
0.0065110838040709496,
-0.005338202230632305,
0.005929787643253803,
-0.01955289952456951,
0.013806382194161415,
-0.022881174460053444,
0.061315812170505524,
-0.047804318368434906,
0.03147701546549797,
-0.010438714176416397,
-0.035881634801626205,
-0.020301956683397293,
0.005371443927288055,
-0.01779564656317234,
0.05667498707771301,
-0.01620275340974331,
0.005129498895257711,
-0.024473687633872032,
-0.021943224593997,
0.05188923701643944,
0.02348124049603939,
-0.006382355932146311,
0.0025725048035383224,
0.025972897186875343,
0.029371675103902817,
0.05165370553731918,
-0.027078980579972267,
-0.018039220944046974,
0.0029523943085223436,
-0.02987208031117916,
0.009982620365917683,
0.010325057432055473,
0.0009097984875552356,
0.016446592286229134,
0.008881858550012112,
0.0073628812097013,
-0.02426973171532154,
-0.052256423979997635,
-0.048465244472026825,
0.027803543955087662,
0.021314622834324837,
0.002452744171023369,
0.03544430807232857,
-0.01854519732296467,
0.0080347815528512,
0.015153761021792889,
0.033180758357048035,
0.004624740686267614,
-0.06765523552894592,
-0.016505420207977295,
-0.005072842817753553,
-0.030167127028107643,
0.0631449967622757,
0.026036713272333145,
-0.03016689606010914,
0.027248503640294075,
-0.00037081187474541366,
0.01969468966126442,
0.009998474270105362,
0.021414853632450104,
-0.05024221912026405,
0.07364434003829956,
-0.05846696346998215,
0.026848487555980682,
0.0085050780326128,
0.026181301102042198,
0.10570940375328064,
0.07761415094137192,
0.010329634882509708,
-0.026665089651942253,
0.03578432276844978,
-0.04441478103399277,
-0.03564897179603577,
-0.061305124312639236,
0.014267247170209885,
0.021834328770637512,
-0.004704405087977648,
-0.0028219230007380247,
0.05142885819077492,
-0.03914877027273178,
-0.014625795185565948,
0.07595725357532501,
-0.03119448386132717,
-0.019376905634999275,
0.004381251055747271,
-0.01877727173268795,
-0.03373241797089577,
0.008839113637804985,
-0.010931525379419327,
0.030737146735191345,
-0.030898666009306908,
-0.005540063139051199,
-0.017941555008292198,
-0.023571280762553215,
0.03745049610733986,
-0.002861638320609927,
-0.04868817329406738,
-0.045900605618953705,
0.010954407975077629,
-0.0108175128698349,
-0.02570873498916626,
0.03277325630187988,
-0.0016621846007183194,
-0.00043954193824902177,
0.0047625224106013775,
0.0029546350706368685,
-0.020188702270388603,
-0.00466350931674242,
0.009892846457660198,
0.0007716983673162758,
-0.05697554722428322,
0.01565510220825672,
-0.04965196177363396,
-0.007749304175376892,
-0.025249594822525978,
-0.0036753499880433083,
0.020543284714221954,
-0.005736679770052433,
0.020021922886371613,
-0.02648993954062462,
-0.016879305243492126,
-0.027366070076823235,
0.027691487222909927,
-0.004077437799423933,
0.011747092939913273,
0.008196637034416199,
-0.0007777774590067565,
0.052684884518384933,
0.02770407870411873,
0.01370559073984623,
-0.009302685968577862,
0.007023032288998365,
-0.03080233931541443,
0.042351990938186646,
-0.03488120436668396,
-0.03754478320479393,
-0.053778961300849915,
-0.003999630454927683,
-0.02963278256356716,
-0.010147102177143097,
0.013268518261611462,
0.05273503437638283,
0.01932976394891739,
-0.016364308074116707,
0.01810712367296219,
-0.021699655801057816,
-0.03925594687461853,
0.039992913603782654,
0.0004516290791798383,
0.00048255620640702546,
-0.034606900066137314,
-0.023403825238347054,
0.03585851192474365,
0.042220499366521835,
0.0025090777780860662,
0.010715572163462639,
-0.04672033712267876,
0.006680062972009182,
-0.009967334568500519,
-0.0466047003865242,
-0.018710138276219368,
0.0001902797375805676,
-0.05203889682888985,
0.0008776679169386625,
-0.024513477459549904,
0.01189394574612379,
0.04185326769948006,
-0.00730455107986927,
-0.03051464445888996,
0.026605620980262756,
-0.034726712852716446,
0.014649921096861362,
0.042147498577833176,
-0.008869062177836895,
-0.023263022303581238,
-0.014747089706361294,
-0.000890819588676095,
-0.03625635430216789,
-0.04578986018896103,
-0.03497876226902008,
-0.04099378362298012,
0.014478176832199097,
0.027526292949914932,
-0.0010608640732243657,
0.005725728813558817,
-0.026904111728072166,
-0.012683839537203312,
-0.031618453562259674,
-0.009042080491781235,
-0.05382794514298439,
0.0009807466994971037,
-0.025454863905906677,
-0.00687542837113142,
-0.030991926789283752,
0.01000156719237566,
-0.05320831760764122,
-0.00796498078852892,
0.004509270656853914,
-0.004171921405941248,
-0.034054018557071686,
-0.054928913712501526,
-0.010920790955424309,
0.028057491406798363,
0.04265294224023819,
-0.04734715074300766,
-0.03596840053796768,
-0.001783702988177538,
-0.03463888168334961,
-0.04693084582686424,
0.01810932531952858,
-0.013939832337200642,
0.023633459582924843,
0.04078938812017441,
-0.06154936924576759,
-0.03366904705762863,
0.038571909070014954,
-0.03019821085035801,
-0.008714957162737846,
0.006235914770513773,
0.0100256884470582,
-0.01760571263730526,
0.020083211362361908,
-0.01234996784478426,
-0.06650035828351974,
-0.034359049052000046,
0.013052642345428467,
0.026628199964761734,
0.017787456512451172,
0.02325565740466118,
0.025363702327013016,
0.010268437676131725,
-0.005139595363289118,
0.027388064190745354,
0.010198344476521015,
0.0016035267617553473,
0.04260943830013275,
-0.044682372361421585,
0.0347408764064312,
0.04834004491567612,
0.0009233027813024819,
-0.07524434477090836,
-0.00027088262140750885,
0.0038171340711414814,
-0.037183601409196854,
0.01989353820681572,
-0.05384296178817749,
0.03634849190711975,
-0.0015308528672903776,
-0.06107024848461151,
0.014683634042739868,
-0.04674850404262543,
-0.020029300823807716,
-0.017040371894836426,
-0.0254497230052948,
-0.017300549894571304,
0.023767704144120216,
-0.0039592026732862,
0.04600272327661514,
0.018865033984184265,
0.003826136002317071,
-0.028922587633132935,
0.031243443489074707,
0.002392387017607689,
0.024089178070425987,
-0.016703521832823753,
0.026328932493925095,
0.07345741987228394,
-0.016469361260533333,
-0.04511633887887001,
0.019996503368020058,
0.030638422816991806,
0.026576925069093704,
0.03239482641220093,
0.016241025179624557,
0.009515993297100067,
0.009125779382884502,
-0.0038710569497197866,
0.010323114693164825,
-0.011656605638563633,
0.01786641590297222,
-0.005462366156280041,
0.030185623094439507,
-0.02489602565765381,
0.04044545814394951,
0.015929076820611954,
-0.041949693113565445,
0.005009442567825317,
0.018782343715429306,
-0.06628340482711792,
0.021493736654520035,
-0.022995350882411003,
0.004454724956303835,
0.013067339546978474,
-0.003500582417473197,
0.0052225347608327866,
-0.0536554791033268,
-0.01233404316008091,
0.017710167914628983,
-0.006766396574676037,
-0.005014555063098669,
0.02132175862789154,
-0.008735140785574913,
0.015340762212872505,
-0.014353360049426556,
-0.022655289620161057,
-0.029824700206518173,
-0.03068476915359497,
0.019448690116405487,
-0.013675067573785782,
0.025939378887414932,
-0.016305122524499893,
-0.04484653100371361,
0.0032993166241794825,
0.08214876800775528,
0.028240617364645004,
0.05886721611022949,
0.019511548802256584,
-0.05021945387125015,
0.038386743515729904,
-0.054616086184978485,
0.03057054802775383,
-0.03693189471960068,
-0.0009736983338370919,
-0.0004372300754766911,
-0.03614240512251854,
-0.0042523485608398914,
0.011462182737886906,
0.025212658569216728,
-0.061503708362579346,
0.019231360405683517,
-0.0008751559071242809,
-0.002203479642048478,
-0.003045586170628667,
-0.019128821790218353,
-0.009823363274335861,
0.045398078858852386,
-0.045593298971652985,
-0.01590157113969326,
-0.016514843329787254,
0.0043303584679961205,
-0.015341522172093391,
0.040346864610910416,
-0.0053879739716649055,
0.024705879390239716,
0.006216016598045826,
-0.026283856481313705,
0.027797384187579155,
0.03217165172100067,
-0.03303668275475502,
0.05462603271007538,
-0.025310980156064034,
0.025463854894042015,
0.00884067639708519,
-0.0045366548001766205,
-0.020634211599826813,
0.07244221866130829,
-0.052867740392684937,
0.03215521574020386,
-0.015419285744428635,
-0.03848476707935333,
-0.0023678301367908716,
-0.040237490087747574,
0.015295734629034996,
0.029695291072130203,
-0.01330442726612091,
0.0014616345288231969,
0.05546276271343231,
0.0290403850376606,
0.004249148070812225,
-0.01175269391387701,
0.03059854917228222,
0.042824339121580124,
0.015102782286703587,
-0.017805377021431923,
-0.0017604040913283825,
0.02597174420952797,
-0.015313683077692986,
0.03500896692276001,
0.02059207484126091,
0.009808847680687904,
0.013129604049026966,
0.009570683352649212,
0.003837830387055874,
-0.00039440966793335974,
-0.055465128272771835,
0.002071069786325097,
0.009110438637435436,
0.0066975923255085945,
0.03298044949769974,
-0.028254196047782898,
0.08370956778526306,
-0.001915039261803031,
0.02737794816493988,
0.028211724013090134,
-0.023752819746732712,
0.026329664513468742,
-0.003145477967336774,
-0.012623551301658154,
0.01694893091917038,
0.018787531182169914,
-0.01329056080430746,
0.011788363568484783,
0.015877489000558853,
0.05188757926225662,
-0.010529893450438976,
0.02096003293991089,
-0.04281608387827873,
0.0069001903757452965,
-0.011888661421835423,
-0.04771566763520241,
-0.05396891012787819,
0.0013697646791115403,
0.024714266881346703,
-0.018064357340335846,
0.025083040818572044,
-0.02177351340651512,
-0.005459274630993605,
-0.020073233172297478,
0.05502704530954361,
-0.038496233522892,
0.020269187167286873,
-0.023824747651815414,
0.02741253934800625,
-0.013772065751254559,
0.025795940309762955
] |
<p>I am wondering if someone could provide me with a formula that would tell me at what velocity a projectile can be launched from something using an electromagnetic field. The idea is much like a rail gun or Gauss rifle, but not exactly.</p>
<p>Just looking to find a formula to determine the speed of the projectile.</p>
<p>Thank you,
Michael Vanderpool</p>
| 10,806 |
[
-0.02857888489961624,
-0.02689206227660179,
-0.02300533838570118,
-0.030683031305670738,
0.039300475269556046,
-0.0012221027864143252,
-0.03505830839276314,
-0.0171245988458395,
0.01796099543571472,
0.015793565660715103,
0.04682614281773567,
0.07576064765453339,
0.07044854760169983,
0.002367075067013502,
0.019598133862018585,
0.03061240166425705,
-0.005117170047014952,
0.02753688395023346,
0.015290304087102413,
-0.08132932335138321,
0.02055039070546627,
-0.005714777857065201,
-0.004241567570716143,
-0.008001777343451977,
-0.01263074204325676,
0.0068592228926718235,
0.05373506247997284,
-0.010494079440832138,
0.004969807341694832,
0.028223736211657524,
0.002234981395304203,
-0.03776131942868233,
0.027954885736107826,
0.026419397443532944,
0.01307754684239626,
-0.012644285336136818,
-0.05150728300213814,
-0.05596961826086044,
-0.021318893879652023,
0.007375445682555437,
-0.028006495907902718,
-0.03500070050358772,
0.0010555718326941133,
0.06989861279726028,
-0.03551016002893448,
-0.015935296192765236,
-0.0009980836184695363,
-0.04099246859550476,
0.056291449815034866,
-0.06980381160974503,
0.08593567460775375,
-0.01491385605186224,
0.058367352932691574,
0.0022060617338865995,
-0.01639760658144951,
-0.014668278396129608,
0.09186449646949768,
0.05656998232007027,
-0.003308999352157116,
-0.06946881115436554,
-0.01324902568012476,
-0.030967598780989647,
-0.0036060388665646315,
-0.05753671005368233,
-0.030427351593971252,
0.061871662735939026,
-0.01956718973815441,
-0.019947946071624756,
0.02898946776986122,
-0.0312965027987957,
-0.0007277527474798262,
0.007841050624847412,
0.0028627996798604727,
-0.01902540773153305,
0.006536104716360569,
-0.0381702184677124,
0.029345905408263206,
0.0221610888838768,
0.003475656732916832,
0.035185981541872025,
-0.06595815718173981,
0.007170706521719694,
0.04651244729757309,
0.03488495945930481,
0.027598615735769272,
-0.002141348784789443,
0.048206061124801636,
0.007391632534563541,
0.026273353025317192,
0.019316719844937325,
-0.01905772089958191,
0.009454291313886642,
0.03940153121948242,
-0.026139114052057266,
-0.04110769182443619,
0.047029025852680206,
-0.000011347688086971175,
0.07022809237241745,
0.009855148382484913,
-0.04003642499446869,
0.018970869481563568,
-0.007723954506218433,
-0.00011857261415570974,
0.074855737388134,
-0.007189200259745121,
-0.02982518821954727,
0.0052117714658379555,
0.011080521158874035,
-0.04641328006982803,
-0.008862167596817017,
-0.011358371004462242,
0.044182900339365005,
0.027705375105142593,
-0.003114093327894807,
0.009778662584722042,
-0.012189795263111591,
0.009787563234567642,
-0.01726854033768177,
0.03675932437181473,
0.038718920201063156,
0.04484482854604721,
-0.04978684335947037,
0.028507227078080177,
-0.012215638533234596,
-0.050922002643346786,
-0.015006630681455135,
0.013396574184298515,
0.012749053537845612,
-0.03547891229391098,
0.008204917423427105,
-0.03491682559251785,
-0.048161476850509644,
0.021435080096125603,
-0.02644185535609722,
0.02483723685145378,
-0.024506554007530212,
-0.07049720734357834,
-0.06337813287973404,
0.015037154778838158,
-0.01998155377805233,
-0.012767903506755829,
-0.08151035010814667,
0.0016048282850533724,
0.04027940332889557,
0.06276610493659973,
0.005011443514376879,
0.024230292066931725,
-0.01018429920077324,
0.04797425866127014,
-0.018728071823716164,
-0.021090207621455193,
-0.009462084621191025,
-0.00573107972741127,
-0.03345264494419098,
0.019896572455763817,
-0.037258341908454895,
0.024362770840525627,
0.007790680509060621,
-0.02032511681318283,
-0.00837381836026907,
0.03951752930879593,
-0.03317337483167648,
0.003626273712143302,
0.007620496675372124,
0.04014178737998009,
-0.020593760535120964,
0.08984460681676865,
0.03818024694919586,
-0.0235366839915514,
0.02526654303073883,
-0.00929919071495533,
0.029534028843045235,
0.028460441157221794,
-0.016340725123882294,
0.06602213531732559,
-0.03747046738862991,
-0.02075398899614811,
-0.002918779384344816,
0.017347047105431557,
-0.00317671662196517,
-0.03752744942903519,
-0.05293804034590721,
0.02149876020848751,
0.011530645191669464,
0.021778395399451256,
0.024073423817753792,
0.010656937956809998,
0.018522832542657852,
-0.027975497767329216,
-0.02675742097198963,
-0.006087475456297398,
-0.04963313043117523,
0.058737706393003464,
0.0026559100951999426,
0.01147809624671936,
0.021147899329662323,
-0.008036294020712376,
-0.002188251353800297,
-0.010979173704981804,
-0.03275081142783165,
-0.0031833588145673275,
0.01091888640075922,
-0.015656037256121635,
-0.025299031287431717,
-0.013981515541672707,
0.052239224314689636,
0.039470355957746506,
-0.006531397346407175,
0.03175869584083557,
-0.004012735560536385,
-0.045349787920713425,
-0.01604519598186016,
-0.031738415360450745,
0.029562735930085182,
0.026960358023643494,
-0.013057264499366283,
0.031473614275455475,
-0.0013172834878787398,
0.013255343772470951,
0.031017310917377472,
-0.037371233105659485,
0.10246380418539047,
0.06504705548286438,
0.008127572014927864,
0.006141700316220522,
0.040405839681625366,
0.015809422358870506,
-0.02199358493089676,
0.023541664704680443,
-0.020618706941604614,
-0.02455996163189411,
0.012924021109938622,
0.023307854309678078,
0.002236679894849658,
-0.03992018476128578,
0.014090005308389664,
0.037364233285188675,
0.02854982577264309,
0.05005589500069618,
0.05458489805459976,
-0.06648851186037064,
-0.030573895201086998,
0.0028041021432727575,
-0.008003702387213707,
-0.0460091233253479,
0.010181926190853119,
0.028161758556962013,
0.043970316648483276,
-0.02311212569475174,
0.026189347729086876,
-0.016597425565123558,
0.04089583083987236,
-0.03503156825900078,
-0.004429543390870094,
0.0031517804600298405,
-0.0824986919760704,
0.025806963443756104,
-0.042794883251190186,
0.015469935722649097,
-0.00043632835149765015,
-0.009976038709282875,
0.024434003978967667,
-0.03389420360326767,
0.016955971717834473,
-0.0018265716498717666,
-0.04422203451395035,
-0.006523718126118183,
-0.024286804720759392,
0.032552119344472885,
-0.04571177810430527,
-0.01366751454770565,
-0.006598871201276779,
0.004572672303766012,
-0.03192302957177162,
-0.023771964013576508,
0.004654414486140013,
0.022610019892454147,
0.01905510574579239,
0.0016972013982012868,
-0.05128609389066696,
0.02484004572033882,
-0.049366362392902374,
0.0016508010448887944,
-0.011297646909952164,
-0.03902868553996086,
0.01633453369140625,
-0.018581343814730644,
-0.04648733511567116,
0.07550584524869919,
-0.03900071233510971,
-0.017177904024720192,
0.03674377501010895,
-0.013724865391850471,
-0.06045053154230118,
0.0029395001474767923,
-0.02142401598393917,
0.005698203109204769,
-0.03691461309790611,
-0.007629440166056156,
0.04017294570803642,
-0.015205083414912224,
-0.037860140204429626,
0.009531478397548199,
-0.02236860990524292,
-0.03906376659870148,
-0.015747753903269768,
0.013814423233270645,
0.020113909617066383,
-0.03787197545170784,
0.050835393369197845,
0.028604110702872276,
-0.024617664515972137,
0.010108523070812225,
-0.037377748638391495,
-0.02381906285881996,
0.014591437764465809,
-0.0010002987692132592,
0.046569570899009705,
0.007562796585261822,
-0.04709074646234512,
0.0668712854385376,
0.03845925256609917,
-0.04756719619035721,
-0.01883029192686081,
-0.006564929615706205,
0.03931058943271637,
-0.017983488738536835,
0.0005684643401764333,
0.03197430819272995,
-0.05037533864378929,
0.002049818867817521,
-0.005398458801209927,
-0.010059977881610394,
0.03245951980352402,
-0.008794410154223442,
0.036540694534778595,
-0.02810591831803322,
-0.010333187878131866,
0.009478810243308544,
0.0493914932012558,
0.03984425589442253,
-0.048762135207653046,
0.06460563093423843,
-0.0007885632803663611,
0.048057883977890015,
0.0119828712195158,
-0.023562487214803696,
0.027389947324991226,
-0.009385304525494576,
-0.010683025233447552,
-0.008238283917307854,
0.0294240340590477,
-0.018647821620106697,
0.020786160603165627,
0.004588284529745579,
0.053775496780872345,
0.00635207025334239,
-0.01279766857624054,
0.02122584916651249,
0.024522054940462112,
0.019414003938436508,
-0.022346677258610725,
-0.02077675238251686,
-0.013737067580223083,
-0.016044318675994873,
-0.0017489718738943338,
-0.007273703347891569,
-0.018345434218645096,
0.023247607052326202,
0.0014746285742148757,
0.03420634940266609,
0.016411669552326202,
0.010304338298738003,
0.010487859137356281,
-0.0504535473883152,
0.003353158477693796,
-0.006730570923537016,
0.03468131646513939,
0.00021440134150907397,
0.0507783405482769,
0.005798039957880974,
-0.006912755314260721,
0.044031739234924316,
-0.0073561398312449455,
-0.08133561164140701,
0.06435525417327881,
-0.04075655713677406,
-0.026371359825134277,
-0.023603573441505432,
-0.00834729615598917,
-0.0506572462618351,
0.007291407790035009,
-0.02852451801300049,
0.014488160610198975,
-0.001009957049973309,
-0.050249360501766205,
0.041575394570827484,
-0.045591603964567184,
-0.03016439452767372,
-0.004493074957281351,
0.029037050902843475,
0.009316474199295044,
-0.005413873586803675,
-0.017858143895864487,
0.0017944166902452707,
-0.021327344700694084,
-0.0007182693225331604,
-0.023688141256570816,
0.01228342205286026,
-0.014501607045531273,
0.06475739181041718,
0.016729384660720825,
-0.007229050621390343,
-0.013349652290344238,
0.013808425515890121,
-0.026021145284175873,
0.04751152545213699,
0.0181982833892107,
0.015244647860527039,
-0.07750656455755234,
-0.07470269501209259,
0.016541508957743645,
-0.011824346147477627,
0.047395315021276474,
-0.0022410419769585133,
-0.006666023749858141,
0.046904925256967545,
0.0008229466620832682,
0.010361026972532272,
0.026551783084869385,
0.06872867047786713,
0.011667530983686447,
0.014531604945659637,
-0.03979472815990448,
0.0073859854601323605,
-0.035808585584163666,
-0.023609159514307976,
-0.008702963590621948,
0.008554395288228989,
0.004835193976759911,
0.011367586441338062,
0.03095873072743416,
-0.016970977187156677,
-0.0028700141701847315,
0.0034655630588531494,
-0.0029779020696878433,
-0.002472331514582038,
0.013651764020323753,
-0.020988235250115395,
0.0060302079655230045,
0.03764056786894798,
0.05102362111210823,
0.005899124313145876,
-0.018544558435678482,
-0.0922565683722496,
0.0013216721126809716,
0.05241108685731888,
0.0199202299118042,
-0.003496086224913597,
0.00031898313318379223,
-0.022668270394206047,
0.00661586644127965,
0.06994207203388214,
-0.011097903363406658,
0.025308847427368164,
0.0038568086456507444,
0.016345608979463577,
-0.012273772619664669,
-0.006631734315305948,
-0.0348651222884655,
0.01252745557576418,
0.006730677094310522,
0.007903487421572208,
-0.02580607496201992,
0.029612787067890167,
0.019057242199778557,
0.012486638501286507,
0.0326639786362648,
0.052520908415317535,
0.028523355722427368,
0.0005820758524350822,
0.02001671865582466,
-0.006504140328615904,
-0.017992917448282242,
-0.03881445154547691,
0.022240446880459785,
-0.0132551658898592,
0.010126265697181225,
0.007380170747637749,
-0.03754459321498871,
-0.001892811618745327,
0.0421442948281765,
-0.013937432318925858,
0.010098649188876152,
0.00601214449852705,
-0.058442261070013046,
-0.0022196078207343817,
0.006991352420300245,
0.006002070847898722,
0.023965969681739807,
0.02039548009634018,
-0.010111523792147636,
-0.010774129070341587,
-0.011556357145309448,
0.030750852078199387,
-0.026688240468502045,
-0.024540098384022713,
-0.012431926093995571,
0.04055662080645561,
-0.044953107833862305,
0.06509704887866974,
-0.025035670027136803,
0.004559806082397699,
-0.03210727870464325,
-0.03087998740375042,
-0.03280932083725929,
0.02199903316795826,
-0.02785986103117466,
-0.006249500438570976,
0.0202057845890522,
-0.008245371282100677,
-0.02093389444053173,
-0.012573557905852795,
0.012939874082803726,
0.009396287612617016,
0.028283264487981796,
0.03225655481219292,
-0.023717911913990974,
-0.011560729704797268,
-0.039589546620845795,
-0.018252020701766014,
0.011571208015084267,
-0.0638086274266243,
0.0652688667178154,
-0.034548211842775345,
-0.007916092872619629,
-0.011350843124091625,
-0.06700453162193298,
-0.05258367955684662,
0.032096315175294876,
0.017220543697476387,
0.03304319456219673,
-0.04976916313171387,
-0.0266619510948658,
-0.01835448294878006,
0.02443779446184635,
-0.037305522710084915,
-0.04766133427619934,
0.008680049329996109,
-0.004542987328022718,
-0.0041898759081959724,
-0.03276772424578667,
0.0011190794175490737,
-0.04794921725988388,
-0.02107943594455719,
0.041115500032901764,
0.050488632172346115,
-0.0069230287335813046,
0.011749878525733948,
-0.0038995228242129087,
-0.03813673183321953,
0.06373944133520126,
0.051884159445762634,
-0.0602918341755867,
0.030184637755155563,
-0.012752421200275421,
-0.006100045051425695,
-0.014352671802043915,
0.05093620344996452,
-0.01747063174843788,
-0.006168239749968052,
-0.008766185492277145,
-0.02153613232076168,
0.05905923247337341,
-0.016363393515348434,
0.033643946051597595,
0.029371347278356552,
0.031852543354034424,
-0.027831679210066795,
-0.03172982856631279,
0.04886261746287346,
-0.00290005118586123,
0.007761306595057249,
-0.033067215234041214,
-0.014917751774191856,
-0.05237804353237152,
0.008038234896957874,
0.029445016756653786,
0.015204157680273056,
0.03715506196022034,
-0.01529876608401537,
0.06388280540704727,
0.017888950183987617,
-0.02359723299741745,
0.01573157124221325,
0.004877617582678795,
0.017523599788546562,
0.0024040979333221912,
0.0008739150944165885,
0.01335340179502964,
-0.0020225336775183678,
-0.012856665067374706,
-0.038354165852069855,
-0.007250037509948015,
0.0032441155053675175,
0.07800840586423874,
-0.0725281611084938,
0.052295148372650146,
-0.001461257110349834,
0.029676364734768867,
-0.004318128805607557,
0.012301267124712467,
-0.0018108708318322897,
-0.004244513344019651,
-0.013247099705040455,
0.014147213660180569,
0.022284990176558495,
-0.003537336364388466,
0.016388271003961563,
0.021963020786643028,
-0.0031090991105884314,
0.0008464791462756693,
0.02255159616470337,
0.029415007680654526,
0.02275841310620308,
-0.020268622785806656,
-0.03375504910945892,
0.04752781614661217,
-0.03856310620903969,
0.030559172853827477,
-0.015832122415304184,
-0.003208081005141139,
0.034556444734334946,
0.009783961810171604,
-0.0118638901039958,
0.017139187082648277,
0.007739141583442688,
-0.006709972862154245,
0.0197066031396389,
0.006347137503325939,
-0.01531247515231371,
-0.013539190404117107,
0.027550024911761284,
0.019916992634534836,
0.00606506085023284,
0.03761283680796623,
0.004268656950443983,
-0.03268604353070259,
-0.004073118790984154,
-0.05985875055193901,
-0.05000372976064682,
0.049036234617233276,
0.04787229746580124,
-0.010065289214253426,
0.012123814783990383,
0.022484807297587395,
0.0218970850110054,
-0.0037001946475356817,
0.020064543932676315,
-0.016105789691209793,
0.08835578709840775,
0.004694793373346329,
-0.01782577484846115,
-0.005672185681760311,
0.005678871646523476,
0.09474121034145355,
0.06037400662899017,
0.016044048592448235,
-0.03529132902622223,
0.022034673020243645,
-0.05794869735836983,
0.009765902534127235,
-0.0076669794507324696,
0.016765715554356575,
-0.017854221165180206,
0.0019809375517070293,
0.029126688838005066,
0.022131145000457764,
-0.03160420432686806,
0.00980302318930626,
0.04124513268470764,
-0.01723461225628853,
-0.035677470266819,
-0.00616785092279315,
0.015530459582805634,
0.009818370454013348,
0.02806190773844719,
-0.03568192943930626,
0.030320946127176285,
-0.038540106266736984,
-0.017946163192391396,
-0.00941779837012291,
-0.038548484444618225,
0.016585180535912514,
-0.0014343728544190526,
-0.020184073597192764,
-0.01310720108449459,
-0.0014634643448516726,
-0.0156598761677742,
-0.0385846272110939,
-0.01494618784636259,
0.04004191607236862,
0.017294712364673615,
-0.016639329493045807,
0.0469212606549263,
0.04018506035208702,
0.026528222486376762,
0.016766196116805077,
0.018992818892002106,
-0.036268629133701324,
0.0207540113478899,
-0.05663304775953293,
0.015335538424551487,
-0.00803000945597887,
0.05096884071826935,
0.0048867929726839066,
0.017013749107718468,
0.014736679382622242,
-0.05556776002049446,
-0.013015848584473133,
-0.01600007154047489,
0.03564148396253586,
-0.023031430318951607,
0.016078591346740723,
-0.02380787394940853,
0.03818683698773384,
-0.01757928915321827,
0.018164217472076416,
-0.0010915616294369102,
0.017325453460216522,
0.022937066853046417,
-0.02589884027838707,
0.055146727710962296,
-0.03610427305102348,
-0.07480300217866898,
0.010843564756214619,
-0.0437200702726841,
-0.01984814554452896,
0.011471760459244251,
0.035276636481285095,
0.023684030398726463,
-0.006688973400741816,
0.021667584776878357,
-0.01426383201032877,
0.018434740602970123,
-0.08689168095588684,
0.06033862754702568,
-0.00791128445416689,
-0.008367158472537994,
-0.027846550568938255,
-0.015411711297929287,
0.03701397404074669,
0.03831084817647934,
-0.03633709251880646,
0.04872510954737663,
-0.04084252566099167,
0.013271002098917961,
0.024218415841460228,
-0.03407410532236099,
-0.018136126920580864,
0.00018440811254549772,
-0.02938297763466835,
0.026433618739247322,
-0.03026076778769493,
0.032919880002737045,
0.040314894169569016,
0.01638716459274292,
0.006635792087763548,
0.012856648303568363,
-0.020049823448061943,
-0.0049651009030640125,
-0.007913414388895035,
-0.02183310128748417,
-0.0056063770316541195,
0.0019465693039819598,
0.0024136442225426435,
-0.04025443270802498,
-0.024293679744005203,
-0.029279129579663277,
-0.021327193826436996,
-0.001056376495398581,
0.008053247816860676,
-0.009173060767352581,
0.026820413768291473,
-0.01389699149876833,
-0.03635217994451523,
-0.025999173521995544,
0.033432308584451675,
0.004728250205516815,
0.004272023215889931,
0.013173668645322323,
-0.021519578993320465,
-0.048017386347055435,
0.019533758983016014,
-0.04153202846646309,
0.003377462038770318,
0.02066911570727825,
0.008182263001799583,
0.010979357175529003,
0.009291072376072407,
0.023190459236502647,
0.007615833077579737,
0.051480844616889954,
-0.009989448823034763,
0.017549579963088036,
0.025030385702848434,
-0.051851216703653336,
-0.057112038135528564,
0.03782585635781288,
-0.02086663618683815,
0.05349358543753624,
0.020596105605363846,
-0.028601771220564842,
-0.002550548641011119,
0.07720189541578293,
-0.001702768262475729,
0.006220526993274689,
-0.015237241983413696,
-0.02354406751692295,
0.028539765626192093,
-0.03213690593838692,
0.010890708304941654,
-0.009262359701097012,
-0.013161512091755867,
0.010011514648795128,
0.013413420878350735,
-0.008249199949204922,
0.008307992480695248,
0.03301689028739929,
0.019441861659288406,
-0.03544505685567856,
0.044770319014787674,
-0.013783237896859646,
0.037709761410951614,
0.03902951627969742,
0.0197201669216156,
0.0032654330134391785,
0.007909299805760384,
0.013847867026925087,
-0.13635803759098053,
0.013804428279399872,
-0.006008617114275694,
0.01708829589188099,
0.061601657420396805,
-0.06365130841732025,
-0.0037787933833897114,
0.04234771803021431,
-0.05846254900097847,
-0.008540275506675243,
-0.03886912018060684,
-0.03364124521613121,
-0.032343581318855286,
-0.028531525284051895,
0.03226384148001671,
0.039552364498376846,
0.024754853919148445,
0.0522848442196846,
0.038431450724601746,
0.012170227244496346,
-0.040471505373716354,
-0.012149396352469921,
0.008906587958335876,
0.028623931109905243,
0.01684039644896984,
-0.005160081200301647,
0.04204443842172623,
-0.027172666043043137,
-0.025797860696911812,
0.036121200770139694,
-0.01512405090034008,
0.04492814093828201,
0.008608764968812466,
0.033361148089170456,
0.02847599983215332,
0.030049748718738556,
0.013000942766666412,
0.014714216813445091,
-0.005802428349852562,
0.008829772472381592,
0.03121340274810791,
0.031239530071616173,
-0.06252916157245636,
-0.002205686178058386,
0.028868917375802994,
0.004490794613957405,
-0.025126967579126358,
0.02755754441022873,
-0.0436001792550087,
-0.02280145138502121,
-0.008673313073813915,
0.0012185147497802973,
0.02257523499429226,
-0.0349729061126709,
0.013342252001166344,
-0.05836968496441841,
-0.003564178477972746,
0.0093813082203269,
-0.02209901064634323,
0.000879906234331429,
0.025556808337569237,
0.0008209991501644254,
-0.0394192673265934,
0.009382828138768673,
-0.007441177032887936,
0.01132891420274973,
-0.06442666053771973,
0.022938163951039314,
0.026837999001145363,
-0.01943895034492016,
0.0006699767545796931,
-0.032248757779598236,
-0.007247676607221365,
0.04005449637770653,
0.020760849118232727,
0.010127967223525047,
0.030610864982008934,
0.021398872137069702,
0.00297314184717834,
-0.03996213525533676,
0.017852207645773888,
-0.006293280515819788,
-0.03919345885515213,
-0.02555648796260357,
-0.04993750527501106,
0.053452268242836,
0.00927737820893526,
0.06671606749296188,
-0.06501976400613785,
-0.011575724929571152,
0.03920082375407219,
-0.01957125775516033,
-0.0222336295992136,
-0.07385248690843582,
-0.02113291062414646,
-0.011728908866643906,
-0.05419009178876877,
-0.020549586042761803,
-0.013254096731543541,
-0.0211188942193985,
-0.012094547972083092,
-0.01545057725161314,
0.030889110639691353,
-0.023599963635206223,
-0.020282166078686714,
-0.04748222976922989,
0.016394414007663727,
0.033270981162786484,
-0.026669491082429886,
0.0342441089451313,
-0.03925807401537895,
-0.010339256376028061,
0.017005082219839096,
0.005546673201024532,
-0.04846988245844841,
0.005763656925410032,
-0.018924834206700325,
-0.019881347194314003,
-0.003082803450524807,
-0.004483087919652462,
0.013111303560435772,
-0.06625755876302719,
-0.008870504796504974,
0.048314280807971954,
-0.035974908620119095,
0.0006670281873084605,
0.06802676618099213,
-0.0007727870834060013,
0.06071391701698303,
-0.037799399346113205,
0.044767048209905624,
0.02511725388467312,
-0.03437058627605438,
-0.02387254126369953,
0.019398946315050125,
0.003598871873691678,
0.0008905201684683561,
0.01754149980843067,
0.055460374802351,
-0.015468507073819637,
0.007956761866807938,
0.038876790553331375,
0.010535540990531445,
-0.0014711639378219843,
-0.016726404428482056,
-0.010405666194856167,
-0.027230219915509224,
0.0022435185965150595,
0.019185569137334824,
-0.04325693100690842,
0.05916152894496918,
-0.017333004623651505,
-0.006849165074527264,
-0.01212761178612709,
0.0397883802652359,
0.0002496819361113012,
0.014692203141748905,
-0.006431429646909237,
0.017321143299341202,
-0.003991611767560244,
0.009781028144061565,
0.015444082207977772,
-0.005942963063716888,
0.04264626279473305,
-0.030557524412870407,
0.03802663832902908,
-0.01785675249993801,
0.003703672904521227,
-0.042187221348285675,
-0.009711739607155323,
-0.03204668313264847,
-0.005149371922016144,
0.006745796650648117,
0.01350145973265171,
0.008573085069656372,
-0.00473958533257246,
0.026453210040926933,
-0.021797742694616318,
0.03798127919435501,
-0.06359336525201797,
-0.0009288606815971434,
-0.049248095601797104,
0.014420813880860806,
0.01455119252204895,
0.015655627474188805
] |
<p>When we pierce a balloon with a sharp needle, it pops and produce a great sound. But, It doesn't pop when we open the mouth of the balloon (through which we have blown air)...</p>
<p>So, Why doesn't the gas release slowly when we pierce it with a needle. In fact, it is released slowly when we release the mouth. </p>
| 10,807 |
[
-0.034050870686769485,
-0.001075782347470522,
0.03869911655783653,
-0.045983269810676575,
-0.010321678593754768,
-0.00007619834650540724,
-0.027553852647542953,
0.010478249751031399,
0.00627227732911706,
0.023068612441420555,
0.03202812001109123,
0.0496935173869133,
0.04138777777552605,
0.011112465523183346,
-0.03050142340362072,
-0.005647391080856323,
-0.00003762980850297026,
-0.03434770181775093,
-0.00858982652425766,
-0.018674155697226524,
-0.009098747745156288,
0.024291303008794785,
-0.021509649232029915,
0.032278452068567276,
-0.03569406270980835,
0.03935268148779869,
0.017665527760982513,
-0.007118796929717064,
0.0156815554946661,
0.023463968187570572,
-0.04735381528735161,
-0.013851260766386986,
0.022666331380605698,
-0.018714580684900284,
0.043423205614089966,
-0.0229478906840086,
-0.01966010592877865,
0.0036874304059892893,
-0.02579168602824211,
0.007442055270075798,
-0.04792770743370056,
0.02082354947924614,
-0.008532102219760418,
0.024650750681757927,
-0.06711000204086304,
0.00406202906742692,
-0.01313598733395338,
-0.015531100332736969,
0.05861934274435043,
-0.060905855149030685,
0.01938372477889061,
0.011918989010155201,
0.06604957580566406,
0.04307112842798233,
-0.01795896887779236,
0.03319130465388298,
0.07267215102910995,
0.07287931442260742,
-0.04640912637114525,
-0.026928875595331192,
0.00771397864446044,
-0.017996113747358322,
-0.007297073025256395,
-0.00806379597634077,
-0.024020729586482048,
0.040934499353170395,
-0.01073228009045124,
-0.0020453014876693487,
0.030104001984000206,
0.006699929479509592,
0.017140623182058334,
-0.06381578743457794,
0.024506546556949615,
0.0031769496854394674,
0.017641164362430573,
-0.013665953651070595,
-0.005632578860968351,
0.0036285670939832926,
0.03640612214803696,
0.05777411162853241,
-0.03348052129149437,
0.006594591774046421,
0.06876584142446518,
0.025119148194789886,
-0.04047947749495506,
-0.009507909417152405,
0.07315058261156082,
-0.030935969203710556,
-0.01684708707034588,
0.03581228852272034,
0.011476697400212288,
0.0011396867921575904,
0.02204187586903572,
0.01037624105811119,
0.016877412796020508,
0.043046578764915466,
-0.0002468973689246923,
0.062257319688797,
0.00725352531298995,
-0.028192348778247833,
-0.01407826691865921,
-0.005151562858372927,
0.05235109478235245,
0.06625238806009293,
-0.0025054067373275757,
-0.01983533427119255,
-0.06429588049650192,
0.0068276915699243546,
-0.03478466719388962,
-0.00045894659706391394,
-0.02522915042936802,
-0.027421457692980766,
-0.034259133040905,
-0.02662106417119503,
-0.019619358703494072,
-0.01540885679423809,
-0.007450431119650602,
-0.051380012184381485,
0.04929088056087494,
0.05645843222737312,
0.027735574170947075,
-0.017944227904081345,
0.027431560680270195,
-0.011277890764176846,
-0.05070064216852188,
-0.011152694001793861,
-0.002245689043775201,
-0.041524793952703476,
-0.046040717512369156,
0.038714151829481125,
0.02159138396382332,
-0.019869115203619003,
-0.005939288064837456,
0.005782564636319876,
0.07921571284532547,
0.027654051780700684,
-0.05511568859219551,
-0.06045264005661011,
0.0398763082921505,
0.009251406416296959,
-0.0175325870513916,
-0.053094424307346344,
0.02930614724755287,
0.002189537975937128,
0.05704332888126373,
-0.001622537150979042,
-0.009434198960661888,
-0.011350173503160477,
0.015045776031911373,
-0.0015072200912982225,
-0.01720840111374855,
0.01869368925690651,
0.023797130212187767,
-0.02388044260442257,
-0.011507462710142136,
-0.05250150337815285,
0.03934270143508911,
0.006913754623383284,
0.01106393150985241,
-0.03148186206817627,
0.029490413144230843,
0.0017595890676602721,
-0.023923087865114212,
-0.026059651747345924,
-0.0064963074401021,
-0.04507078975439072,
0.06843044608831406,
0.019153233617544174,
-0.019116081297397614,
0.0515165701508522,
0.0018968936055898666,
0.04535795748233795,
-0.011199289001524448,
-0.001786213368177414,
0.010476214811205864,
-0.03368120640516281,
-0.0007300202851183712,
0.01892099529504776,
0.031121008098125458,
0.02969360165297985,
-0.05575630068778992,
0.01177265215665102,
-0.013577195815742016,
0.029676776379346848,
0.014473259449005127,
0.04977215826511383,
0.01750999130308628,
-0.02724609524011612,
-0.039954543113708496,
-0.050196222960948944,
-0.03480936214327812,
-0.07587359100580215,
0.03406291455030441,
0.020210616290569305,
-0.024208826944231987,
-0.011249602772295475,
0.00043097903835587204,
0.0064796749502420425,
0.00039672834100201726,
0.006883271969854832,
-0.0436590351164341,
-0.008459699340164661,
0.03853505477309227,
-0.006964920554310083,
-0.012854233384132385,
0.055946506559848785,
0.010819361545145512,
0.007844846695661545,
0.023328186944127083,
0.03044094331562519,
-0.021475624293088913,
0.039200007915496826,
-0.04048986732959747,
0.010898121632635593,
-0.001023188466206193,
-0.006453365553170443,
0.023275364190340042,
-0.027224896475672722,
-0.008773863315582275,
0.036743924021720886,
-0.02692701667547226,
0.07589015364646912,
0.05193836987018585,
-0.0071753389202058315,
0.04103078320622444,
0.00528915598988533,
-0.008587408810853958,
0.006198624614626169,
0.02660706453025341,
-0.07209894806146622,
-0.01501139160245657,
-0.021362656727433205,
0.022732771933078766,
0.012392745353281498,
-0.017838729545474052,
0.02863587625324726,
0.020285652950406075,
-0.017943616956472397,
0.014405504800379276,
0.005199800711125135,
0.028169743716716766,
-0.03986857831478119,
-0.0017747979145497084,
0.016748087480664253,
-0.018476661294698715,
0.02557375840842724,
0.03775490075349808,
0.015580793842673302,
0.046011969447135925,
-0.004254317842423916,
0.00904557853937149,
0.0316476970911026,
0.0020369011908769608,
0.004106932319700718,
0.002041565952822566,
-0.004441414959728718,
0.026181118562817574,
-0.012711260467767715,
0.01449536718428135,
-0.0032757094595581293,
0.0130419060587883,
0.030686698853969574,
-0.017523489892482758,
0.01670539751648903,
0.025511443614959717,
0.010178282856941223,
0.003177675884217024,
-0.007966449484229088,
0.03228316083550453,
-0.048226382583379745,
0.015471411868929863,
-0.060911137610673904,
0.0001962382666533813,
-0.014639568515121937,
-0.008494444191455841,
-0.014079575426876545,
0.011973738670349121,
0.004019033629447222,
-0.03924333676695824,
-0.029898708686232567,
-0.022796904668211937,
-0.029859811067581177,
0.007917793467640877,
0.028807587921619415,
-0.0075690858066082,
0.015587951987981796,
0.006436052266508341,
-0.0427987165749073,
0.04324254393577576,
-0.004325634799897671,
-0.02955261804163456,
0.0353425033390522,
-0.014450249262154102,
-0.025743672624230385,
0.022025465965270996,
-0.04791900888085365,
0.028489435091614723,
0.03284972906112671,
0.0072527723386883736,
0.04430621117353439,
-0.030510511249303818,
0.0067144352942705154,
0.053034909069538116,
-0.05146041885018349,
-0.03635483235120773,
-0.03492237627506256,
-0.013407502323389053,
0.023877102881669998,
-0.017112622037529945,
0.002353181131184101,
0.019448107108473778,
-0.03504981845617294,
-0.059823084622621536,
-0.041098110377788544,
-0.011221812106668949,
-0.018478356301784515,
-0.005320405121892691,
0.04003588855266571,
-0.013538062572479248,
-0.06882524490356445,
0.08000637590885162,
-0.01435026340186596,
-0.046512529253959656,
0.0021288504358381033,
-0.05681929364800453,
-0.04363704100251198,
-0.034993842244148254,
0.003181115258485079,
0.04165959358215332,
-0.04076261818408966,
-0.014951284974813461,
0.023851532489061356,
0.0364580899477005,
0.045181501656770706,
0.032224178314208984,
-0.014970463700592518,
-0.03721903637051582,
0.015558965504169464,
0.004525288939476013,
0.03559831157326698,
0.018492665141820908,
-0.007929549552500248,
0.002149129519239068,
-0.016929619014263153,
0.06860829144716263,
0.04208144173026085,
-0.051163200289011,
0.022687867283821106,
-0.000733065593522042,
-0.008105386979877949,
-0.03468652069568634,
0.015058347024023533,
-0.027972711250185966,
-0.0019094051094725728,
-0.026125619187951088,
0.01186820212751627,
0.037341196089982986,
-0.017114683985710144,
-0.04632611945271492,
0.02436862885951996,
0.04880649223923683,
-0.043707653880119324,
-0.022096257656812668,
-0.0016037895111367106,
-0.008913617581129074,
0.06400954723358154,
0.0031408716458827257,
-0.004001913126558065,
0.07673687487840652,
0.035751279443502426,
0.02411949262022972,
0.021072043105959892,
-0.025214213877916336,
-0.007719242945313454,
-0.0677381381392479,
0.01562858372926712,
0.016871726140379906,
0.001870415755547583,
0.0034066932275891304,
0.10972294211387634,
0.03047243505716324,
0.042667634785175323,
0.004935285542160273,
-0.017316101118922234,
-0.047363366931676865,
0.0005688336677849293,
-0.02529820427298546,
-0.03493567928671837,
-0.018801255151629448,
-0.0030742313247174025,
-0.0006234003813005984,
-0.015105168335139751,
0.009108206257224083,
-0.0300493985414505,
0.017585977911949158,
-0.05511409416794777,
0.02555018849670887,
-0.0008816186455078423,
-0.02764124795794487,
-0.020670844241976738,
0.032707471400499344,
0.021347355097532272,
0.029873501509428024,
0.07831122726202011,
0.020127827301621437,
0.009788413532078266,
0.06530267745256424,
-0.002719795098528266,
-0.029682902619242668,
-0.010040290653705597,
0.02346687577664852,
0.0042839571833610535,
-0.015365341678261757,
-0.002453808905556798,
0.01443402748554945,
0.047767382115125656,
0.03696989268064499,
0.004286267329007387,
0.014669659547507763,
-0.03751664236187935,
-0.061798322945833206,
-0.01960604637861252,
0.037147317081689835,
0.040813058614730835,
-0.023977087810635567,
0.0002102852304233238,
-0.00005317259274306707,
-0.031005889177322388,
0.014982186257839203,
0.026523446664214134,
0.030684590339660645,
-0.023801885545253754,
-0.016266629099845886,
-0.036978669464588165,
-0.013169643469154835,
-0.03699495270848274,
-0.02021384984254837,
-0.00845685601234436,
0.03182774782180786,
-0.023680517449975014,
-0.006789627019315958,
0.013239918276667595,
0.014332740567624569,
0.03149472177028656,
-0.017000190913677216,
0.01426704041659832,
0.011409731581807137,
-0.04989409074187279,
0.009419603273272514,
0.04454346001148224,
0.05486498028039932,
0.013765126466751099,
0.005011874716728926,
-0.051610276103019714,
-0.07921866327524185,
-0.01798544079065323,
0.006430968642234802,
0.02352333255112171,
-0.025578387081623077,
-0.00005237874938757159,
-0.06501498818397522,
-0.008327825926244259,
0.049946535378694534,
-0.008280633017420769,
0.004935339093208313,
-0.04195432737469673,
-0.00319300196133554,
-0.012736218050122261,
-0.034539591521024704,
-0.02159075438976288,
0.007511513773351908,
-0.0005675180582329631,
-0.004111326765269041,
0.018050935119390488,
-0.015274008736014366,
-0.002394355135038495,
-0.03602446988224983,
-0.004217382520437241,
0.04288451373577118,
-0.007796355523169041,
0.017337145283818245,
-0.01406795997172594,
-0.002681650221347809,
-0.03446594998240471,
-0.050220001488924026,
0.026224244385957718,
-0.005475728306919336,
-0.04811578616499901,
0.04762129485607147,
-0.02711142972111702,
-0.05231350287795067,
0.04169926792383194,
-0.005371447652578354,
-0.007040418218821287,
-0.0037695663049817085,
-0.011747102253139019,
0.011362265795469284,
0.02031712234020233,
0.01693745143711567,
0.04928158223628998,
0.03212291747331619,
-0.003859862918034196,
0.009738566353917122,
-0.028583768755197525,
0.013821981847286224,
-0.026551993563771248,
0.02052842266857624,
-0.014712134376168251,
0.006986474152654409,
-0.01087369304150343,
0.035868410021066666,
0.036716148257255554,
0.0059675551019608974,
-0.0009918281575664878,
-0.025670824572443962,
0.02688235603272915,
0.02400178276002407,
0.021898627281188965,
0.050657156854867935,
0.03536367416381836,
0.002087122295051813,
0.002126014558598399,
0.017699766904115677,
0.04407617077231407,
0.009067198261618614,
-0.004043358378112316,
0.04132453352212906,
-0.0024017328396439552,
-0.0029484573751688004,
-0.014525714330375195,
-0.01044680830091238,
0.012891890481114388,
-0.056555069983005524,
0.04275549203157425,
-0.018027450889348984,
-0.008289831690490246,
0.015947233885526657,
-0.013417192734777927,
0.011869925074279308,
0.010416815988719463,
-0.022128397598862648,
0.02507900446653366,
-0.06327808648347855,
0.04986236244440079,
-0.010895966552197933,
0.010554531589150429,
-0.05868333950638771,
-0.03699047118425369,
0.03969579190015793,
0.0448765829205513,
-0.03419110178947449,
-0.0152430459856987,
0.014025806449353695,
-0.020567279309034348,
-0.04310698062181473,
0.03489731252193451,
0.005781921092420816,
-0.00072780332993716,
0.02238977514207363,
0.03716791048645973,
0.0032330122776329517,
0.06244651973247528,
0.022852245718240738,
-0.011994950473308563,
-0.015449886210262775,
-0.0034067488741129637,
-0.06170220300555229,
-0.029836401343345642,
0.042598094791173935,
-0.01025800034403801,
-0.03264887258410454,
0.01109246350824833,
0.002662945305928588,
0.021842239424586296,
-0.044228892773389816,
0.011441909708082676,
0.05080100893974304,
0.007877189666032791,
0.000003149098802168737,
-0.00001015901580103673,
0.030242154374718666,
0.008211538195610046,
0.05150429159402847,
-0.026229968294501305,
0.04264732450246811,
-0.024082494899630547,
-0.022597290575504303,
-0.01132400706410408,
0.019432077184319496,
0.020835600793361664,
-0.025473887100815773,
0.05468575283885002,
-0.015818817541003227,
-0.003849103581160307,
0.030575627461075783,
-0.010774301365017891,
0.026890050619840622,
0.005936245433986187,
-0.021865855902433395,
0.03338657692074776,
0.015134425833821297,
-0.011686817742884159,
-0.01408625952899456,
0.0003086657088715583,
0.002830160316079855,
0.03843042254447937,
-0.011243426240980625,
0.06714438647031784,
0.005048767197877169,
-0.01757793501019478,
-0.017524544149637222,
-0.0660749077796936,
-0.02538660354912281,
-0.027102483436465263,
-0.01264858990907669,
0.02514144591987133,
-0.001129594282247126,
0.014995940029621124,
0.041613440960645676,
0.02728930301964283,
-0.031990908086299896,
0.0004627543385140598,
0.060941725969314575,
0.046769216656684875,
0.023532528430223465,
0.014430754818022251,
-0.03098755143582821,
0.041218407452106476,
-0.03980749100446701,
0.0511988140642643,
-0.02325766533613205,
0.02178357169032097,
0.03556087985634804,
-0.003253960981965065,
-0.005982683040201664,
-0.0524393767118454,
0.023754728958010674,
-0.01532483845949173,
-0.021626170724630356,
-0.01222576480358839,
-0.0042830039747059345,
-0.0028801974840462208,
-0.02555336058139801,
0.015972450375556946,
-0.025972966104745865,
0.022926965728402138,
-0.005188900977373123,
-0.03862079605460167,
-0.008645832538604736,
-0.01404669787734747,
-0.015851641073822975,
0.05857710540294647,
-0.02092629112303257,
-0.04598682001233101,
0.0156822819262743,
-0.02121535874903202,
0.0025969899725168943,
-0.01475259754806757,
0.009877447970211506,
-0.03021467849612236,
0.06457606703042984,
0.009753388352692127,
0.013324744999408722,
-0.01652112789452076,
0.01780249923467636,
0.1235986053943634,
0.045358508825302124,
0.014560206793248653,
-0.01637766882777214,
0.014453605748713017,
-0.021482285112142563,
0.03113948367536068,
-0.01576782763004303,
0.012798698619008064,
-0.013447021134197712,
0.018600095063447952,
0.027970874682068825,
0.0816044732928276,
-0.03285565972328186,
0.002085616812109947,
0.032358113676309586,
-0.029027629643678665,
-0.0060704415664076805,
-0.014296280220150948,
0.03573679178953171,
-0.012678036466240883,
0.06243852525949478,
-0.03608967363834381,
0.007942181080579758,
-0.015483775176107883,
-0.008324197493493557,
-0.0038003111258149147,
-0.04115051031112671,
0.024714551866054535,
-0.02557922713458538,
-0.03337782248854637,
0.01812405325472355,
0.020169593393802643,
-0.04436013475060463,
-0.019506437703967094,
0.03733185678720474,
0.017303744331002235,
-0.013237867504358292,
-0.008555077947676182,
0.03397393599152565,
-0.0012976675061509013,
0.018624741584062576,
-0.007666954770684242,
0.06759636849164963,
-0.04440763592720032,
0.0015905894106253982,
0.015180539339780807,
0.025761308148503304,
0.0010037132306024432,
0.013963893055915833,
-0.007200960069894791,
0.014880030415952206,
-0.0018497515702620149,
-0.04461191967129707,
-0.025536248460412025,
-0.016216492280364037,
-0.005273958668112755,
-0.001633101492188871,
-0.07477936148643494,
-0.047495439648628235,
0.016294879838824272,
-0.014247783459722996,
-0.015650451183319092,
-0.04189736768603325,
0.01115921325981617,
0.014165488071739674,
0.011576562188565731,
0.01896650902926922,
-0.05192526429891586,
-0.0008218250586651266,
-0.006072758696973324,
0.0066095273941755295,
-0.052390579134225845,
0.060715317726135254,
0.0008288196404464543,
-0.00989849679172039,
0.02860449254512787,
-0.02698243223130703,
-0.01720692217350006,
-0.004941559862345457,
-0.05842636153101921,
0.08342038840055466,
0.03421436995267868,
-0.025579378008842468,
-0.05711354315280914,
-0.01396738551557064,
0.021197764202952385,
0.03681426867842674,
-0.03497825190424919,
0.007181898690760136,
-0.013467422686517239,
0.015641024336218834,
0.004833942279219627,
-0.041127461940050125,
-0.09072933346033096,
0.02309470809996128,
-0.011150466278195381,
-0.009680486284196377,
0.029445715248584747,
0.04981832206249237,
-0.0008882043766789138,
0.05045776069164276,
0.006012315396219492,
0.019063293933868408,
-0.014912249520421028,
0.004227655939757824,
0.027013126760721207,
-0.0030460762791335583,
-0.02852674573659897,
0.017690809443593025,
-0.003071173094213009,
-0.048614781349897385,
0.0073835719376802444,
-0.03447655588388443,
0.0480438731610775,
0.0022521489299833775,
0.026593195274472237,
-0.005473550874739885,
0.019646605476737022,
-0.03463636711239815,
0.0024519385769963264,
-0.06187298521399498,
0.016637923195958138,
-0.0914863720536232,
-0.025273378938436508,
0.02403442934155464,
0.01320554781705141,
0.028084315359592438,
0.02726690284907818,
-0.06460050493478775,
-0.017939459532499313,
-0.004742943216115236,
0.019737854599952698,
-0.04516693949699402,
0.02865280583500862,
0.04784344136714935,
0.00552774453535676,
0.01713191159069538,
-0.018061161041259766,
-0.02317776344716549,
0.011933823116123676,
-0.04919019341468811,
-0.10461478680372238,
-0.0025021820329129696,
0.021484484896063805,
0.03468545153737068,
0.04542767256498337,
-0.03492007032036781,
-0.02571292221546173,
0.06661403924226761,
-0.02596437744796276,
-0.0534665584564209,
0.0009731345344334841,
-0.0035212517250329256,
-0.0026822565123438835,
-0.0045542302541434765,
0.00023803059593774378,
-0.023612486198544502,
0.005789846181869507,
0.03564608469605446,
-0.011542498134076595,
0.009807607159018517,
-0.0031166018452495337,
0.009756720624864101,
0.006133112125098705,
0.024380650371313095,
0.013295651413500309,
0.029996195808053017,
0.03795896843075752,
0.05994798615574837,
-0.005483947694301605,
0.02571835182607174,
-0.0016527693951502442,
-0.010368512012064457,
-0.10920295864343643,
-0.007105412892997265,
-0.0344153493642807,
-0.017000015825033188,
0.032033972442150116,
-0.02073260210454464,
-0.0008772464352659881,
0.024308163672685623,
-0.09326887875795364,
-0.005880344193428755,
0.00042967277113348246,
-0.034056272357702255,
-0.047314681112766266,
-0.014739826321601868,
-0.018489200621843338,
0.06674744933843613,
0.031327858567237854,
0.033564064651727676,
0.02100425399839878,
0.024430908262729645,
0.019456015899777412,
0.002938981866464019,
-0.015261170454323292,
0.020516151562333107,
0.013471102342009544,
0.016855141147971153,
0.0965190902352333,
-0.04138121381402016,
0.014869754202663898,
0.047895729541778564,
-0.04028499126434326,
-0.001440530875697732,
0.012159854173660278,
0.01654749922454357,
0.03216848149895668,
-0.018803395330905914,
0.004374748561531305,
-0.002333829877898097,
0.00937653612345457,
0.048369742929935455,
-0.00003040444789803587,
-0.013559558428823948,
-0.05297876521945,
0.011972215957939625,
0.014268606901168823,
-0.010400643572211266,
-0.01834144815802574,
-0.012700269930064678,
-0.0020008799619972706,
-0.00850242841988802,
0.03050331585109234,
0.030715106055140495,
-0.03158734738826752,
-0.002961240941658616,
-0.019570112228393555,
-0.020524553954601288,
0.02654959261417389,
0.04066336899995804,
0.032243065536022186,
-0.04262059926986694,
0.05087221786379814,
-0.0140540711581707,
0.012044942006468773,
-0.006857989355921745,
0.008963143453001976,
0.016759756952524185,
-0.031320661306381226,
-0.022256264463067055,
0.02072339691221714,
-0.0018334838096052408,
0.003530887421220541,
-0.01689545437693596,
0.006616313010454178,
0.034242238849401474,
0.03937841206789017,
0.04207872226834297,
-0.01847092993557453,
-0.0549466535449028,
-0.03485128656029701,
-0.08045100420713425,
-0.00042755118920467794,
-0.03975781053304672,
0.02619030885398388,
-0.07635723799467087,
-0.07770390063524246,
0.0029230760410428047,
0.03328995406627655,
0.061450641602277756,
0.0033330328296869993,
-0.01525861769914627,
0.0369255468249321,
0.015874437987804413,
0.002134219743311405,
-0.040624551475048065,
0.0025468694511801004,
0.020518021658062935,
0.010525883175432682,
-0.0026229219511151314,
0.005964583717286587,
-0.009518003091216087,
0.020802995190024376,
0.03197547793388367,
-0.0013529338175430894,
0.008996108546853065,
-0.015439934097230434,
-0.020649926736950874,
0.01294666901230812,
0.034376103430986404,
-0.03594331070780754,
0.06044991686940193,
-0.052240367978811264,
0.007200927007943392,
0.002246836433187127,
-0.0156277846544981,
-0.052456390112638474,
0.03668758645653725,
-0.0014963188441470265,
-0.004163766745477915,
-0.02854176051914692,
-0.03156573325395584,
-0.004085593856871128,
-0.036060504615306854,
-0.018336493521928787,
-0.03610758110880852,
-0.0658857524394989,
0.011655324138700962,
0.04217659309506416,
-0.020360862836241722,
0.06736298650503159,
-0.04800635576248169,
-0.006509745493531227,
0.025807565078139305,
0.005965304095298052,
-0.00852962676435709,
0.055924464017152786,
-0.006647998467087746,
-0.01055246964097023,
-0.011828235350549221,
0.005574967712163925,
0.016018109396100044,
0.02752058207988739,
0.045308567583560944,
0.03875945881009102,
0.0027718618512153625,
-0.04064973443746567,
-0.010744658298790455,
-0.01616813987493515,
-0.0019493382424116135,
-0.004072769079357386,
0.003140160581097007,
0.05992342159152031,
-0.000792942417319864,
0.03641385957598686,
-0.0230695940554142,
0.028962844982743263,
-0.035729099065065384,
0.01738879829645157,
-0.0005307763931341469,
0.007390117738395929,
-0.012413310818374157,
-0.025180449709296227,
-0.037315841764211655,
-0.0004675408999901265,
-0.0012879623100161552,
0.0014774476876482368,
-0.03141479194164276,
-0.00048138576676137745,
-0.009065460413694382,
-0.025631925091147423,
0.03727900981903076,
-0.0037819172721356153,
-0.009633134119212627,
0.06141648441553116,
0.024459369480609894,
-0.009582924656569958,
-0.003563801059499383,
0.0007691936916671693,
-0.027242135256528854,
0.013856060802936554,
-0.07267504930496216,
0.011684399098157883,
-0.011224953457713127,
0.011014558374881744,
-0.0035568447783589363,
-0.02056139148771763
] |
<p>I have an electron moving with speed $u'$ in a frame $S'$ moving with speed $v'$ relative to a rest frame $S$.</p>
<p>How do I find the total energy and momentum of the electron in the rest frame $S$?</p>
<p>I thought the equations were:</p>
<p>$E_{total} = \gamma \times mc^2$<br>
$p = \gamma \times mv$</p>
<p>But, that doesn't look right... Could someone point out to me what is wrong here?</p>
| 10,808 |
[
0.016644341871142387,
-0.051275502890348434,
-0.01876826584339142,
-0.013911851681768894,
0.02666175179183483,
0.004829778335988522,
-0.043066225945949554,
-0.027056893333792686,
-0.011377742514014244,
-0.03373827785253525,
0.06321892142295837,
0.047987453639507294,
0.06975856423377991,
0.02770788036286831,
0.0245650801807642,
-0.005394715815782547,
-0.01210017316043377,
0.012002971023321152,
-0.001635738299228251,
-0.02918257936835289,
0.009313874877989292,
0.0037297054659575224,
0.007260742597281933,
-0.013736769556999207,
-0.005796288605779409,
0.03957867994904518,
0.03436233103275299,
0.003477228106930852,
0.03016345575451851,
0.07019799947738647,
-0.03456428274512291,
-0.039348118007183075,
0.028208410367369652,
-0.0013880293117836118,
0.01908765360713005,
-0.00315466639585793,
-0.038083627820014954,
-0.027850735932588577,
-0.01651804894208908,
0.05263570696115494,
-0.04293973743915558,
-0.00109338469337672,
-0.017404276877641678,
0.0553535632789135,
-0.029600385576486588,
0.00695659639313817,
0.004536106251180172,
0.01922965794801712,
0.04225131496787071,
-0.03680529445409775,
0.09403093159198761,
-0.008937464095652103,
0.05339377373456955,
-0.011617692187428474,
-0.007260902319103479,
0.02600260265171528,
0.07170403003692627,
0.04993722587823868,
0.022644411772489548,
-0.04834989085793495,
-0.008985393680632114,
-0.034924425184726715,
0.0006738727097399533,
-0.0392247810959816,
-0.0007180387037806213,
0.03544404357671738,
-0.004280654713511467,
-0.006511090788990259,
0.022988587617874146,
-0.02066842094063759,
0.025133341550827026,
0.028604621067643166,
0.023654451593756676,
-0.03341532126069069,
0.0023109507746994495,
-0.03880252689123154,
0.04062695428729057,
0.04130708426237106,
0.023543041199445724,
0.03870938718318939,
-0.022212466225028038,
0.016980696469545364,
0.03634466603398323,
0.05552646890282631,
0.005621564108878374,
-0.035723987966775894,
0.055607814341783524,
0.03602581098675728,
-0.019660279154777527,
0.04540164768695831,
-0.013167833909392357,
0.036295633763074875,
0.022857138887047768,
-0.009213387966156006,
-0.015015855431556702,
0.027878664433956146,
-0.0012529466766864061,
0.07675614207983017,
-0.003917973954230547,
-0.03464217111468315,
0.03798156976699829,
-0.010138705372810364,
0.02538616769015789,
0.08970969170331955,
-0.025522053241729736,
-0.03350905701518059,
-0.05058044195175171,
-0.0019672021735459566,
-0.0047514610923826694,
-0.038365237414836884,
-0.012952055782079697,
0.02683844044804573,
-0.0027344059199094772,
0.005960516165941954,
0.00280372379347682,
-0.03327165171504021,
0.0028176221530884504,
-0.0025598828215152025,
0.053744133561849594,
0.040869347751140594,
0.00966581329703331,
-0.03930819034576416,
0.012963579967617989,
-0.001370786689221859,
-0.08193500339984894,
0.02168971113860607,
0.02574215456843376,
-0.013330326415598392,
-0.03832705318927765,
-0.005461700260639191,
-0.020516760647296906,
-0.024844219908118248,
0.014190356247127056,
-0.006258200854063034,
0.04052770137786865,
-0.017397865653038025,
-0.10808217525482178,
-0.07233097404241562,
0.013553137890994549,
-0.03254569321870804,
-0.0275392085313797,
-0.08690307289361954,
-0.012602257542312145,
0.01407186035066843,
0.07248089462518692,
-0.024580636993050575,
-0.011148958466947079,
0.004000288434326649,
0.02915307506918907,
0.01770077645778656,
-0.0018869114574044943,
-0.026476670056581497,
-0.03348284959793091,
-0.012816461734473705,
0.022091256454586983,
-0.03531436622142792,
-0.00362655078060925,
0.033912431448698044,
-0.002185495337471366,
0.022264840081334114,
0.06006842851638794,
0.005633809138089418,
0.01405071746557951,
-0.01067319419234991,
-0.01908215880393982,
-0.027914464473724365,
0.05205472931265831,
0.028769632801413536,
-0.009418729692697525,
0.04117819294333458,
0.009774797596037388,
0.009034423157572746,
-0.0031129803974181414,
0.013216637074947357,
0.04176545888185501,
-0.0005962767754681408,
-0.04473055154085159,
-0.01763594150543213,
0.0007765810005366802,
0.009985907934606075,
-0.03705940023064613,
-0.07013193517923355,
0.02082102932035923,
0.018293946981430054,
0.02318737842142582,
0.04273683577775955,
0.00565823120996356,
-0.002368279965594411,
-0.05852941423654556,
-0.021556125953793526,
-0.008534093387424946,
-0.08641403913497925,
0.02207622490823269,
-0.026539616286754608,
-0.003096914617344737,
0.036150284111499786,
0.0005375787150114775,
0.0335138663649559,
-0.025280524045228958,
-0.03792152181267738,
0.027849731966853142,
0.07035204023122787,
-0.011418366804718971,
-0.011700370348989964,
0.029893722385168076,
0.028879757970571518,
0.05321890115737915,
0.018218660727143288,
-0.0059763407334685326,
0.01467686053365469,
-0.049994178116321564,
0.014434071257710457,
-0.02412555180490017,
0.016891738399863243,
0.01758481003344059,
-0.01953577809035778,
-0.009957665577530861,
-0.008765584789216518,
0.02134108357131481,
0.04487230256199837,
0.018781712278723717,
0.07775573432445526,
0.029036851599812508,
0.010069995187222958,
0.02328120358288288,
0.030933527275919914,
0.015997912734746933,
0.055965401232242584,
0.008367699570953846,
-0.013345256447792053,
-0.00805529486387968,
0.011745420284569263,
0.025500154122710228,
-0.009515653364360332,
-0.0635974332690239,
-0.0106683149933815,
0.026447108015418053,
0.027224889025092125,
0.02319072186946869,
0.03913184255361557,
-0.012582904659211636,
-0.06585279852151871,
0.005097095388919115,
0.01182037778198719,
-0.02208072505891323,
0.010496034286916256,
0.020994361490011215,
0.03225529566407204,
0.01347020361572504,
-0.011023021303117275,
-0.012312674894928932,
0.04983772337436676,
-0.022012485191226006,
-0.0029528792947530746,
0.0005204363260418177,
-0.07337804138660431,
0.042120013386011124,
-0.024488648399710655,
0.06367453187704086,
0.033529672771692276,
-0.025726204738020897,
-0.02066277712583542,
-0.016373585909605026,
-0.017071571201086044,
0.02244221791625023,
-0.004841607064008713,
-0.018167052417993546,
0.02084626443684101,
0.02080065757036209,
-0.04389183595776558,
0.0059191277250647545,
-0.017272120341658592,
-0.005674622021615505,
-0.049619823694229126,
0.0057869465090334415,
0.022334188222885132,
0.012915760278701782,
0.017848843708634377,
-0.023572716861963272,
-0.07614338397979736,
0.0072523485869169235,
-0.03464943543076515,
-0.013852182775735855,
0.016940096393227577,
-0.04766317829489708,
0.030756013467907906,
-0.03733177110552788,
-0.02157408557832241,
0.029688557609915733,
0.008535063825547695,
0.007968100719153881,
0.06008676439523697,
-0.02728191949427128,
-0.049397919327020645,
-0.02524666115641594,
0.006514234468340874,
-0.005508529022336006,
-0.02507866360247135,
0.02751605398952961,
0.06797274202108383,
-0.004426674917340279,
-0.0003459336294326931,
0.0068550449796020985,
-0.028957461938261986,
-0.049356188625097275,
-0.011084139347076416,
0.02050243504345417,
0.04446437954902649,
-0.009039048105478287,
0.04499159753322601,
0.03243691101670265,
-0.05179053172469139,
0.01010827999562025,
-0.05126121640205383,
-0.0242141280323267,
-0.00018733381875790656,
0.029620567336678505,
0.01917385868728161,
0.00650846678763628,
-0.05000019446015358,
0.07101284712553024,
-0.00012477322889026254,
-0.011859513819217682,
-0.03114197589457035,
0.004112076014280319,
-0.011199094355106354,
-0.03184337168931961,
-0.006002113223075867,
0.015948140993714333,
-0.019252633675932884,
0.007671333383768797,
-0.019505657255649567,
0.05732637271285057,
0.016490794718265533,
0.030409837141633034,
0.005900652147829533,
-0.019292978569865227,
-0.0037732047494500875,
-0.002305320929735899,
0.057820387184619904,
-0.005507654510438442,
-0.021143151447176933,
-0.000043961692426819354,
0.035354819148778915,
0.06570233404636383,
-0.012139640748500824,
-0.052575670182704926,
0.03935379534959793,
0.01636965200304985,
0.006290299352258444,
-0.017850374802947044,
0.029461871832609177,
0.032715532928705215,
-0.028341522440314293,
-0.006620453204959631,
0.045807644724845886,
0.03225761651992798,
-0.005563721526414156,
0.0072662499733269215,
0.046213649213314056,
0.0430026538670063,
-0.02788383886218071,
-0.0747615322470665,
-0.003070338163524866,
-0.0195198692381382,
-0.006668511312454939,
-0.006918568629771471,
-0.03706090897321701,
0.03914398327469826,
0.03728785738348961,
0.05765359848737717,
-0.01752960868179798,
-0.06371049582958221,
-0.015768731012940407,
-0.05671210214495659,
-0.0025590246077626944,
-0.007765316404402256,
0.04429290443658829,
0.0067663295194506645,
0.0735703706741333,
0.031161976978182793,
0.026344459503889084,
0.04487335681915283,
0.01181491743773222,
-0.05206546187400818,
0.061772119253873825,
-0.023715578019618988,
-0.02974545583128929,
-0.003516601165756583,
0.009076075628399849,
-0.007408191915601492,
-0.051927026361227036,
0.006251854356378317,
-0.014498054049909115,
-0.014150981791317463,
-0.053394071757793427,
0.008428644388914108,
-0.05672430247068405,
0.007346996106207371,
-0.012238023802638054,
0.03866247087717056,
0.02535196766257286,
-0.036778826266527176,
-0.009904528968036175,
0.061684515327215195,
-0.037489064037799835,
-0.017269298434257507,
-0.02130034938454628,
0.0032660202123224735,
-0.006601102650165558,
0.021080614998936653,
0.047801531851291656,
0.022755714133381844,
-0.0061959922313690186,
0.012958432547748089,
0.003106654155999422,
0.055405620485544205,
-0.006580654066056013,
-0.033406682312488556,
-0.031926196068525314,
-0.0196321252733469,
0.00985740590840578,
-0.02976636216044426,
0.04656914249062538,
-0.011956884525716305,
0.01628469116985798,
0.03412594646215439,
0.028892172500491142,
-0.012999312952160835,
0.04360099881887436,
0.049800656735897064,
-0.02243194356560707,
-0.016125651076436043,
-0.04184285178780556,
0.03258789703249931,
-0.03757684305310249,
-0.017856698483228683,
0.00899878516793251,
-0.011377573944628239,
-0.05299661308526993,
-0.031647197902202606,
0.0035792251583188772,
-0.01706518605351448,
-0.016821129247546196,
-0.013992768712341785,
-0.018045008182525635,
0.008436870761215687,
0.028462640941143036,
-0.04525360092520714,
-0.02375268004834652,
0.01989988051354885,
0.012239387258887291,
-0.009477436542510986,
0.007275906391441822,
-0.04248909652233124,
-0.011418149806559086,
0.02318255975842476,
0.0544106625020504,
-0.003236340591683984,
-0.023940209299325943,
-0.04102163016796112,
-0.005387189798057079,
0.04087235778570175,
-0.027867404744029045,
0.015799270942807198,
0.00369301182217896,
0.020003460347652435,
-0.008025351911783218,
-0.03143102303147316,
-0.0318259634077549,
0.02579764649271965,
-0.034620579332113266,
0.019157947972416878,
-0.04566783830523491,
0.002924172207713127,
-0.025326630100607872,
0.014140368439257145,
0.008956065401434898,
0.05725309997797012,
0.04205463454127312,
-0.02618728019297123,
0.0017490037716925144,
0.06135043129324913,
-0.03837904334068298,
-0.0991760715842247,
-0.03199092671275139,
-0.008294139988720417,
-0.009712335653603077,
0.004024970810860395,
-0.0401608869433403,
-0.04930002614855766,
0.0526219867169857,
-0.011652979999780655,
0.005110695958137512,
-0.011637295596301556,
-0.06555373966693878,
0.027187174186110497,
0.038273315876722336,
0.012191789224743843,
0.03809025138616562,
0.03217720240354538,
-0.021087097004055977,
-0.024224240332841873,
-0.02363644912838936,
0.02103007212281227,
-0.04080558568239212,
-0.00584791973233223,
-0.014712460339069366,
0.01300733257085085,
-0.013898585923016071,
0.030275775119662285,
-0.04749046266078949,
0.04084568843245506,
-0.005026255268603563,
-0.03725137561559677,
-0.030858229845762253,
0.036069080233573914,
0.00513417785987258,
-0.006162140518426895,
-0.00544729782268405,
-0.018094731494784355,
-0.03034088760614395,
-0.03971142694354057,
0.00616416335105896,
0.01646815426647663,
-0.020328057929873466,
0.027507683262228966,
0.017787860706448555,
0.04202348738908768,
-0.007440931163728237,
-0.01569194346666336,
0.02199643664062023,
-0.05420169606804848,
0.011214596219360828,
-0.012585993856191635,
-0.013296895660459995,
0.005978440400213003,
-0.03330478444695473,
-0.057922445237636566,
-0.006170002743601799,
-0.0021003081928938627,
0.024495912715792656,
-0.060478370636701584,
0.014947249554097652,
0.03314751014113426,
0.04402640089392662,
-0.08239669352769852,
-0.04339340329170227,
0.026962077245116234,
-0.031168607994914055,
-0.018222978338599205,
-0.025770971551537514,
0.012037754990160465,
-0.04086190462112427,
-0.016340559348464012,
-0.004778953269124031,
0.02213422581553459,
-0.030294278636574745,
-0.026569869369268417,
-0.008535514585673809,
0.009503873996436596,
0.012889026664197445,
-0.011314532719552517,
-0.009377834387123585,
-0.012340988963842392,
-0.014058384113013744,
-0.013018516823649406,
0.01236359216272831,
0.06424479931592941,
-0.012023944407701492,
-0.04669468104839325,
0.014661157503724098,
-0.01982993260025978,
0.03206166252493858,
-0.0064092460088431835,
0.02223542332649231,
0.03562353923916817,
0.025811463594436646,
0.004742824472486973,
-0.013848738744854927,
0.03429132327437401,
-0.0005723455687984824,
0.03932780772447586,
0.01672256365418434,
-0.0028827940113842487,
-0.05295933410525322,
-0.03999236971139908,
0.001404368318617344,
-0.02209988795220852,
0.04050609841942787,
-0.015922319144010544,
0.054246678948402405,
0.01162529643625021,
0.03470495715737343,
0.028302647173404694,
0.0059185023419559,
0.0066367764957249165,
-0.014882518909871578,
0.02383742481470108,
0.02155587449669838,
0.0004140922974329442,
-0.015361320227384567,
0.01286174263805151,
-0.02919868379831314,
0.0008380659855902195,
0.0776364877820015,
-0.023428363725543022,
0.04306608438491821,
-0.01375993900001049,
0.010863672010600567,
0.029014332219958305,
-0.0024798770900815725,
-0.017652790993452072,
-0.004278935492038727,
0.022954611107707024,
0.025894369930028915,
0.012358410283923149,
-0.011741706170141697,
0.014481956139206886,
0.05684784799814224,
-0.024799112230539322,
0.025169461965560913,
0.020941346883773804,
0.02004067972302437,
-0.00863971933722496,
0.010733898729085922,
-0.038134533911943436,
0.03095102496445179,
-0.0022277827374637127,
0.01215012650936842,
0.007068134844303131,
-0.037184298038482666,
0.05289760231971741,
0.004834194667637348,
0.00806135032325983,
-0.003625268116593361,
0.00669667636975646,
-0.022039728239178658,
0.006923201028257608,
0.013907268643379211,
-0.017183303833007812,
-0.043851085007190704,
0.03746090084314346,
0.021362870931625366,
0.03031812608242035,
0.03903218358755112,
-0.019663764163851738,
-0.044929154217243195,
-0.00932129193097353,
-0.0432179719209671,
-0.029589353129267693,
0.03968321159482002,
-0.02673392742872238,
0.027451731264591217,
0.006896671373397112,
-0.0003422200679779053,
0.013858525082468987,
0.022759974002838135,
0.02860557846724987,
-0.011036825366318226,
0.05570979416370392,
0.005569230765104294,
-0.0035561807453632355,
0.0037947215605527163,
0.01711772009730339,
0.09911773353815079,
0.038182392716407776,
0.018036404624581337,
-0.04336821660399437,
0.003467757487669587,
-0.04186407849192619,
0.019473453983664513,
-0.015152218751609325,
0.03659757226705551,
-0.03739763796329498,
0.0018212215509265661,
-0.0080924266949296,
0.04732321947813034,
-0.005047603044658899,
0.0017027448629960418,
0.04024267569184303,
-0.04153033718466759,
-0.04403439909219742,
-0.006968178786337376,
0.011419530026614666,
-0.011768100783228874,
0.0025433406699448824,
-0.02673850767314434,
0.03740011900663376,
-0.04248179495334625,
0.004494788125157356,
-0.04700979217886925,
-0.060050271451473236,
0.012786912731826305,
-0.020602790638804436,
-0.02992512658238411,
-0.004352557938545942,
-0.009627214632928371,
0.010468857362866402,
-0.040846455842256546,
-0.010201653465628624,
0.050976790487766266,
-0.011533500626683235,
0.04050052538514137,
0.019731299951672554,
0.01044649351388216,
0.021489497274160385,
0.006508461199700832,
0.013716321438550949,
-0.04464521259069443,
0.0023723191116005182,
-0.008497371338307858,
0.08241888135671616,
0.009237033315002918,
0.020614633336663246,
-0.0026769149117171764,
0.020569952204823494,
-0.0021800650283694267,
-0.054962072521448135,
0.0043842969462275505,
-0.013640617951750755,
0.028719864785671234,
0.016798600554466248,
-0.00048648877418600023,
-0.04236086457967758,
0.027197852730751038,
-0.016809074208140373,
0.01041853241622448,
-0.014208497479557991,
0.01209520548582077,
-0.007255030330270529,
-0.02190740406513214,
0.01571914739906788,
-0.015359800308942795,
-0.012224793434143066,
0.005500179249793291,
-0.049978651106357574,
-0.03972882032394409,
-0.02281111851334572,
0.044650349766016006,
0.011398116126656532,
0.024979151785373688,
-0.006030718330293894,
-0.00004789552258444019,
-0.04288974404335022,
-0.10850139707326889,
0.03730781376361847,
-0.018486840650439262,
-0.014103151857852936,
-0.007609992753714323,
0.03790506348013878,
0.015558302402496338,
0.05872325971722603,
-0.02223927341401577,
0.017398782074451447,
0.010146048851311207,
-0.005728607997298241,
0.026034552603960037,
-0.030252356082201004,
0.01206823717802763,
0.013349673710763454,
0.007206094916909933,
0.02425868809223175,
-0.02854399010539055,
-0.018535058945417404,
0.0033262164797633886,
0.034873925149440765,
-0.008461564779281616,
0.04194283485412598,
-0.02620146982371807,
-0.018297366797924042,
0.02346661500632763,
-0.008879912085831165,
0.0075416844338178635,
0.018410852178931236,
0.015978990122675896,
-0.03239055722951889,
-0.0033053604420274496,
-0.022469421848654747,
0.020834242925047874,
-0.010603422299027443,
0.021445589140057564,
-0.021387262269854546,
0.027533365413546562,
-0.013914478942751884,
0.027476858347654343,
-0.021857913583517075,
0.014832216314971447,
-0.03820324316620827,
0.05325497314333916,
-0.022762687876820564,
-0.003534102812409401,
-0.061257366091012955,
0.03317203372716904,
0.004898015409708023,
-0.023055419325828552,
0.01735830307006836,
0.040948957204818726,
-0.00657310988754034,
-0.026841968297958374,
0.03295256942510605,
0.006401414982974529,
0.034735057502985,
-0.00006954208947718143,
-0.002444898011162877,
0.041984930634498596,
-0.04244793951511383,
-0.03579117730259895,
0.02805252932012081,
-0.007533353753387928,
0.027182554826140404,
0.029497439041733742,
-0.043576620519161224,
-0.016808178275823593,
0.061473291367292404,
-0.029114559292793274,
0.006207309663295746,
0.012044577859342098,
-0.059550072997808456,
-0.010906048119068146,
-0.008380569517612457,
-0.0018530176021158695,
0.026786554604768753,
-0.0030630372930318117,
0.05160396546125412,
0.009308326989412308,
-0.023297473788261414,
0.04370446503162384,
-0.006850140634924173,
0.01027331780642271,
0.01230149157345295,
0.06045101210474968,
-0.024737609550356865,
0.02235988713800907,
0.04863270744681358,
-0.024452442303299904,
0.02466944232583046,
-0.0032356707379221916,
0.016680249944329262,
-0.09870447963476181,
0.002826370531693101,
-0.04536525905132294,
0.006409063003957272,
0.031024344265460968,
-0.05124194547533989,
0.01856430061161518,
0.04999450594186783,
-0.06289499253034592,
0.004282272886484861,
-0.04172246903181076,
-0.004057569894939661,
0.0034654808696359396,
0.0007174538332037628,
-0.016005968675017357,
0.07151681929826736,
0.012279348447918892,
0.0754074677824974,
0.028527429327368736,
-0.011990826576948166,
0.008347376249730587,
-0.039611537009477615,
-0.030662205070257187,
0.0241934135556221,
-0.009218394756317139,
-0.013034644536674023,
0.051972176879644394,
-0.016962353140115738,
-0.019925998523831367,
0.022842666134238243,
0.03340185433626175,
0.015835214406251907,
-0.04034244641661644,
0.040807101875543594,
0.002724941587075591,
0.03730444982647896,
0.027189169079065323,
-0.01479080505669117,
-0.02542303316295147,
0.005552979186177254,
0.01928587257862091,
0.0217906441539526,
-0.016931727528572083,
-0.03057335503399372,
0.007926451042294502,
-0.03357236832380295,
-0.058146167546510696,
0.03997059911489487,
-0.016212578862905502,
-0.024746190756559372,
-0.003031448693946004,
0.01889115944504738,
-0.004100032616406679,
-0.06553276628255844,
0.0032559216488152742,
-0.07222267240285873,
0.001768589369021356,
0.045551590621471405,
-0.05262719839811325,
0.02324540540575981,
0.010903846472501755,
0.019831065088510513,
-0.023600773885846138,
0.008721277117729187,
-0.0015462917508557439,
-0.009966070763766766,
-0.04931621253490448,
-0.006384947802871466,
0.04272851720452309,
-0.022246526554226875,
0.010144839063286781,
-0.04161209985613823,
-0.03630393370985985,
0.022084303200244904,
0.03190789744257927,
0.014555937610566616,
0.010322551243007183,
-0.011574470438063145,
0.016355084255337715,
-0.03608172386884689,
0.016307802870869637,
0.017536267638206482,
-0.04448060691356659,
-0.03312171623110771,
-0.00983351469039917,
0.017409132793545723,
0.025703763589262962,
0.07059212774038315,
-0.01898568868637085,
-0.008025999180972576,
0.017862828448414803,
-0.010233961045742035,
0.02778259478509426,
-0.051548559218645096,
-0.008896075189113617,
-0.017287231981754303,
-0.04673284292221069,
-0.020276125520467758,
-0.013849909417331219,
-0.019982872530817986,
0.030408503487706184,
0.008003455586731434,
-0.029479417949914932,
-0.0048232669942080975,
-0.00518866628408432,
-0.018934668973088264,
0.02852371521294117,
0.017025718465447426,
-0.04093765839934349,
0.057244766503572464,
-0.003679902059957385,
0.025693826377391815,
0.07154113054275513,
-0.03797535225749016,
-0.028712036088109016,
0.002609306713566184,
-0.026614945381879807,
-0.027547257021069527,
-0.016871681436896324,
0.0007813940173946321,
0.046624407172203064,
-0.051665179431438446,
-0.01049366220831871,
0.038709647953510284,
-0.05045490711927414,
0.008793583139777184,
0.05835956707596779,
0.019174963235855103,
0.03620162606239319,
0.022940795868635178,
0.02552737668156624,
0.029909735545516014,
-0.004034876823425293,
0.015686003491282463,
0.06836488097906113,
0.03607499226927757,
-0.013647404499351978,
0.005938912276178598,
0.06069207936525345,
-0.025533292442560196,
0.008781028911471367,
-0.02297448180615902,
0.02691015787422657,
-0.022670838981866837,
0.004381059668958187,
-0.02581062726676464,
-0.008675294928252697,
0.01389260869473219,
0.010924016125500202,
-0.05732257664203644,
0.06938882917165756,
-0.035453781485557556,
0.005422124173492193,
-0.012723961845040321,
-0.004826270509511232,
-0.011692145839333534,
0.024707095697522163,
-0.004652037285268307,
0.033638983964920044,
0.00006274932093219832,
-0.04167308658361435,
-0.031407251954078674,
-0.014313670806586742,
0.030913395807147026,
-0.031715068966150284,
0.013362692669034004,
0.021617678925395012,
-0.01651444286108017,
-0.029497262090444565,
-0.009422832168638706,
-0.015906397253274918,
-0.03179868310689926,
0.013745169155299664,
0.011028757318854332,
-0.0018889836501330137,
-0.019977280870079994,
-0.011318324133753777,
-0.02850804477930069,
0.04969937726855278,
-0.04710010066628456,
-0.0358724445104599,
-0.01843838021159172,
0.01696966588497162,
-0.025478502735495567,
-0.01780494675040245
] |
<p>Is the S-matrix the only observable in string theory? What about time varying spacetime backgrounds, or thermal states then?</p>
| 10,809 |
[
-0.009184010326862335,
-0.009247761219739914,
0.009234738536179066,
-0.06867373734712601,
0.00972752645611763,
0.03368489444255829,
-0.04604758322238922,
0.00022256834199652076,
-0.02613641507923603,
-0.03218016028404236,
-0.001317665446549654,
-0.0012891283258795738,
-0.0021470601204782724,
0.015536661259829998,
0.010520157404243946,
-0.005957677494734526,
0.006587341893464327,
-0.005598556250333786,
-0.014960810542106628,
0.019293561577796936,
0.01678558439016342,
0.0485222265124321,
-0.00468253530561924,
0.0018623596988618374,
-0.019892117008566856,
0.014216228388249874,
-0.013086458668112755,
0.04186716303229332,
0.03724020719528198,
0.050047557801008224,
-0.013781169429421425,
-0.029490411281585693,
-0.00015338489902205765,
0.023726897314190865,
0.023652950301766396,
-0.04492735490202904,
-0.017207136377692223,
-0.008502710610628128,
-0.0083688423037529,
-0.009552046656608582,
-0.01866191253066063,
-0.029283445328474045,
-0.023674018681049347,
0.06776122003793716,
-0.022471314296126366,
0.025677701458334923,
-0.027393123134970665,
0.00950216967612505,
0.05461472272872925,
-0.09815635532140732,
0.07538548856973648,
-0.011301858350634575,
0.010359849780797958,
0.014285202138125896,
-0.035272661596536636,
0.009000472724437714,
0.0882829800248146,
0.04457229748368263,
0.008278953842818737,
-0.03913460671901703,
-0.02121988870203495,
0.014318580739200115,
0.011321626603603363,
-0.046186406165361404,
-0.01867349073290825,
0.01418251357972622,
0.019664112478494644,
-0.008006546646356583,
0.013182016089558601,
-0.015257352031767368,
-0.016749396920204163,
0.0004224481526762247,
0.045498985797166824,
0.026132138445973396,
0.009565573185682297,
0.004389414098113775,
0.011558414436876774,
0.010546986944973469,
0.03843696042895317,
0.0362255685031414,
0.012540740892291069,
-0.025182677432894707,
0.02224358730018139,
0.01087462343275547,
0.011221123859286308,
0.0010625752620398998,
0.04407046362757683,
0.004433609079569578,
-0.0038095498457551003,
0.08710818737745285,
-0.02279551327228546,
0.0038340690080076456,
0.032369956374168396,
-0.028593141585588455,
-0.04322696477174759,
0.009119310416281223,
0.030452262610197067,
0.041940320283174515,
-0.024283045902848244,
-0.02704438753426075,
-0.007662742864340544,
0.0008705782820470631,
0.027746504172682762,
0.08604629337787628,
-0.01787247136235237,
0.0016565911937505007,
-0.028282510116696358,
0.02355552837252617,
-0.015133638866245747,
-0.017877276986837387,
-0.0787462368607521,
0.01609245501458645,
-0.01976979896426201,
-0.01285893376916647,
0.01115055289119482,
-0.05790787562727928,
0.009507008828222752,
-0.016059137880802155,
0.015613099560141563,
0.08679432421922684,
0.025776661932468414,
-0.006461941171437502,
-0.02202189899981022,
-0.00988264475017786,
-0.04513334855437279,
0.0280885212123394,
0.06024458631873131,
-0.02378631755709648,
-0.025672296062111855,
0.018855521455407143,
-0.018095511943101883,
-0.017063338309526443,
0.019966287538409233,
-0.025921426713466644,
0.07895921915769577,
-0.03121919371187687,
-0.08962970972061157,
-0.04335610568523407,
0.040803391486406326,
-0.01734926737844944,
-0.025193579494953156,
-0.027304204180836678,
-0.010752030648291111,
0.043139323592185974,
0.06811407208442688,
-0.01928039640188217,
-0.011316363699734211,
0.036115676164627075,
0.05792902037501335,
0.014053696766495705,
-0.020010482519865036,
-0.014557470567524433,
0.018795471638441086,
-0.06326335668563843,
-0.008866747841238976,
-0.05016816034913063,
0.02118730917572975,
0.07516514509916306,
-0.008181439712643623,
0.0073180655017495155,
0.0597703792154789,
0.009357726201415062,
0.02854599989950657,
0.029734663665294647,
-0.009245707653462887,
-0.02785678766667843,
0.07185351848602295,
-0.016718789935112,
0.01743294857442379,
0.01568184606730938,
0.0012490367516875267,
-0.001633159350603819,
0.034834105521440506,
0.04294509068131447,
-0.005584296304732561,
-0.0401860810816288,
-0.03515531122684479,
0.050710324198007584,
-0.006320419255644083,
-0.0015973233385011554,
-0.06122937425971031,
-0.010872605256736279,
0.034018777310848236,
0.006971518974751234,
-0.027003638446331024,
0.05807944014668465,
-0.031184105202555656,
-0.019920246675610542,
0.012580711394548416,
-0.04585028067231178,
-0.004396917764097452,
-0.040729325264692307,
-0.006116632837802172,
-0.008163483813405037,
0.021066496148705482,
0.018152734264731407,
0.038567546755075455,
0.007967399433255196,
-0.023985251784324646,
-0.056035466492176056,
0.010814307257533073,
0.05491352081298828,
-0.004405243322253227,
-0.025457486510276794,
0.01741011254489422,
0.024333635345101357,
0.06412526220083237,
-0.03163095936179161,
-0.003970492165535688,
-0.06355121731758118,
-0.03980577364563942,
-0.010878979228436947,
-0.0343923456966877,
0.04527748003602028,
-0.017151813954114914,
0.0009675690089352429,
0.004090035799890757,
-0.029324447736144066,
-0.04172375798225403,
0.05687777325510979,
-0.04113242030143738,
0.05158042535185814,
0.013837652280926704,
0.006281424779444933,
-0.03170425072312355,
0.044186782091856,
-0.007167380303144455,
0.02064680866897106,
-0.0024133461993187666,
-0.027717938646674156,
-0.08875317871570587,
-0.009168293327093124,
0.03710866719484329,
0.058394577354192734,
-0.018202118575572968,
0.04205981269478798,
0.031682271510362625,
0.029353506863117218,
0.009495798498392105,
0.017333179712295532,
-0.027534570544958115,
-0.02024739421904087,
-0.014644484966993332,
0.0011362845543771982,
-0.006556935142725706,
-0.008429612964391708,
0.04236598312854767,
0.008268589153885841,
-0.0004275793326087296,
0.014654730446636677,
-0.031537726521492004,
0.0316644050180912,
-0.022788438946008682,
0.02885173261165619,
0.021228110417723656,
-0.0641544833779335,
-0.006040687672793865,
-0.012748387642204762,
0.0212973915040493,
0.04209383204579353,
0.012691196985542774,
0.014563844539225101,
-0.018698761239647865,
-0.0223538801074028,
-0.013248475268483162,
-0.018125245347619057,
-0.006932416930794716,
-0.003977511078119278,
0.03547019138932228,
-0.03075576387345791,
0.013754610903561115,
-0.021873271092772484,
-0.006542714312672615,
0.0016083380905911326,
0.03209741413593292,
0.03572596609592438,
-0.02683829516172409,
0.03356735780835152,
-0.060490723699331284,
-0.03663046285510063,
0.02404722385108471,
-0.01998845674097538,
0.0034372603986412287,
0.0421818345785141,
-0.06770036369562149,
0.02576078101992607,
-0.03799901157617569,
-0.06776775419712067,
0.03869028016924858,
-0.0037851312663406134,
0.020995553582906723,
0.01885450817644596,
-0.01883350871503353,
-0.0030198500026017427,
-0.015268291346728802,
0.0033469742629677057,
0.02195868268609047,
-0.054287418723106384,
0.021102983504533768,
0.028505835682153702,
0.011268651112914085,
-0.029138313606381416,
0.008690759539604187,
-0.021859169006347656,
-0.03117091953754425,
-0.008506654761731625,
-0.03810032084584236,
0.04158293455839157,
-0.025910601019859314,
0.04580362141132355,
0.0475224107503891,
-0.07088066637516022,
0.02003667689859867,
-0.03435048833489418,
-0.04002796858549118,
0.041497211903333664,
-0.00471719354391098,
0.03921259194612503,
-0.02063664421439171,
-0.03860437870025635,
0.06858102977275848,
0.025576714426279068,
-0.01365454588085413,
0.021905213594436646,
-0.008341506123542786,
-0.040849000215530396,
-0.0439019575715065,
0.03494224697351456,
0.015972407534718513,
-0.023600054904818535,
0.006658852566033602,
0.036319613456726074,
-0.005360334180295467,
0.04474826902151108,
0.019609583541750908,
-0.04270637407898903,
-0.01879359781742096,
-0.006968064233660698,
0.027497699484229088,
0.03896642476320267,
-0.011825762689113617,
0.012721278704702854,
-0.01955442689359188,
0.027546115219593048,
0.020335562527179718,
0.01137131080031395,
-0.03354159742593765,
0.07454534620046616,
0.013968560844659805,
0.009296102449297905,
-0.017436005175113678,
0.02277671918272972,
0.005313379690051079,
0.00936690904200077,
-0.045658696442842484,
0.0009568922105245292,
0.027209052816033363,
0.012255308218300343,
0.016591856256127357,
0.04427468031644821,
0.030674895271658897,
-0.028396662324666977,
-0.023199763149023056,
0.006063804961740971,
-0.02122984454035759,
0.028454497456550598,
-0.016922997310757637,
-0.04628107696771622,
0.007290670648217201,
0.027635008096694946,
0.01801072433590889,
0.008749714121222496,
-0.05399439111351967,
-0.009013662114739418,
-0.05783369392156601,
-0.005230539944022894,
-0.011678097769618034,
0.03135379031300545,
0.025112301111221313,
0.03151169419288635,
0.0067441524006426334,
0.010936059057712555,
0.044823888689279556,
-0.006556794047355652,
-0.056325364857912064,
-0.018247192725539207,
-0.06495734304189682,
0.01044358592480421,
0.0007256562821567059,
0.030405329540371895,
-0.00285011506639421,
0.004466079641133547,
-0.001223759725689888,
-0.008586304262280464,
-0.0054525891318917274,
-0.08101377636194229,
-0.013832216151058674,
-0.05398028716444969,
-0.03465687111020088,
-0.03053012676537037,
0.03133365884423256,
0.05992278456687927,
-0.016942767426371574,
0.02999155968427658,
0.03233269974589348,
-0.03322620689868927,
0.011616736650466919,
-0.008228638209402561,
0.038000982254743576,
-0.0014867319259792566,
0.05554864928126335,
0.03068429045379162,
0.027140596881508827,
-0.0596311017870903,
0.005850654095411301,
0.03804260119795799,
0.039429984986782074,
-0.03360247611999512,
-0.03519773855805397,
-0.0077821677550673485,
-0.05433184280991554,
-0.021042976528406143,
0.02468830719590187,
0.05816015601158142,
0.019100667908787727,
-0.025084683671593666,
0.05719278007745743,
0.01080877985805273,
-0.01572239212691784,
0.03678325191140175,
0.029177293181419373,
-0.004213002044707537,
-0.012238021939992905,
-0.02378753200173378,
-0.006290242541581392,
-0.03842691704630852,
0.010384202003479004,
0.006876516621559858,
-0.024018678814172745,
-0.016224125400185585,
0.01608365774154663,
-0.014750676229596138,
0.021454980596899986,
0.011023242957890034,
-0.039072029292583466,
0.016660187393426895,
0.025017891079187393,
-0.027512095868587494,
0.0075758229941129684,
0.014529368840157986,
0.05634007602930069,
0.019598936662077904,
0.014462867751717567,
-0.03256711736321449,
-0.08732912689447403,
0.01231437548995018,
0.005726609379053116,
0.002803633688017726,
0.02349586971104145,
-0.040862247347831726,
-0.044040974229574203,
-0.024077989161014557,
0.06336923688650131,
0.003911301027983427,
0.036359645426273346,
-0.007900182157754898,
-0.017722023651003838,
-0.058108385652303696,
0.009189649485051632,
0.04975414276123047,
0.0460464283823967,
-0.005190790165215731,
0.0013343245955184102,
0.00002097413562296424,
-0.022964155301451683,
0.006373019423335791,
0.02890402264893055,
0.0011770905693992972,
0.043870940804481506,
0.04373987764120102,
0.0345463752746582,
0.028314368799328804,
0.036962058395147324,
-0.05627087876200676,
-0.07785896211862564,
0.021793564781546593,
0.014283263124525547,
-0.05825778469443321,
0.03177845850586891,
-0.004893997218459845,
-0.03289300575852394,
-0.010924829170107841,
-0.004890343174338341,
0.005836639553308487,
0.028759514912962914,
-0.04009395092725754,
0.015962691977620125,
-0.0008755443850532174,
-0.030792418867349625,
0.01883695274591446,
0.026708809658885002,
0.005683165043592453,
0.005237038712948561,
0.001243378035724163,
0.05189427360892296,
-0.028246890753507614,
0.01767433062195778,
-0.02420344203710556,
0.011596431024372578,
-0.059607524424791336,
0.0041309078224003315,
0.004801285918802023,
0.016523735597729683,
0.02264716662466526,
-0.03900256007909775,
-0.030897097662091255,
0.015611596405506134,
-0.0017625987529754639,
0.014058848842978477,
0.029254797846078873,
0.003951210994273424,
-0.028042778372764587,
-0.029501095414161682,
0.024037200957536697,
-0.011627723462879658,
0.0018049855716526508,
0.007689681835472584,
0.025926874950528145,
0.041198596358299255,
-0.02936640940606594,
-0.015290993265807629,
0.024636536836624146,
-0.024982746690511703,
0.050826966762542725,
-0.004405369516462088,
0.018510600551962852,
0.025713782757520676,
-0.06428338587284088,
-0.009346695616841316,
0.014789904467761517,
-0.019903911277651787,
0.001361603382974863,
-0.05949680879712105,
0.059355881065130234,
0.026789100840687752,
0.019152935594320297,
-0.06907162070274353,
-0.03902970626950264,
0.017650963738560677,
0.015428230166435242,
-0.01662740297615528,
-0.021636296063661575,
0.018170876428484917,
-0.04856850579380989,
0.0001741722517181188,
-0.02927224338054657,
0.024559279903769493,
-0.01976311020553112,
-0.0071041397750377655,
0.004689747467637062,
0.0699298307299614,
0.03213777765631676,
0.02678714506328106,
-0.03008881025016308,
0.002711937064304948,
-0.011513990350067616,
0.021558145061135292,
-0.0205457154661417,
0.013489835895597935,
0.0032525069545954466,
0.0022872788831591606,
-0.03213083744049072,
-0.004016990307718515,
0.01828284189105034,
0.010459905490279198,
0.029722994193434715,
0.05688786879181862,
0.0414273627102375,
0.027761060744524002,
-0.013071522116661072,
0.02682705596089363,
-0.03564159572124481,
0.011867895722389221,
-0.01853369176387787,
0.002053385367617011,
0.017590662464499474,
-0.03483511880040169,
0.019595246762037277,
0.00047515088226646185,
-0.02324409782886505,
0.024137916043400764,
0.05269927158951759,
0.04637309908866882,
-0.03526981547474861,
0.011260450817644596,
-0.013793492689728737,
-0.0012222680961713195,
-0.011708580888807774,
0.03149263188242912,
0.00014293732238002121,
-0.02180153876543045,
-0.026845775544643402,
-0.0670013353228569,
-0.014581333845853806,
0.003143250709399581,
0.029192304238677025,
-0.0007007568492554128,
0.031236322596669197,
0.024357197806239128,
0.0041833003051579,
0.04119507595896721,
-0.016775019466876984,
0.0256823543459177,
0.02881477028131485,
-0.0270603708922863,
0.0013283553998917341,
-0.015347315929830074,
0.014276056550443172,
0.025092681869864464,
0.052533477544784546,
-0.040663477033376694,
0.009358789771795273,
0.04191378876566887,
0.006190536078065634,
0.047352127730846405,
-0.003366407472640276,
-0.050883159041404724,
0.03939300402998924,
-0.04404236376285553,
0.02439355105161667,
-0.013982294127345085,
-0.0032249554060399532,
0.030915219336748123,
-0.00800339225679636,
0.03590011969208717,
0.0021012250799685717,
-0.0037973474245518446,
-0.058094095438718796,
0.017075475305318832,
0.006450435146689415,
0.06132424250245094,
0.016911456361413002,
0.005932099651545286,
0.056282587349414825,
0.022043809294700623,
0.019911350682377815,
0.015177255496382713,
-0.07541009783744812,
-0.03787438943982124,
-0.0111932922154665,
-0.037155069410800934,
0.07168444246053696,
0.013224164955317974,
0.009195519611239433,
0.006862393114715815,
-0.008385296911001205,
0.031799450516700745,
0.03935697674751282,
0.07113683223724365,
-0.030908498913049698,
0.014089916832745075,
-0.02310541644692421,
-0.003474630182608962,
-0.02070540562272072,
0.012441486120223999,
0.13629837334156036,
0.06516048312187195,
0.02926386520266533,
-0.07466339319944382,
0.004182792268693447,
-0.04225694388151169,
0.01727944239974022,
-0.026831839233636856,
0.02350810170173645,
-0.0015520201995968819,
0.010054532438516617,
-0.011596307158470154,
0.05675450339913368,
-0.0032826517708599567,
-0.025614043697714806,
0.036236271262168884,
-0.07551952451467514,
-0.0036301675718277693,
-0.0006345291621983051,
0.024195654317736626,
-0.018782490864396095,
0.027970897033810616,
-0.051314566284418106,
0.0028386281337589025,
-0.009174852631986141,
0.000571871583815664,
-0.025710085406899452,
-0.03932034224271774,
-0.00790493655949831,
-0.02618679217994213,
-0.0028432554099708796,
0.0071450467221438885,
0.010487322695553303,
-0.00274550449103117,
-0.05119536817073822,
0.01564716175198555,
-0.0053940205834805965,
0.02556859888136387,
0.02724979817867279,
0.011248566210269928,
-0.006854069884866476,
-0.011192677542567253,
-0.0029815875459462404,
0.01197193656116724,
-0.04748561978340149,
-0.027188770473003387,
0.003846190171316266,
0.0521605983376503,
-0.02263130620121956,
0.025914400815963745,
0.0014148910995572805,
-0.002923776628449559,
-0.010128398425877094,
-0.02815832942724228,
-0.015334886498749256,
0.005640476010739803,
0.04621224105358124,
-0.036452554166316986,
-0.025692405179142952,
-0.014605395495891571,
0.010242654010653496,
-0.00041273870738223195,
0.01127284113317728,
0.031112851575016975,
0.018401984125375748,
-0.010212503373622894,
0.009239756502211094,
0.034641772508621216,
-0.0003008433268405497,
-0.01075554545968771,
-0.034446001052856445,
-0.03678214177489281,
-0.021580304950475693,
-0.017144344747066498,
-0.0018684804672375321,
0.022938525304198265,
0.02474517747759819,
0.02013508416712284,
0.01785399578511715,
-0.009356631897389889,
-0.03619138151407242,
-0.011279185302555561,
-0.027242232114076614,
-0.018692074343562126,
-0.01400771550834179,
0.024111991748213768,
0.01798967830836773,
0.027823863551020622,
-0.011007568798959255,
0.02519870735704899,
0.00942505244165659,
0.03447949141263962,
0.014840577729046345,
-0.037660274654626846,
-0.01193502452224493,
-0.006402322091162205,
-0.02249964326620102,
-0.009986873716115952,
-0.017297284677624702,
0.01848006248474121,
0.02717643976211548,
-0.0026484595146030188,
-0.019738122820854187,
0.038736678659915924,
-0.03973623737692833,
-0.005453036166727543,
0.04804062098264694,
-0.04061882570385933,
0.018688617274165154,
0.021989986300468445,
-0.007949446327984333,
-0.025815092027187347,
-0.042037177830934525,
-0.024312488734722137,
0.04072237014770508,
-0.0077169849537312984,
-0.0010098462225869298,
-0.045995451509952545,
0.003768153255805373,
-0.00504313362762332,
0.012862712144851685,
-0.0631115511059761,
-0.028759390115737915,
-0.04563252255320549,
0.007727963849902153,
-0.0026558702811598778,
0.017080480232834816,
0.006685793865472078,
0.03657910227775574,
-0.027603887021541595,
-0.045956358313560486,
0.01702144369482994,
-0.0005879052332602441,
-0.025068648159503937,
-0.030528105795383453,
0.028196020051836967,
-0.015316866338253021,
0.036945439875125885,
-0.005638696253299713,
-0.06723177433013916,
0.018979521468281746,
-0.054276708513498306,
-0.030712181702256203,
0.06682091951370239,
-0.013848230242729187,
0.023788724094629288,
0.05296654626727104,
-0.017857110127806664,
0.011225075460970402,
0.024349836632609367,
-0.03069903701543808,
-0.01672295853495598,
0.0247186366468668,
-0.052331674844026566,
-0.016089437529444695,
-0.00940980575978756,
0.017717717215418816,
0.006996111012995243,
-0.023339780047535896,
0.029437996447086334,
0.029015962034463882,
0.010500006377696991,
-0.008397813886404037,
-0.018440738320350647,
-0.03256914019584656,
0.03113701194524765,
0.022473298013210297,
0.001739841653034091,
0.028457455337047577,
0.02046680450439453,
-0.027987917885184288,
0.017860496416687965,
0.03872599080204964,
0.01491272822022438,
-0.07893262803554535,
0.010602817870676517,
0.02680853009223938,
0.011638895608484745,
0.04652794450521469,
-0.04567723348736763,
0.015541346743702888,
0.036947157233953476,
-0.06668300926685333,
0.062218327075242996,
-0.012804062105715275,
-0.002011061878874898,
-0.016224093735218048,
-0.0000784622025093995,
-0.039993323385715485,
0.0588601678609848,
0.04433078318834305,
0.06418196856975555,
-0.011585022322833538,
0.03160441294312477,
0.0006855511455796659,
-0.0182125773280859,
-0.05296904593706131,
0.03024192526936531,
-0.0068077691830694675,
-0.008337507024407387,
0.04124516248703003,
0.0021255039609968662,
0.0013831311371177435,
-0.006664585322141647,
0.022630726918578148,
-0.024735111743211746,
-0.011268364265561104,
0.03601408749818802,
0.02217370830476284,
0.023139329627156258,
0.029155714437365532,
-0.05074269697070122,
-0.0004264035087544471,
0.0066132741048932076,
-0.01739666424691677,
0.041902922093868256,
-0.02890513651072979,
0.021406060084700584,
-0.04098263382911682,
-0.07815280556678772,
-0.043393734842538834,
-0.03614001348614693,
-0.022778306156396866,
-0.02307012304663658,
-0.002115841954946518,
0.019977174699306488,
0.004485344979912043,
0.018008526414632797,
-0.033621665090322495,
-0.04231719300150871,
0.0035523553378880024,
0.008758128620684147,
0.019991248846054077,
-0.017683610320091248,
0.01390171516686678,
0.0055507454089820385,
-0.039251960813999176,
0.03907555714249611,
0.0031167224515229464,
-0.017817379906773567,
-0.05612744390964508,
-0.01985893025994301,
0.014514478854835033,
0.008814647793769836,
-0.013298572972416878,
-0.04911003261804581,
-0.024173444136977196,
0.050754379481077194,
0.015284272842109203,
0.026972385123372078,
-0.018103115260601044,
-0.05996700003743172,
-0.013684704899787903,
-0.06529037654399872,
0.02377055026590824,
-0.015803994610905647,
0.0270986407995224,
-0.023388870060443878,
0.018689598888158798,
0.010975319892168045,
0.032203640788793564,
0.030371669679880142,
-0.00943137239664793,
-0.002609427087008953,
0.030346179381012917,
0.01042939256876707,
0.013685342855751514,
0.0007319865981116891,
0.025021931156516075,
-0.014499766752123833,
-0.0347956046462059,
-0.04169510677456856,
-0.013411976397037506,
0.0009786931332200766,
0.019413236528635025,
0.046770159155130386,
-0.02564922720193863,
0.008474688977003098,
-0.0323309451341629,
-0.04808991774916649,
0.06818623095750809,
0.01781424693763256,
-0.041627075523138046,
0.052606768906116486,
-0.035278432071208954,
0.03518322855234146,
0.0358896404504776,
-0.005885603372007608,
-0.00409892201423645,
0.018295062705874443,
0.004395557567477226,
-0.023373030126094818,
0.020886173471808434,
0.020402906462550163,
-0.0016330756479874253,
-0.012019757181406021,
-0.041565343737602234,
0.05642436072230339,
-0.01585211232304573,
-0.02526160329580307,
0.03740734979510307,
-0.037143606692552567,
0.024586772546172142,
-0.002499089576303959,
0.03327181190252304,
0.044131215661764145,
0.002931613940745592,
0.0000308626658807043,
0.04437350854277611,
0.03561324253678322,
0.005949351005256176,
0.008587213233113289,
-0.014534113928675652,
-0.04502381011843681,
0.0020472167525440454,
-0.011671870946884155,
0.027018211781978607,
-0.055638354271650314,
0.002547712065279484,
0.01653307117521763,
-0.025375626981258392,
-0.003030964871868491,
0.0260624922811985,
-0.03607836365699768,
0.07183561474084854,
-0.01818811520934105,
0.0016614905325695872,
-0.03496457636356354,
-0.01988298073410988,
-0.015485835261642933,
-0.0004492834268603474,
0.010275215841829777,
0.052639953792095184,
-0.01276734285056591,
-0.007923168130218983,
0.005867679603397846,
-0.0035361694172024727,
0.014052544720470905,
-0.06610272824764252,
0.00364686525426805,
-0.006684531457722187,
0.001043072552420199,
-0.041363269090652466,
-0.03782811015844345,
-0.030094657093286514,
-0.009114274755120277,
0.018774718046188354,
0.027834368869662285,
0.00019376896671019495,
-0.04856106638908386,
-0.011568265035748482,
-0.04362059012055397,
0.03144971281290054,
-0.028562208637595177,
0.01874200440943241,
-0.036375146359205246,
0.04606732353568077,
-0.006176523398607969,
0.006628239061683416
] |
<p>A theoretical question which thought about instead of writing my C++ code. I know it is poorly defined however I am now intrigued as to the answer!</p>
<p>If you got into a boat in the middle of the sea before sunrise, and as the sun cam up sailed directly towards it, and continued to do so throughout the day until you were heading west in the evening at sunset, and then stopped at sun down. Repeat this for say a week/month, then look on a GPS device as to the path you have traveled, what shape would your path/footprint be?</p>
<p>Everyone I have asked has come up with a different answer, and short of buying a boat not sure how to work it out.</p>
| 10,810 |
[
0.017171194776892662,
-0.040613677352666855,
-0.011122521013021469,
0.014650916680693626,
0.054435379803180695,
0.03199649229645729,
0.02775627002120018,
-0.01115336362272501,
0.002212965628132224,
-0.016993561759591103,
-0.0034923513885587454,
0.052598580718040466,
0.04412940889596939,
-0.006306856404989958,
0.012980389408767223,
0.002912307856604457,
0.020461294800043106,
-0.016763677820563316,
-0.008534238673746586,
-0.03455816209316254,
-0.017254071310162544,
-0.007973426021635532,
0.016288094222545624,
-0.03127305582165718,
-0.04226023331284523,
0.02209695801138878,
0.03326646238565445,
-0.015261279419064522,
0.013222143985331059,
0.0556272529065609,
-0.023214180022478104,
-0.04731469973921776,
0.01136705745011568,
0.04581492394208908,
0.0040551587007939816,
0.0002760858042165637,
-0.03947678953409195,
-0.005010192282497883,
-0.07747510820627213,
0.021532010287046432,
-0.01909872144460678,
-0.014116374775767326,
-0.02745489589869976,
0.06973092257976532,
0.005389208439737558,
0.017106255516409874,
-0.010164027102291584,
0.005741311237215996,
0.06748674064874649,
-0.03812285140156746,
0.0921810194849968,
-0.01985369808971882,
0.01026652380824089,
0.0029600956477224827,
0.030137795954942703,
-0.006640165578573942,
0.07619618624448776,
0.03826066851615906,
-0.017934538424015045,
-0.009815685451030731,
-0.023218780755996704,
0.01413922943174839,
0.004234306048601866,
-0.03670588135719299,
-0.01775905303657055,
-0.017131634056568146,
-0.020297840237617493,
-0.018763277679681778,
0.049821265041828156,
0.00469627883285284,
-0.014764862135052681,
0.010294429957866669,
0.03413768112659454,
0.0026069716550409794,
0.03094632364809513,
-0.022146722301840782,
0.028657931834459305,
0.06156305596232414,
0.0354480966925621,
-0.0010834907880052924,
-0.027127580717206,
0.012615765444934368,
0.029270078986883163,
0.048059843480587006,
0.04463052377104759,
0.01284088660031557,
0.0015870356000959873,
-0.028861306607723236,
-0.01298485603183508,
0.054527703672647476,
0.002898221369832754,
0.008611349388957024,
0.007476010825484991,
-0.017072224989533424,
0.008038638159632683,
0.04512794688344002,
-0.0034714918583631516,
0.0018753450131043792,
0.01713459938764572,
-0.012176549062132835,
-0.000344125583069399,
-0.04672473669052124,
0.007402168586850166,
0.03853408247232437,
0.007994310930371284,
0.05322990566492081,
-0.03122377023100853,
-0.017953870818018913,
-0.00820950511842966,
0.014540047384798527,
-0.030874386429786682,
-0.01666165702044964,
0.04193364828824997,
-0.007665187586098909,
0.040542423725128174,
-0.032378189265728,
0.0041275774128735065,
-0.02135232649743557,
0.013426566496491432,
0.021732138469815254,
0.052794504910707474,
-0.01942063495516777,
0.038314782083034515,
-0.05836156755685806,
-0.05941326916217804,
0.03331431746482849,
0.011259791441261768,
-0.03258366137742996,
0.014327198266983032,
0.038934119045734406,
0.008936534635722637,
-0.02776658721268177,
0.024696188047528267,
-0.032581835985183716,
0.042365916073322296,
-0.02841290459036827,
-0.09171728789806366,
-0.0478973314166069,
0.054435648024082184,
0.028783485293388367,
0.00017172731168102473,
-0.05431170016527176,
0.015435945242643356,
-0.0014375216560438275,
0.04762842506170273,
-0.005375451873987913,
0.020984234288334846,
0.04343084618449211,
0.021013032644987106,
-0.03359367325901985,
-0.028157977387309074,
-0.006776142865419388,
-0.022363727912306786,
-0.042930833995342255,
0.03510273993015289,
-0.061208534985780716,
0.008746237494051456,
0.03496643900871277,
0.008217580616474152,
-0.05368028208613396,
0.10240869969129562,
-0.004447946324944496,
0.0029937259387224913,
0.0062079355120658875,
-0.025282906368374825,
-0.046833399683237076,
0.08915308117866516,
0.030656075105071068,
-0.024271178990602493,
0.004030423238873482,
0.038722943514585495,
-0.01231514010578394,
0.02417483925819397,
0.02611367590725422,
0.09448855370283127,
-0.031385887414216995,
-0.00022342380543705076,
-0.002221830654889345,
-0.009947176091372967,
0.008353563956916332,
-0.03785677254199982,
-0.07917004078626633,
-0.0059358482249081135,
-0.014494865201413631,
0.04165564849972725,
0.07068128138780594,
-0.03295612335205078,
-0.005895028356462717,
0.0048171235248446465,
-0.04121183976531029,
0.005829292349517345,
-0.015908563509583473,
0.014050524681806564,
0.010718080215156078,
0.004109743516892195,
-0.0006282165995799005,
-0.011664135381579399,
0.03051457740366459,
-0.034295253455638885,
-0.04367468133568764,
-0.030485616996884346,
0.019273243844509125,
0.011953966692090034,
-0.019817272201180458,
-0.01371503621339798,
0.06780827045440674,
0.016252825036644936,
0.0016787105705589056,
-0.0036860303953289986,
-0.024615420028567314,
-0.014555754140019417,
-0.025819072499871254,
-0.035626232624053955,
0.028110219165682793,
0.005195694509893656,
0.00120033067651093,
-0.007589936722069979,
0.02351084165275097,
0.03456856682896614,
0.025880686938762665,
-0.023565351963043213,
0.05025302991271019,
0.03475762531161308,
-0.009548778645694256,
0.02004220522940159,
0.0027984404005110264,
-0.01927945390343666,
-0.013690627180039883,
0.007809862028807402,
-0.03614068776369095,
0.01936955191195011,
0.009632852859795094,
0.001493213465437293,
-0.01753121055662632,
0.0011467259610071778,
0.0009588914108462632,
0.03261704370379448,
0.06412859261035919,
0.015347006730735302,
0.05560307577252388,
0.03833514451980591,
0.026891978457570076,
0.004084487911313772,
0.03799271956086159,
0.011804187670350075,
0.016027098521590233,
0.003584712976589799,
0.019092492759227753,
-0.029125481843948364,
-0.006644560489803553,
-0.06666355580091476,
0.07519090175628662,
0.019528226926922798,
0.011180339381098747,
-0.042155735194683075,
0.017418282106518745,
0.061773113906383514,
-0.037335675209760666,
0.007346344646066427,
0.007989843375980854,
-0.007746483664959669,
-0.04599219560623169,
-0.03631489723920822,
-0.0056480285711586475,
-0.004307587165385485,
0.07355903834104538,
0.011116747744381428,
-0.008401721715927124,
0.0343572273850441,
-0.010449405759572983,
0.06390297412872314,
-0.05049644410610199,
-0.035853538662195206,
-0.0010581552051007748,
0.005854157265275717,
0.058568648993968964,
0.004403588827699423,
0.008518046699464321,
0.009534163400530815,
-0.03743511810898781,
-0.020596420392394066,
-0.01661473512649536,
-0.0061396765522658825,
0.014493400231003761,
-0.060645315796136856,
-0.00288972700946033,
0.0034030030947178602,
-0.020269937813282013,
0.045302003622055054,
-0.014573868364095688,
0.007838328368961811,
0.03378191962838173,
-0.022860931232571602,
-0.03836077079176903,
-0.024996871128678322,
-0.04556557908654213,
-0.019134048372507095,
-0.020462460815906525,
-0.019318602979183197,
0.04713016748428345,
0.02121296152472496,
-0.07582058757543564,
0.042085908353328705,
-0.03131583333015442,
-0.03235097974538803,
-0.0034043691121041775,
-0.011332872323691845,
0.007010444533079863,
-0.03007381223142147,
0.0375179685652256,
0.01455412246286869,
-0.03303674980998039,
-0.0072365109808743,
-0.05713814124464989,
-0.05826365575194359,
0.03757832199335098,
-0.01763770543038845,
0.011227450333535671,
0.010884784162044525,
-0.013839749619364738,
0.08869346231222153,
0.015333827584981918,
-0.01581084355711937,
-0.016078541055321693,
-0.0027726732660084963,
-0.010615679435431957,
-0.01479589007794857,
-0.01623896323144436,
0.007799705024808645,
-0.011514539830386639,
0.002735329093411565,
-0.006473470013588667,
0.018259912729263306,
0.028862744569778442,
0.002392445458099246,
-0.0003108126111328602,
0.03261803835630417,
-0.009668789803981781,
0.0357387401163578,
0.023785848170518875,
0.027841869741678238,
-0.030471784994006157,
0.0005069759208709002,
-0.020940836519002914,
0.012456304393708706,
0.041339658200740814,
-0.04794120788574219,
0.04095608741044998,
0.0014891796745359898,
0.021956300362944603,
-0.010213153436779976,
0.006784375756978989,
-0.01971820741891861,
-0.014710351824760437,
-0.00706116808578372,
0.011222404427826405,
0.06954105198383331,
-0.015500698238611221,
-0.002789934864267707,
0.02798481285572052,
0.04994714632630348,
-0.009742261841893196,
-0.029216036200523376,
-0.03471129387617111,
0.04111631587147713,
-0.03640981391072273,
0.028185255825519562,
-0.051069632172584534,
0.02489905059337616,
0.019712140783667564,
0.022803185507655144,
0.015625108033418655,
-0.05800393223762512,
-0.03515336290001869,
-0.07575435936450958,
-0.022654682397842407,
0.005678866524249315,
0.05030154809355736,
-0.018824467435479164,
0.009364352561533451,
0.0022983287926763296,
-0.02912922576069832,
0.018530255183577538,
0.012668726965785027,
-0.07847148925065994,
-0.007574877701699734,
-0.0378519669175148,
-0.03525417298078537,
0.009571533650159836,
-0.013999918475747108,
0.009077616967260838,
-0.01200322899967432,
-0.008135209791362286,
0.04447922483086586,
-0.023022232577204704,
-0.03482994809746742,
0.03509536013007164,
0.0013865374494343996,
-0.0036294797901064157,
-0.020580120384693146,
0.01318198349326849,
0.03506205230951309,
-0.010074361227452755,
0.06944993883371353,
0.058054011315107346,
-0.020501086488366127,
-0.028435131534934044,
-0.033877719193696976,
0.0190395750105381,
-0.004896685015410185,
0.0034449684899300337,
0.03603663668036461,
0.024928368628025055,
-0.022273298352956772,
-0.006256249267607927,
-0.031563472002744675,
-0.005626627244055271,
-0.02831675484776497,
-0.0062738931737840176,
-0.04779301583766937,
-0.032191500067710876,
-0.00028213916812092066,
0.05639101192355156,
-0.012805149890482426,
0.02977805770933628,
0.029257629066705704,
0.056501831859350204,
-0.006477584596723318,
-0.023807363584637642,
0.04531360790133476,
0.0577276349067688,
-0.009602653793990612,
-0.04048033431172371,
-0.03548093140125275,
0.009063887409865856,
0.010885580442845821,
0.0020424833055585623,
-0.026608897373080254,
-0.04860702529549599,
-0.0044873906299471855,
-0.023792043328285217,
0.004082310479134321,
-0.023288728669285774,
-0.0025686915032565594,
0.0415671244263649,
-0.01959722489118576,
0.0597338043153286,
-0.02404923550784588,
-0.004604771733283997,
0.01729298196732998,
0.018708109855651855,
0.02113584615290165,
0.013133974745869637,
-0.01598316803574562,
-0.060206152498722076,
-0.004876314662396908,
0.02128591202199459,
0.02722533792257309,
-0.01348112616688013,
-0.0035745124332606792,
-0.05886409431695938,
-0.031579773873090744,
0.053658924996852875,
-0.006029771640896797,
0.016826944425702095,
-0.011529654264450073,
-0.018655873835086823,
0.0019011945696547627,
-0.02739638276398182,
-0.042071737349033356,
0.025339968502521515,
-0.020555049180984497,
0.003768349764868617,
0.00983492936939001,
0.012164234183728695,
-0.004895006772130728,
0.07163446396589279,
0.0304566640406847,
0.01829027384519577,
-0.022753503173589706,
0.006733460817486048,
-0.0267390888184309,
0.03380942717194557,
0.012628414668142796,
-0.06481467932462692,
0.0006543502095155418,
0.0683116540312767,
-0.022403448820114136,
0.04001835733652115,
0.0004930498544126749,
-0.06547632813453674,
0.04033093899488449,
0.009494210593402386,
-0.021372005343437195,
0.0009988162200897932,
-0.02017517015337944,
0.027099447324872017,
0.021070700138807297,
-0.030406968668103218,
0.02903553657233715,
0.0002963416918646544,
-0.021190067753195763,
-0.008806235156953335,
-0.005889719817787409,
-0.0009788759052753448,
-0.019512517377734184,
-0.01968640275299549,
-0.011346105486154556,
-0.03786030784249306,
-0.03072185628116131,
0.021457377821207047,
0.00952889584004879,
-0.0032335056457668543,
-0.021905124187469482,
-0.04495774582028389,
-0.05617847293615341,
0.03076859377324581,
-0.0068953800946474075,
-0.0067077698186039925,
-0.019824769347906113,
0.023598842322826385,
0.02009555511176586,
-0.04370782896876335,
0.0010906666284427047,
-0.018893271684646606,
0.02006109245121479,
-0.01653911918401718,
-0.0016497161705046892,
-0.015929127112030983,
0.003177107311785221,
0.010760086588561535,
0.006293199025094509,
-0.022051597014069557,
0.04120096564292908,
-0.009323395788669586,
-0.022604256868362427,
0.032811086624860764,
-0.08520278334617615,
-0.03787393122911453,
0.03159279376268387,
0.0032057794742286205,
0.006924727000296116,
-0.03144653141498566,
0.009704533033072948,
0.01707547716796398,
0.016183901578187943,
-0.07851626724004745,
-0.05200762674212456,
0.04483117535710335,
0.0005052496562711895,
0.0003403679293114692,
0.0028176461346447468,
-0.00513280276209116,
-0.02863210439682007,
-0.03460625931620598,
-0.03078523837029934,
0.0017153106164187193,
-0.026425903663039207,
-0.03260358050465584,
0.008904575370252132,
0.014690441079437733,
0.07653744518756866,
-0.020804589614272118,
0.015327905304729939,
0.04007459059357643,
-0.005502520594745874,
-0.012977627106010914,
-0.024186480790376663,
0.05670465901494026,
-0.019227685406804085,
-0.025575239211320877,
-0.020863842219114304,
-0.0074923899956047535,
0.06308525055646896,
-0.02408287674188614,
0.003383130766451359,
-0.0005992923979647458,
-0.00517734419554472,
0.026904117316007614,
0.0024563975166529417,
0.023168405517935753,
0.012664338573813438,
-0.02492973394691944,
0.003959387540817261,
-0.01214310061186552,
0.028901124373078346,
-0.017562130466103554,
0.041206326335668564,
0.003749547526240349,
-0.013095233589410782,
-0.002501759212464094,
0.01606711745262146,
-0.01758129522204399,
-0.01778433285653591,
0.04247252270579338,
0.010352514684200287,
0.02194005623459816,
0.0043704514391720295,
-0.0037170452997088432,
0.0027783517725765705,
0.00960716512054205,
-0.02804172970354557,
-0.008498790673911572,
-0.02077876776456833,
0.004145171493291855,
0.07059980183839798,
-0.01696263812482357,
0.041988953948020935,
0.005616540554910898,
0.0318155512213707,
0.01822371780872345,
0.032435256987810135,
-0.013539898209273815,
-0.009459533728659153,
-0.018764739856123924,
0.05305851995944977,
-0.0456232875585556,
-0.029765093699097633,
0.016114654019474983,
0.04310541972517967,
-0.018700774759054184,
0.022256335243582726,
-0.004182691220194101,
0.012728855945169926,
0.046781912446022034,
0.026268286630511284,
-0.03060242533683777,
0.004875965416431427,
-0.03497474640607834,
0.016600772738456726,
0.007907693274319172,
0.012872560881078243,
0.06986375898122787,
0.0127412099391222,
0.008275944739580154,
-0.02340216189622879,
-0.008799707517027855,
-0.010206545703113079,
-0.0008951025083661079,
0.011410931125283241,
0.020562980324029922,
-0.006019722204655409,
0.025288129225373268,
0.04241763427853584,
-0.03851228207349777,
-0.013693084008991718,
-0.02590157464146614,
-0.061372432857751846,
-0.054601218551397324,
-0.036571986973285675,
-0.052818864583969116,
0.06418365985155106,
0.019113028421998024,
0.002057311125099659,
0.0023524833377450705,
-0.0373532734811306,
-0.030601592734456062,
0.03730540722608566,
0.04355577751994133,
-0.0006968866218812764,
0.09460284560918808,
-0.006936936639249325,
0.0346929095685482,
-0.057263072580099106,
-0.00970127061009407,
0.11024612188339233,
0.050244685262441635,
0.021950945258140564,
-0.06427372246980667,
0.023028435185551643,
-0.038065116852521896,
0.007415375672280788,
-0.0199617650359869,
0.07369931787252426,
0.04930020123720169,
0.0050430092960596085,
0.038023050874471664,
0.01469972264021635,
-0.02394571527838707,
0.019491834565997124,
0.019710440188646317,
-0.03912244737148285,
-0.04665714129805565,
0.01810065284371376,
-0.00384001387283206,
-0.016876036301255226,
0.011850242502987385,
-0.05794776603579521,
0.042635153979063034,
-0.042331814765930176,
-0.001515262178145349,
0.00935448333621025,
-0.030340641736984253,
0.03486064821481705,
0.010919689200818539,
-0.05625392124056816,
-0.00856710597872734,
-0.013051883317530155,
-0.004286007024347782,
-0.05047418549656868,
0.0010626539587974548,
0.02595599927008152,
-0.0007732947706244886,
0.0054938611574471,
0.034706491976976395,
0.05228438600897789,
-0.009171740151941776,
-0.01657417230308056,
-0.000450330349849537,
-0.009017816744744778,
-0.04164830595254898,
-0.0238731000572443,
0.04568611457943916,
-0.018514053896069527,
-0.01494694221764803,
-0.016941454261541367,
0.036171428859233856,
0.016825838014483452,
-0.07548375427722931,
0.004176733084022999,
0.03504636138677597,
0.05929461866617203,
0.02560463547706604,
-0.02577662654221058,
0.007580692879855633,
0.02555071748793125,
0.01838958077132702,
0.004718337673693895,
0.019222542643547058,
-0.023288508877158165,
-0.02611854113638401,
0.002261859131976962,
0.060889918357133865,
0.008463759906589985,
-0.030493037775158882,
-0.016731930896639824,
-0.008342702873051167,
-0.0358271524310112,
0.009324708953499794,
0.0005395729094743729,
0.0019999456126242876,
-0.027335932478308678,
-0.010827934369444847,
-0.0056542204692959785,
-0.007034492678940296,
-0.0011501654516905546,
0.013066653162240982,
-0.03422586992383003,
-0.02372739464044571,
0.02014344185590744,
-0.013413245789706707,
0.03765453025698662,
0.05139604210853577,
-0.019906217232346535,
0.0023056131321936846,
-0.010336562059819698,
0.05019153654575348,
0.010974176228046417,
-0.041568733751773834,
-0.008558670058846474,
0.039008211344480515,
-0.011545389890670776,
0.030078161507844925,
-0.04064737260341644,
0.04565362632274628,
-0.011599480174481869,
0.014913207851350307,
-0.02443237602710724,
0.03073575533926487,
-0.015889698639512062,
0.0052098617888987064,
0.027414526790380478,
-0.03967899829149246,
-0.050462719053030014,
0.006467590108513832,
-0.014885764569044113,
-0.06449677050113678,
-0.015468837693333626,
-0.01808956451714039,
0.0048578581772744656,
-0.02915041707456112,
-0.007126240525394678,
-0.005099303554743528,
0.044820304960012436,
-0.04942915216088295,
0.023025093600153923,
-0.039745911955833435,
0.01767727918922901,
-0.0607098750770092,
0.0215140487998724,
0.009690816514194012,
-0.0030062103178352118,
0.010870572179555893,
0.04063813388347626,
-0.05290071293711662,
-0.018295735120773315,
0.026692533865571022,
-0.01668599247932434,
0.0014737483579665422,
0.011981353163719177,
0.005568919237703085,
-0.02994622476398945,
0.030733538791537285,
-0.03525479882955551,
-0.04734145849943161,
0.044007644057273865,
-0.028665410354733467,
-0.030881604179739952,
0.0441243015229702,
-0.04577339068055153,
0.055629462003707886,
-0.007247782777994871,
-0.0035331998951733112,
0.027402671054005623,
0.09056679904460907,
0.02832881733775139,
0.0069396402686834335,
-0.007692350540310144,
0.0049553015269339085,
-0.009128378704190254,
0.012734192423522472,
0.026006460189819336,
-0.011338782496750355,
-0.03237306699156761,
0.001792824943549931,
0.0011578197591006756,
-0.011271479539573193,
0.018482185900211334,
-0.023067893460392952,
-0.015504577197134495,
-0.03815468028187752,
-0.016857972368597984,
-0.04488225653767586,
0.01703624054789543,
0.04386589676141739,
-0.043388716876506805,
0.029141904786229134,
0.01457386463880539,
-0.005040682386606932,
-0.024791626259684563,
-0.0007376699359156191,
0.023462427780032158,
-0.00411132862791419,
0.03720206767320633,
-0.04624433442950249,
-0.010212166234850883,
0.03960734233260155,
-0.1036655455827713,
-0.010681548155844212,
0.008538145571947098,
0.019036592915654182,
-0.049722425639629364,
0.0007679426344111562,
-0.033606696873903275,
0.028862377628684044,
0.0534428171813488,
-0.00989336334168911,
0.012670189142227173,
0.05144534632563591,
0.0006371435010805726,
-0.07567927986383438,
0.023076128214597702,
0.018396571278572083,
-0.018729956820607185,
0.02245057187974453,
0.03284446895122528,
-0.03349331021308899,
0.0050239888951182365,
0.009600046090781689,
-0.05643823370337486,
0.05325150862336159,
-0.039259761571884155,
0.015266118571162224,
0.044103752821683884,
0.009962831623852253,
0.016992447897791862,
0.007260623387992382,
-0.018578343093395233,
0.010117366909980774,
0.021952558308839798,
0.014406077563762665,
0.011762822978198528,
-0.004059473983943462,
-0.019597213715314865,
-0.033946458250284195,
-0.04307748004794121,
0.05628465116024017,
0.00612910371273756,
-0.013133994303643703,
-0.01645510084927082,
-0.0004110143636353314,
0.0002949951740447432,
-0.028009269386529922,
-0.04271518066525459,
-0.054227009415626526,
0.017568746581673622,
0.016196511685848236,
0.0005433754995465279,
-0.028509197756648064,
-0.026772229000926018,
-0.007026562932878733,
-0.04141411557793617,
0.03795497119426727,
0.0011274691205471754,
-0.010269866324961185,
-0.03421754390001297,
-0.01015998050570488,
-0.025365864858031273,
-0.00855620950460434,
0.02392764762043953,
-0.009828273206949234,
-0.0140642449259758,
0.044233132153749466,
0.03586914762854576,
0.03135542944073677,
0.0163510013371706,
-0.006700325291603804,
-0.021053360775113106,
-0.05133636295795441,
0.07619208097457886,
0.003464839421212673,
0.001171944779343903,
-0.05677392706274986,
-0.016546418890357018,
0.0016796475974842906,
0.012690645642578602,
0.01678617112338543,
-0.019921615719795227,
-0.01929435320198536,
-0.00668792799115181,
-0.005239436868578196,
-0.021177375689148903,
-0.015497206710278988,
0.006208913400769234,
-0.029500825330615044,
-0.06081833317875862,
-0.0007530044531449676,
-0.03369384631514549,
-0.03464183583855629,
0.0056728459894657135,
0.03487740457057953,
0.02264343574643135,
0.015020942315459251,
0.0029851289000362158,
0.0035977682564407587,
0.033295802772045135,
0.020584825426340103,
0.016149267554283142,
0.059317171573638916,
0.0228272695094347,
-0.008567496202886105,
0.04862827807664871,
-0.05327111482620239,
-0.033681292086839676,
0.057469017803668976,
-0.028465235605835915,
-0.0013287134934216738,
0.0021702107042074203,
-0.009066462516784668,
0.050834935158491135,
-0.04042082279920578,
-0.040187735110521317,
0.0077188340947031975,
0.0016277212416753173,
-0.014157382771372795,
0.04395722970366478,
0.009445005096495152,
0.01466743741184473,
-0.027828184887766838,
0.0055742948316037655,
0.04274442046880722,
0.014964441768825054,
0.027984105050563812,
0.015536212362349033,
0.02989572286605835,
-0.0037665357813239098,
0.028856342658400536,
-0.014750356785953045,
0.019216151908040047,
0.07933085411787033,
-0.006766481325030327,
0.04656865820288658,
-0.006740081589668989,
-0.0014307672390714288,
0.023596180602908134,
-0.0034003849141299725,
-0.01163566205650568,
0.003658605506643653,
-0.02337656170129776,
0.03510616347193718,
-0.03031308576464653,
-0.000025425793864997104,
0.0018345260759815574,
0.004338258411735296,
-0.02511017397046089,
0.03293892741203308,
0.009838342666625977,
0.021813837811350822,
-0.016908900812268257,
-0.02112872153520584,
0.016748473048210144,
0.017026105895638466,
0.023907456547021866,
0.007239074446260929,
0.05061928555369377,
-0.011277284473180771,
-0.013784172013401985,
-0.02413369156420231,
0.002146479208022356,
-0.030005548149347305,
-0.0037453467957675457,
0.009135457687079906,
0.07241499423980713,
-0.015594486147165298,
0.020151017233729362,
-0.02192949689924717,
0.008750027976930141,
0.04716787487268448,
-0.07912517338991165,
-0.03616444393992424,
-0.03303643316030502,
0.06752176582813263,
-0.020503250882029533,
-0.04979958385229111
] |
<p>Norton's dome is the curve $$h(r) = -\frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$. </p>
<p><img src="http://i.stack.imgur.com/t7JI7.gif" alt=" "></p>
<p><em>Via <a href="http://www.pitt.edu/~jdnorton/Goodies/Dome/index.html">Norton's web.</a></em></p>
<p>If we put a point mass on top of the dome and let it slide down from the force of gravity (assume no friction, mass won't slide off dome), then we will get the equation of motion $$\frac{d^2r}{dt^2} ~=~ r^{1/2}$$ (Not just me, lots of sources give this answer).</p>
<p>But this equation of motion doesn't make sense. Because as $r$ becomes large, the tangential force is also becoming large. The tangential force should always be less than or equal to the drive force from gravity. What am I seeing wrong? </p>
| 10,811 |
[
-0.022431056946516037,
-0.02242218144237995,
-0.009205983951687813,
-0.023114871233701706,
0.022267261520028114,
-0.005179327912628651,
-0.031365495175123215,
-0.007566181011497974,
-0.0072702681645751,
-0.04746784642338753,
-0.009183350950479507,
0.02780497819185257,
0.05404873937368393,
0.043053753674030304,
0.02625870145857334,
-0.013324005529284477,
0.00043007946806028485,
-0.013664564117789268,
0.022025151178240776,
-0.07479990273714066,
-0.008773663081228733,
0.013211105950176716,
0.0008061886765062809,
-0.019784890115261078,
0.009089566767215729,
0.03194418177008629,
0.04731210693717003,
-0.037935420870780945,
-0.038680411875247955,
0.04670819640159607,
-0.0145023288205266,
-0.00422099232673645,
-0.007425702176988125,
-0.0034349795896559954,
0.05656712129712105,
0.012340540066361427,
-0.004973921924829483,
-0.015301666222512722,
0.023148182779550552,
0.028741983696818352,
-0.022509504109621048,
-0.004256338346749544,
-0.02857389859855175,
0.04888292774558067,
-0.023199385032057762,
0.004713702015578747,
0.04216531664133072,
-0.006507911719381809,
0.05717506259679794,
-0.058700453490018845,
0.05398596450686455,
0.021820014342665672,
0.009036239236593246,
0.021151216700673103,
-0.029438484460115433,
-0.016915587708353996,
0.048673875629901886,
0.05278410762548447,
-0.014161341823637486,
-0.032672420144081116,
-0.0046945009380578995,
-0.03384790197014809,
-0.056127648800611496,
0.006873719394207001,
0.030015017837285995,
0.023479020223021507,
-0.021366668865084648,
0.010143463499844074,
0.016789639368653297,
-0.023646891117095947,
0.041594378650188446,
-0.0011891532922163606,
0.012267489917576313,
-0.025957444682717323,
0.02161996066570282,
-0.010655888356268406,
0.029042424634099007,
0.03425142168998718,
0.024293025955557823,
0.026548132300376892,
-0.0003501292667351663,
0.011189624667167664,
0.05577622726559639,
0.04624335467815399,
-0.008007420226931572,
0.03639138117432594,
0.05767666548490524,
0.011310306377708912,
0.01792566291987896,
0.027772044762969017,
-0.01304728351533413,
0.01638706773519516,
0.0178958959877491,
0.0020535059738904238,
0.01495130080729723,
0.03702113404870033,
-0.009773909114301205,
0.05258052051067352,
0.019358331337571144,
-0.010024504736065865,
-0.02594883367419243,
-0.047562193125486374,
-0.0045263152569532394,
0.061617739498615265,
0.02391817420721054,
-0.0013279459672048688,
-0.012316751293838024,
0.012495051138103008,
-0.001541202887892723,
-0.007102834060788155,
-0.04581150412559509,
0.01359116192907095,
0.005253146402537823,
-0.04008873552083969,
-0.005295875947922468,
-0.01651904173195362,
0.013897539116442204,
-0.01649882085621357,
0.011806526221334934,
-0.007778661325573921,
0.02888949029147625,
-0.03818580135703087,
0.04471411183476448,
-0.07550317794084549,
-0.056734710931777954,
0.044116709381341934,
0.0557292215526104,
-0.031531721353530884,
-0.019063834100961685,
-0.00971170049160719,
0.022266477346420288,
-0.010240050964057446,
-0.00045395438792183995,
0.027497366070747375,
0.029497725889086723,
-0.015216581523418427,
-0.08989042788743973,
-0.047802068293094635,
0.04131545126438141,
0.04917830228805542,
0.018490204587578773,
-0.06565044820308685,
0.0010733649833127856,
0.02761102095246315,
0.05945061147212982,
0.0069374400191009045,
-0.01145127322524786,
0.01412627287209034,
0.01753954216837883,
-0.012307386845350266,
0.00014543961151503026,
0.017030004411935806,
0.03059510327875614,
-0.062189359217882156,
-0.05346706137061119,
-0.09443700313568115,
0.040789783000946045,
-0.004803696181625128,
0.02925276942551136,
-0.02901502698659897,
0.05232532322406769,
-0.017274029552936554,
0.0006970363319851458,
-0.015232942998409271,
-0.017457878217101097,
-0.0037390533834695816,
0.0640396997332573,
0.012575255706906319,
-0.006393122021108866,
0.061188701540231705,
0.06661353260278702,
0.06006292998790741,
0.00965351052582264,
-0.0009333040798082948,
0.0508926697075367,
-0.07104991376399994,
0.03563104569911957,
-0.0387834832072258,
-0.01175633817911148,
-0.004994555842131376,
-0.051934946328401566,
-0.027117714285850525,
0.009315752424299717,
0.02183072455227375,
0.04555125534534454,
0.03496255353093147,
-0.014348003081977367,
0.00939815305173397,
0.018549324944615364,
-0.015953173860907555,
-0.007649442180991173,
-0.06414615362882614,
0.02563204988837242,
-0.01185193844139576,
-0.017096325755119324,
-0.014286903664469719,
0.009662817232310772,
0.00849129818379879,
-0.008556182496249676,
0.003938071429729462,
0.005484581924974918,
0.02601289376616478,
-0.023368507623672485,
-0.0025948425754904747,
0.011881029233336449,
0.06893586367368698,
0.06643711030483246,
0.02263052947819233,
-0.018999777734279633,
-0.05588351935148239,
-0.003159735817462206,
-0.0066713932901620865,
0.019159860908985138,
0.00793327298015356,
-0.022568276152014732,
0.03186660632491112,
0.013077239505946636,
0.004915590863674879,
0.01228136196732521,
0.0009437049739062786,
-0.06284783035516739,
0.07558860629796982,
0.0629957839846611,
0.015493059530854225,
0.03490779548883438,
0.0267754178494215,
0.006425285711884499,
0.022900262847542763,
0.005314999725669622,
-0.016969118267297745,
-0.03626224398612976,
0.03492594137787819,
0.028433239087462425,
0.00012502670870162547,
-0.01558019407093525,
0.034683845937252045,
0.03233593329787254,
0.01738733798265457,
-0.011008495464920998,
-0.025126472115516663,
0.03187728673219681,
-0.038889773190021515,
0.022625122219324112,
0.008870583027601242,
0.0055840155109763145,
0.006297580897808075,
-0.014599149115383625,
0.0167843084782362,
0.01749207265675068,
-0.03644130751490593,
-0.01640382409095764,
0.039086151868104935,
0.003640423994511366,
0.011903747916221619,
0.01882067508995533,
-0.008319877088069916,
0.06427985429763794,
-0.04344605654478073,
0.015029548667371273,
0.04539545625448227,
0.019678466022014618,
0.030053865164518356,
-0.062481630593538284,
-0.011671614833176136,
0.013535404577851295,
0.009247706271708012,
-0.008732003159821033,
-0.017828885465860367,
0.03133850172162056,
-0.05420789122581482,
0.010182434692978859,
-0.02292463183403015,
-0.025494733825325966,
-0.05207239091396332,
-0.015403397381305695,
0.010154510848224163,
0.03694809228181839,
-0.007061641663312912,
-0.013381004333496094,
-0.007969247177243233,
-0.02057999186217785,
-0.033212810754776,
-0.00858173705637455,
0.005839717574417591,
-0.03714795410633087,
0.027536513283848763,
-0.01898076757788658,
0.011808710172772408,
0.04799447953701019,
0.0069924695417284966,
-0.02103692665696144,
0.014239132404327393,
-0.013932894915342331,
-0.06674374639987946,
-0.021289821714162827,
-0.07171630859375,
-0.01296307984739542,
-0.03034895285964012,
-0.018880805000662804,
0.06702597439289093,
-0.006571502890437841,
-0.0008247005171142519,
0.03852464258670807,
-0.05434368550777435,
-0.026738660410046577,
-0.012375363148748875,
0.013893892988562584,
0.001027965685352683,
-0.009384808130562305,
0.028335120528936386,
0.010607680305838585,
-0.009561716578900814,
-0.01256350614130497,
-0.033471621572971344,
-0.03534264862537384,
-0.00689267972484231,
-0.030160021036863327,
0.05983847752213478,
-0.005188502371311188,
-0.03436906635761261,
0.10661644488573074,
0.026360640302300453,
0.007297977339476347,
-0.022714244201779366,
0.018141767010092735,
-0.014311972074210644,
-0.03771218657493591,
-0.008791590109467506,
0.021832002326846123,
0.008745436556637287,
-0.019149407744407654,
-0.01121304091066122,
0.007838677614927292,
0.00807962380349636,
0.010689572431147099,
0.02025509625673294,
0.0009379576076753438,
0.011363244615495205,
-0.029651358723640442,
0.043446023017168045,
0.03462706506252289,
0.003927180077880621,
-0.017791619524359703,
-0.028567515313625336,
0.04892658814787865,
-0.00464168656617403,
-0.06013605371117592,
0.0038249341305345297,
-0.010875092819333076,
0.011465504765510559,
-0.008458912372589111,
-0.01945634000003338,
-0.009271523915231228,
0.029300903901457787,
-0.017325138673186302,
0.05714638903737068,
0.07403265684843063,
-0.010050573386251926,
-0.02083665318787098,
0.031061798334121704,
0.011157049797475338,
-0.01687745749950409,
-0.0005634811823256314,
-0.020321302115917206,
-0.03812157362699509,
0.029822610318660736,
0.037203576415777206,
-0.0018107563955709338,
0.04266374930739403,
0.00013890450645703822,
0.035594142973423004,
0.013241920620203018,
-0.02827266976237297,
0.0021778768859803677,
-0.04556012898683548,
0.007855073548853397,
-0.02959405817091465,
0.02240327186882496,
0.018221119418740273,
0.023412441834807396,
0.03338905796408653,
0.004083463456481695,
0.04679960012435913,
0.0033908465411514044,
-0.08971937745809555,
0.0064138793386518955,
-0.05238046124577522,
-0.013388336636126041,
-0.0032189476769417524,
-0.0022404780611395836,
-0.01417484600096941,
-0.03177136555314064,
-0.003601607633754611,
-0.004620589781552553,
0.005556622054427862,
-0.055360712110996246,
-0.006296271458268166,
-0.016811486333608627,
-0.030443696305155754,
-0.002010637428611517,
0.02505055069923401,
0.022866591811180115,
-0.02883818931877613,
0.031077463179826736,
0.058105822652578354,
-0.004527551122009754,
0.008687733672559261,
-0.006470701657235622,
-0.005800461396574974,
-0.006679245736449957,
0.020737433806061745,
-0.016564471647143364,
-0.0024732656311243773,
0.009209168143570423,
-0.011577186174690723,
-0.014949611388146877,
0.03579150140285492,
0.03324500098824501,
-0.005217413417994976,
-0.026123059913516045,
-0.015056997537612915,
-0.018597949296236038,
0.006495383568108082,
0.02839609980583191,
-0.013782982714474201,
0.026245402172207832,
0.020622193813323975,
-0.023732688277959824,
0.03905710577964783,
0.035258930176496506,
0.027307962998747826,
0.010195579379796982,
-0.02228313870728016,
-0.04141354188323021,
-0.02280915528535843,
-0.041380513459444046,
-0.001997127430513501,
-0.029231902211904526,
-0.001173699158243835,
-0.04737251624464989,
-0.015598206780850887,
0.018251046538352966,
0.008189062587916851,
0.029551832005381584,
-0.009320405311882496,
-0.013414156623184681,
0.019284801557660103,
-0.015936098992824554,
-0.002006001304835081,
0.004215165041387081,
0.03671518340706825,
0.08041200041770935,
-0.0009172993595711887,
0.015824733301997185,
-0.0836070254445076,
-0.041404273360967636,
0.033593639731407166,
0.043203793466091156,
-0.030032342299818993,
-0.0036234960425645113,
-0.08387565612792969,
-0.035620562732219696,
0.04568379744887352,
-0.025240080431103706,
0.020063763484358788,
-0.00588701106607914,
0.043754853308200836,
0.0049883960746228695,
-0.038087356835603714,
-0.04215848445892334,
-0.017452113330364227,
-0.030224258080124855,
0.014280672185122967,
-0.02248896285891533,
0.04137512668967247,
0.013643663376569748,
-0.004942693281918764,
0.057890284806489944,
0.02526165544986725,
0.030468013137578964,
0.004954623058438301,
-0.0025303189177066088,
0.006235428620129824,
-0.05744694173336029,
-0.06963517516851425,
-0.008434171788394451,
0.012631235644221306,
-0.030993379652500153,
-0.003878258867189288,
-0.04609786719083786,
-0.05523359403014183,
0.027600515633821487,
0.02960381656885147,
0.00820385292172432,
0.02169906720519066,
-0.028739532455801964,
-0.0054076616652309895,
0.04166042432188988,
-0.014736511744558811,
0.05146786943078041,
0.019072892144322395,
-0.008994410745799541,
0.0007939001079648733,
0.007017585914582014,
0.015770725905895233,
0.004978149197995663,
-0.02952822856605053,
-0.02434304542839527,
0.006369315087795258,
-0.01928836666047573,
0.02778768539428711,
0.004261500667780638,
0.02101995423436165,
-0.005891813896596432,
-0.016099033877253532,
0.03367198631167412,
0.011893244460225105,
0.030096758157014847,
0.04201468825340271,
-0.016685757786035538,
0.0102305943146348,
0.038482796400785446,
-0.033186908811330795,
-0.0006423617014661431,
-0.026949426159262657,
0.009110975079238415,
0.03392760455608368,
-0.015500040724873543,
0.02972816489636898,
-0.011841240338981152,
0.0006754506030119956,
-0.007125966716557741,
-0.06812827289104462,
0.07530131936073303,
-0.05000962316989899,
0.007352914195507765,
0.016710501164197922,
0.0001287288177991286,
-0.0040402463637292385,
-0.022166473791003227,
0.006159257143735886,
-0.003516135271638632,
-0.030592037364840508,
-0.015678897500038147,
0.020275484770536423,
0.026355858892202377,
-0.039380889385938644,
-0.02317645214498043,
0.05055062100291252,
-0.0260173212736845,
-0.030064458027482033,
-0.01497380156069994,
0.025813058018684387,
-0.03818826004862785,
-0.08222327381372452,
0.0024617002345621586,
0.05075014382600784,
-0.041145797818899155,
0.01757068932056427,
0.031994376331567764,
-0.006566376890987158,
0.04625320807099342,
-0.03326326608657837,
-0.021556438878178596,
0.005598279647529125,
0.019290070980787277,
-0.023260660469532013,
-0.016964638605713844,
0.05308537930250168,
-0.027849188074469566,
-0.02764003723859787,
-0.007796207908540964,
-0.030968012288212776,
0.021411005407571793,
-0.03041492961347103,
-0.01290113665163517,
0.017972836270928383,
0.0028902217745780945,
-0.035216618329286575,
-0.025473523885011673,
0.03488007187843323,
0.025964904576539993,
0.02846568450331688,
-0.021539537236094475,
0.022265929728746414,
-0.0010804833145812154,
-0.028576554730534554,
0.04295867681503296,
-0.004206486511975527,
0.016542477533221245,
-0.03447139635682106,
0.0801197737455368,
-0.012900445610284805,
-0.029012814164161682,
0.01716085523366928,
-0.0158834271132946,
0.03467404842376709,
0.01365284901112318,
-0.01933997869491577,
0.014455774798989296,
0.010452346876263618,
-0.022691762074828148,
-0.02487238496541977,
-0.03157354146242142,
0.009782337583601475,
0.08132439851760864,
-0.040481582283973694,
0.04425286874175072,
0.02008521370589733,
-0.007846234366297722,
0.015164651907980442,
-0.022528894245624542,
-0.02172137424349785,
-0.013209016993641853,
0.02423505112528801,
0.006748868152499199,
-0.04794403538107872,
0.026674292981624603,
0.014682907611131668,
0.05200817435979843,
-0.0369521789252758,
-0.00851618591696024,
0.016780154779553413,
0.014132440090179443,
0.004341337829828262,
-0.030798837542533875,
-0.015499507077038288,
0.048102572560310364,
0.012037309817969799,
0.035070814192295074,
0.01592910662293434,
0.018171226605772972,
0.03596885874867439,
0.04665003716945648,
-0.010003278031945229,
-0.06194208562374115,
-0.010459785349667072,
-0.047166284173727036,
0.01377398893237114,
0.004592963494360447,
-0.008228054270148277,
-0.0033627599477767944,
0.04954461008310318,
0.026529965922236443,
-0.013853986747562885,
0.017556319013237953,
-0.06535033136606216,
-0.033821821212768555,
0.0023002317175269127,
-0.01800551265478134,
-0.025822801515460014,
0.07237062603235245,
0.004196054767817259,
0.0029415148310363293,
0.022275149822235107,
-0.020011186599731445,
-0.0029227386694401503,
0.05230925232172012,
0.028675071895122528,
0.048190150409936905,
0.06383814662694931,
-0.01237509772181511,
-0.00819414108991623,
-0.045218952000141144,
0.00040365059976466,
0.15120470523834229,
0.05331273376941681,
-0.017021503299474716,
-0.03385176137089729,
-0.008126728236675262,
-0.014684351161122322,
-0.005712238606065512,
-0.0016023723874241114,
0.005944117903709412,
-0.007173732854425907,
0.017459651455283165,
0.05667654052376747,
0.03368498012423515,
-0.012141815386712551,
-0.0061355819925665855,
0.016826307401061058,
-0.014204259030520916,
-0.028090214356780052,
-0.03309737518429756,
0.013518938794732094,
-0.023150665685534477,
-0.004448319785296917,
-0.01017187349498272,
0.060959961265325546,
-0.049727849662303925,
-0.0017785546369850636,
-0.022070759907364845,
-0.06034798175096512,
0.002572068478912115,
0.010042035020887852,
-0.061725761741399765,
0.05369376018643379,
-0.025136498734354973,
-0.030568111687898636,
-0.03179369866847992,
0.045368827879428864,
-0.030882220715284348,
-0.05043181777000427,
-0.00812244787812233,
0.04437818005681038,
-0.010493150912225246,
0.013445059768855572,
0.009045452810823917,
0.03591258451342583,
-0.04565994441509247,
0.041946880519390106,
-0.023960191756486893,
0.024348249658942223,
-0.033640626817941666,
0.003069821046665311,
0.0007275101961567998,
0.008762011304497719,
0.01178913377225399,
-0.06160297244787216,
0.01491500437259674,
0.006599942222237587,
0.03039386309683323,
0.003904477460309863,
-0.026104016229510307,
-0.007884780876338482,
0.017761923372745514,
0.03925912082195282,
-0.006083967164158821,
0.007044375408440828,
0.02487471140921116,
0.007682980038225651,
-0.029616450890898705,
0.0865599662065506,
-0.02284115180373192,
-0.023379303514957428,
-0.03593451529741287,
-0.003545469371601939,
-0.03595268726348877,
0.013489345088601112,
-0.017117492854595184,
0.0432116761803627,
0.02289765328168869,
0.0314071923494339,
-0.017890799790620804,
-0.02283645048737526,
-0.027864454314112663,
0.05344383791089058,
-0.017641479149460793,
-0.026908375322818756,
-0.048016875982284546,
-0.04494286701083183,
0.019982168450951576,
0.01209661178290844,
0.028160130605101585,
0.007320973090827465,
0.008983500301837921,
0.05083572119474411,
-0.01299915462732315,
-0.021853141486644745,
-0.00736848171800375,
0.016566049307584763,
-0.022691814228892326,
0.026356292888522148,
0.007683500647544861,
0.014683164656162262,
0.014944393187761307,
0.011061578057706356,
-0.02443593554198742,
0.0275947954505682,
-0.03283141180872917,
0.0018837620737031102,
0.0015323463594540954,
0.00460301386192441,
0.046455468982458115,
0.006960428319871426,
0.01739947684109211,
-0.053761135786771774,
0.01196229737251997,
-0.02637328766286373,
-0.029252387583255768,
-0.019600223749876022,
0.001512211631052196,
0.002080222824588418,
0.054558031260967255,
-0.010332305915653706,
0.022784464061260223,
-0.02463575266301632,
0.001340518705546856,
-0.030344480648636818,
-0.025456862524151802,
0.020216237753629684,
0.01272817887365818,
-0.03403010219335556,
0.038429927080869675,
-0.029363928362727165,
-0.007725120987743139,
-0.0027610277757048607,
-0.010285847820341587,
-0.018225064501166344,
0.00698764156550169,
0.018529227003455162,
0.012392629869282246,
0.06472556293010712,
-0.005357208661735058,
-0.01700299046933651,
0.0037906707730144262,
-0.011690817773342133,
-0.07896704226732254,
0.0458793118596077,
0.01223131362348795,
0.03898800164461136,
-0.0030063337180763483,
-0.06270495802164078,
0.007616887334734201,
0.0618118941783905,
-0.014244475401937962,
0.013949057087302208,
-0.006689843256026506,
-0.025664903223514557,
0.04274880886077881,
-0.03627099096775055,
0.02136474847793579,
-0.05583347752690315,
-0.0016788647044450045,
0.009391946718096733,
-0.00784424040466547,
-0.0590658001601696,
-0.004034984391182661,
-0.01785031519830227,
-0.02043657936155796,
-0.0410102941095829,
-0.005607681814581156,
0.04596036672592163,
0.055049967020750046,
0.020564712584018707,
-0.02262944169342518,
0.013685861602425575,
0.009760310873389244,
0.0028260222170501947,
-0.09241537749767303,
-0.011658905074000359,
-0.036367423832416534,
-0.00203447206877172,
0.012850970961153507,
-0.07408707588911057,
-0.016709981486201286,
-0.0015604475047439337,
-0.052348364144563675,
0.010074186138808727,
-0.012218487448990345,
-0.04216005653142929,
-0.023431243374943733,
-0.020564408972859383,
0.008437561802566051,
0.012520053423941135,
0.0021437748800963163,
0.06634441018104553,
0.002480839379131794,
0.019299060106277466,
-0.051465414464473724,
-0.03165087848901749,
-0.003935538697987795,
0.0377018004655838,
-0.03892447426915169,
0.011716392822563648,
0.04982217028737068,
-0.01667976938188076,
-0.007233876269310713,
0.031182443723082542,
-0.04506458714604378,
0.02933262474834919,
-0.006855006795376539,
0.015659527853131294,
-0.007161460816860199,
0.030652262270450592,
0.037912819534540176,
0.010491976514458656,
-0.006993762217462063,
-0.007113244384527206,
-0.02382558211684227,
0.027126438915729523,
-0.032241594046354294,
0.005157670937478542,
0.030477434396743774,
-0.016487229615449905,
-0.06113016605377197,
0.05517048388719559,
-0.06082569435238838,
-0.000875850731972605,
-0.02359081245958805,
0.0013246493181213737,
-0.02970455400645733,
-0.022868119180202484,
0.012278543785214424,
-0.020598087459802628,
0.025438575074076653,
0.02468067780137062,
-0.02217703126370907,
0.013541572727262974,
-0.001583644887432456,
-0.008151103742420673,
-0.03176654875278473,
-0.00001923356467159465,
-0.015424034558236599,
-0.021701384335756302,
-0.030340053141117096,
0.01221663411706686,
-0.026060933247208595,
-0.009599268436431885,
-0.022426672279834747,
-0.02043004333972931,
-0.0577014684677124,
0.04597286880016327,
0.031002208590507507,
0.013246193528175354,
0.022198759019374847,
-0.02545984834432602,
0.006051014177501202,
-0.0853227823972702,
0.0002913825446739793,
-0.0040455712005496025,
-0.051941610872745514,
-0.006284335628151894,
-0.03595936298370361,
0.02564961276948452,
-0.008158065378665924,
0.07260832190513611,
-0.04150494188070297,
0.019638944417238235,
0.036870431154966354,
-0.017242956906557083,
0.043150484561920166,
-0.046428315341472626,
0.007718551903963089,
0.01903792843222618,
0.009085644036531448,
0.011493081226944923,
-0.005328927654772997,
-0.014879639260470867,
-0.004141069948673248,
0.03124498575925827,
0.03300512209534645,
0.08148004859685898,
0.011065594851970673,
-0.026372846215963364,
0.017938682809472084,
0.006267208140343428,
0.01566994935274124,
0.0811774879693985,
0.00482966611161828,
-0.012679860927164555,
0.048494208604097366,
-0.02584982104599476,
-0.050139959901571274,
0.032649192959070206,
-0.014309697784483433,
-0.03152848407626152,
-0.03966662287712097,
-0.028798934072256088,
0.017435817047953606,
0.001086264499463141,
-0.0028720302507281303,
0.029556646943092346,
-0.0317222885787487,
-0.01128235924988985,
0.030016163364052773,
-0.020706651732325554,
0.04336300119757652,
-0.02108195051550865,
0.05724349990487099,
0.025399552658200264,
-0.03475143387913704,
0.030529918149113655,
-0.014165576547384262,
0.05114786699414253,
-0.005467117298394442,
-0.016928663477301598,
0.044166404753923416,
-0.010704086162149906,
-0.003780100727453828,
0.005795254837721586,
0.012326550669968128,
-0.011896701529622078,
-0.03857596963644028,
-0.005031642038375139,
-0.0015706091653555632,
-0.036768462508916855,
0.005862055346369743,
-0.0022479926701635122,
0.06772362440824509,
0.012176413089036942,
-0.01277795061469078,
0.009199540130794048,
-0.01640406996011734,
-0.02124794013798237,
0.06741879135370255,
-0.008433716371655464,
0.002941231243312359,
-0.005980215035378933,
-0.00288727437146008,
0.009690042585134506,
-0.01427316851913929,
-0.005361511372029781,
0.048294566571712494,
0.02174662984907627,
-0.005727959796786308,
-0.005028076935559511,
0.004737732466310263,
-0.011980880051851273,
0.018011126667261124,
-0.01583811454474926,
0.06706514209508896,
0.014299940317869186,
-0.008075611665844917,
0.003992338199168444,
0.008513889275491238,
-0.03154047206044197,
0.04795617237687111,
-0.08961562812328339,
-0.04991793632507324,
-0.010111468844115734,
0.05349550023674965,
0.009716144762933254,
-0.016203835606575012
] |
<p>Proca action/equation describes massive spin-1 particle, but I was unable to find an equation that describes massless spin-1 particle. </p>
<p>Can anyone tell me what the name of this equation is?</p>
| 10,812 |
[
-0.008653934113681316,
0.008078951388597488,
-0.029446497559547424,
-0.039363812655210495,
0.026649562641978264,
0.006214359775185585,
-0.06194980442523956,
0.0064566428773105145,
0.0006622670916840434,
-0.07357773929834366,
0.05573003366589546,
0.04064212366938591,
0.0808323472738266,
0.014975717291235924,
0.00553916348144412,
0.0017294033896178007,
0.026525050401687622,
0.0025825712364166975,
-0.028266770765185356,
-0.0591449998319149,
0.018946979194879532,
0.006387760862708092,
0.03257984295487404,
0.025571323931217194,
0.040792301297187805,
0.03688544034957886,
0.014668881893157959,
0.04273217171430588,
-0.007776990998536348,
0.06815089285373688,
-0.013373982161283493,
-0.05306728184223175,
-0.021853361278772354,
0.01663048006594181,
-0.0049129389226436615,
-0.02358255907893181,
0.02535535953938961,
-0.0396435521543026,
0.02486380748450756,
0.006549122743308544,
-0.006985893938690424,
-0.0241544246673584,
-0.015077258460223675,
0.016059890389442444,
-0.0503968708217144,
0.0328163243830204,
0.019262760877609253,
0.012787660583853722,
0.07077108323574066,
-0.06951636075973511,
0.07650984823703766,
0.00007822169573046267,
0.04392070323228836,
-0.03243691101670265,
-0.018296116963028908,
-0.008724546991288662,
0.06442375481128693,
0.06971342116594315,
-0.007164244074374437,
-0.07812882959842682,
-0.05085454136133194,
-0.01429190207272768,
0.010572233237326145,
0.002475858898833394,
-0.021105822175741196,
0.01828218810260296,
0.005319878458976746,
-0.02233925275504589,
0.03027172200381756,
0.026714617386460304,
0.002469615312293172,
-0.02649020589888096,
0.05181751400232315,
-0.017664024606347084,
0.00008450762106804177,
-0.036810025572776794,
0.012816050089895725,
0.00814091321080923,
0.026072051376104355,
0.030223699286580086,
-0.02764759585261345,
0.04109407961368561,
0.011327932588756084,
-0.022883892059326172,
-0.017856257036328316,
0.002331821946427226,
0.06799765676259995,
0.023229168727993965,
-0.008362185209989548,
0.03934629261493683,
-0.027857301756739616,
0.014278742484748363,
0.07053250074386597,
0.00523112528026104,
-0.006938861683011055,
0.030092308297753334,
0.01790047064423561,
0.053652770817279816,
0.013272725045681,
-0.004408788401633501,
0.014482955448329449,
-0.04789067059755325,
-0.022966979071497917,
0.053807079792022705,
0.018421728163957596,
0.015787523239850998,
-0.030794180929660797,
0.0116232605651021,
-0.03278869763016701,
0.005349806044250727,
-0.042526502162218094,
0.01216938067227602,
-0.019429421052336693,
-0.018438829109072685,
-0.01266858447343111,
-0.04289194568991661,
0.01125637348741293,
-0.020682156085968018,
0.044667597860097885,
0.06151008978486061,
0.03522379696369171,
-0.041019901633262634,
0.05542043223977089,
-0.03403216972947121,
-0.088590107858181,
-0.01433350145816803,
0.0014140101848170161,
0.006321545224636793,
-0.027010122314095497,
0.020476169884204865,
0.024574751034379005,
-0.07424847036600113,
0.03655732795596123,
-0.0021989913657307625,
0.019825907424092293,
-0.014669847674667835,
-0.0820094645023346,
-0.05670852214097977,
0.018630996346473694,
-0.0018331431783735752,
-0.025809282436966896,
-0.04766435921192169,
0.018814245238900185,
0.03231406956911087,
0.12038863450288773,
0.00922184158116579,
0.026600899174809456,
0.04270699620246887,
0.041158728301525116,
-0.020503351464867592,
0.0045951055362820625,
-0.04917345196008682,
0.022578256204724312,
-0.026465293020009995,
-0.033557720482349396,
-0.038638170808553696,
0.009575875476002693,
0.020686622709035873,
-0.015513752587139606,
0.014497642405331135,
0.054965049028396606,
-0.026911616325378418,
0.03200209140777588,
0.04701274633407593,
0.0027047651819884777,
-0.025093279778957367,
0.06050648167729378,
0.004600028973072767,
-0.0124900471419096,
0.05107484757900238,
0.017989730462431908,
0.03258570656180382,
0.0025870290119200945,
0.030789321288466454,
0.022972140461206436,
-0.046200841665267944,
-0.034022700041532516,
0.0012979896273463964,
0.0007225445588119328,
0.02118765376508236,
-0.028057189658284187,
-0.02692032791674137,
0.003299763659015298,
0.017564700916409492,
-0.0031493676360696554,
0.033446166664361954,
-0.01746738888323307,
-0.017989326268434525,
0.03283888101577759,
-0.02859979309141636,
-0.01641559600830078,
-0.06539955735206604,
0.005988639779388905,
0.009830099530518055,
0.01645125448703766,
0.024570787325501442,
0.024827536195516586,
0.016848087310791016,
-0.0579054057598114,
-0.011327577754855156,
-0.014850429259240627,
0.02946712076663971,
0.025217171758413315,
0.011098073795437813,
0.0031160563230514526,
0.037642888724803925,
0.03663197532296181,
-0.008969130925834179,
0.017055969685316086,
0.0015373481437563896,
0.015139980241656303,
-0.003456493141129613,
0.008718439377844334,
0.014300940558314323,
-0.016330312937498093,
0.006677321158349514,
0.015159878879785538,
-0.018237456679344177,
-0.0171283520758152,
0.030727826058864594,
-0.023993268609046936,
0.05654189735651016,
0.013988964259624481,
0.0036126994527876377,
0.032019928097724915,
0.03406741842627525,
0.005926077254116535,
-0.012632792815566063,
-0.009018797427415848,
-0.024131307378411293,
-0.008970598690211773,
-0.03637802600860596,
0.027144361287355423,
0.01704104244709015,
-0.03957151994109154,
0.007279029116034508,
0.04619104787707329,
0.014180664904415607,
0.026814747601747513,
0.047040294855833054,
-0.014008942991495132,
-0.02296443097293377,
0.01364113949239254,
-0.015137708745896816,
-0.03399714455008507,
-0.005699926987290382,
0.04491765424609184,
0.015428273007273674,
0.018361015245318413,
0.01597888395190239,
-0.024669598788022995,
0.00578727014362812,
-0.022003173828125,
0.009760702028870583,
0.023302581161260605,
-0.059415303170681,
0.051872532814741135,
-0.02861640602350235,
0.04137074947357178,
0.02157352678477764,
-0.0060109300538897514,
-0.003981842193752527,
-0.01607617363333702,
-0.004674694966524839,
0.004702382255345583,
-0.0020436032209545374,
-0.03563563898205757,
-0.03848496451973915,
0.027176933363080025,
-0.03512261435389519,
0.01712939515709877,
0.021187584847211838,
-0.02559554949402809,
-0.01759374514222145,
0.00928821787238121,
0.030279571190476418,
0.022799888625741005,
0.06862810254096985,
0.006498680915683508,
-0.023330479860305786,
0.027431383728981018,
-0.0590941458940506,
0.04339413344860077,
0.053053200244903564,
-0.028006507083773613,
0.03171103075146675,
-0.07327937334775925,
-0.034415457397699356,
0.011818080209195614,
-0.006719858851283789,
-0.007257399614900351,
0.02475719526410103,
-0.024130551144480705,
-0.04502417519688606,
-0.04262980446219444,
-0.04077521711587906,
-0.0022154715843498707,
-0.036501381546258926,
0.0301318671554327,
0.04723277688026428,
-0.014874445274472237,
-0.052723199129104614,
0.003101353533565998,
-0.050041742622852325,
-0.04409056156873703,
-0.022492635995149612,
0.01042878907173872,
0.013015354052186012,
-0.02542857825756073,
0.027615630999207497,
0.03588297590613365,
-0.016744280233979225,
-0.005415222141891718,
-0.04623844102025032,
-0.04091954231262207,
0.05089942738413811,
-0.008141289465129375,
0.014102373272180557,
0.01763296127319336,
-0.04176352545619011,
0.06920719891786575,
0.006120180245488882,
-0.042994171380996704,
-0.03553037345409393,
0.004284727852791548,
-0.02492787316441536,
-0.02491334080696106,
0.01984071359038353,
-0.010666003450751305,
0.016835475340485573,
0.024621501564979553,
0.033772557973861694,
-0.0008300244226120412,
0.014927996322512627,
0.03856861591339111,
-0.030097393319010735,
-0.02168913185596466,
-0.03774289786815643,
-0.02289293147623539,
0.042802222073078156,
0.013211308047175407,
-0.01256018690764904,
0.03183460235595703,
0.03292735666036606,
0.027086231857538223,
0.0012430576607584953,
-0.06332474201917648,
0.040390461683273315,
-0.0011876658536493778,
0.02143891155719757,
-0.009774250909686089,
0.0389692597091198,
-0.021527249366044998,
-0.0070305014960467815,
-0.013035744428634644,
0.04036228358745575,
0.017869416624307632,
-0.036551523953676224,
0.002028441522270441,
0.01357006561011076,
0.032581087201833725,
-0.03023422136902809,
-0.02435488998889923,
0.003605337580665946,
0.0138828344643116,
0.011864899657666683,
-0.018742399290204048,
-0.01482207141816616,
0.04933891445398331,
0.004749355372041464,
0.0280691459774971,
-0.0060740625485777855,
-0.05128902569413185,
0.009265722706913948,
-0.04818971827626228,
0.02859889343380928,
-0.05008351057767868,
0.010592104867100716,
0.021483836695551872,
0.03452514111995697,
0.02866450510919094,
-0.006026152987033129,
0.024190794676542282,
0.024462489411234856,
-0.09544568508863449,
0.020885318517684937,
-0.05741118639707565,
-0.0035043840762227774,
0.010580227710306644,
-0.020721031352877617,
-0.019404685124754906,
-0.020312979817390442,
-0.041256699711084366,
-0.025462890043854713,
-0.015749555081129074,
-0.06374986469745636,
0.012850753031671047,
-0.012729392386972904,
-0.017929697409272194,
-0.008937467820942402,
-0.0004328385111875832,
0.052432116121053696,
-0.01198986079543829,
-0.0017329155234619975,
0.06061500310897827,
-0.007060660980641842,
0.0034907683730125427,
-0.017684025689959526,
-0.010571534745395184,
0.026426460593938828,
0.005297769792377949,
0.025073863565921783,
0.007900606840848923,
-0.029056791216135025,
-0.00035214354284107685,
-0.0067115058191120625,
0.07418233156204224,
0.024796083569526672,
-0.03735405206680298,
-0.02369983308017254,
-0.0346018448472023,
-0.012171858921647072,
0.018039561808109283,
0.0341620072722435,
0.003765573026612401,
0.019599569961428642,
0.015637239441275597,
-0.00559448916465044,
-0.01773178018629551,
0.058182183653116226,
0.06984498351812363,
0.03465529903769493,
-0.03447601944208145,
-0.023041490465402603,
0.004826823249459267,
-0.02496929094195366,
-0.033469200134277344,
-0.013309394009411335,
0.015520737506449223,
-0.047126516699790955,
-0.006121871992945671,
0.01175590418279171,
0.03005925752222538,
-0.02574959024786949,
-0.02536570094525814,
-0.0000917230499908328,
-0.015831423923373222,
0.018514709547162056,
-0.01643524318933487,
-0.018760988488793373,
0.030580027028918266,
0.013115082867443562,
-0.009923109784722328,
0.017025882378220558,
-0.07888645678758621,
-0.012772277928888798,
0.0441540963947773,
0.034424565732479095,
0.0037521631456911564,
-0.019068507477641106,
-0.04068441689014435,
-0.01881779544055462,
0.022357016801834106,
-0.04075915366411209,
0.017245296388864517,
-0.018372826278209686,
0.008901610970497131,
0.026310432702302933,
-0.011448029428720474,
-0.04627155140042305,
0.01189090870320797,
-0.008660813793540001,
-0.03807690739631653,
0.0013991078594699502,
0.02297796495258808,
0.02503071539103985,
0.028238927945494652,
-0.014117326587438583,
0.024873532354831696,
0.03024117834866047,
0.02772446908056736,
0.017620928585529327,
0.023485902696847916,
-0.013359010219573975,
-0.10046086460351944,
-0.012637617066502571,
0.00945640355348587,
-0.034800708293914795,
0.01931832917034626,
-0.06307229399681091,
-0.038772206753492355,
-0.0029917515348643064,
-0.01560997124761343,
-0.006708573084324598,
-0.013914600946009159,
-0.0624464675784111,
-0.010917050763964653,
0.06112949922680855,
-0.03285781666636467,
0.01523593720048666,
0.026439042761921883,
-0.002523360773921013,
-0.0543423630297184,
-0.02296258695423603,
0.007549848407506943,
-0.003397380467504263,
-0.018622547388076782,
-0.03495803475379944,
0.008347421884536743,
-0.03800179809331894,
0.036085259169340134,
-0.008237898349761963,
0.021984193474054337,
0.01497557107359171,
-0.014379406347870827,
-0.05586452782154083,
0.021384183317422867,
-0.00963549129664898,
-0.02510867640376091,
-0.011177943088114262,
-0.0004473797744140029,
0.01536403875797987,
-0.03103923238813877,
0.025672512128949165,
0.0017693162662908435,
-0.03686283156275749,
0.013424316421151161,
0.019277937710285187,
0.019319547340273857,
-0.025077058002352715,
-0.04407369717955589,
0.018553581088781357,
-0.04979357495903969,
0.052296001464128494,
-0.01474363636225462,
0.0033415458165109158,
0.02224608324468136,
-0.043615516275167465,
-0.02881125919520855,
0.03503994643688202,
0.0011244243942201138,
0.008208566345274448,
-0.0067834979854524136,
-0.030931411311030388,
0.006481112912297249,
-0.01414728257805109,
-0.06423690915107727,
-0.05987687408924103,
0.018481120467185974,
-0.016500653699040413,
-0.006698330398648977,
0.002426126040518284,
-0.02455095946788788,
-0.002377873519435525,
-0.023046746850013733,
0.040282249450683594,
0.059982821345329285,
-0.05223403126001358,
0.0194231066852808,
-0.0014301021583378315,
0.02232767827808857,
0.024584127590060234,
-0.021057413890957832,
-0.03334992006421089,
0.019578050822019577,
-0.008603006601333618,
0.008001415058970451,
0.027007535099983215,
0.08943921327590942,
-0.022486085072159767,
-0.0213380828499794,
-0.02976877987384796,
0.000695306749548763,
0.023583775386214256,
-0.014028275385499,
0.02913581021130085,
0.03244952857494354,
0.046006713062524796,
-0.01709257997572422,
-0.010669236071407795,
0.025717558339238167,
0.0015062622260302305,
0.034947410225868225,
-0.005572938360273838,
-0.008371458388864994,
-0.035296157002449036,
-0.018104473128914833,
0.036220550537109375,
-0.016169676557183266,
-0.006852604914456606,
0.00663274759426713,
0.03726683184504509,
0.0281385388225317,
-0.020899606868624687,
0.0482574887573719,
-0.012125284411013126,
-0.002068976638838649,
-0.008527037687599659,
0.025468451902270317,
-0.009577891789376736,
-0.020385587587952614,
-0.01870613358914852,
-0.01164739765226841,
0.009883438237011433,
0.021692125126719475,
0.057678528130054474,
0.01061261910945177,
0.030231250450015068,
-0.0022182778920978308,
0.015313897281885147,
0.0015333452029153705,
0.0213853120803833,
-0.019042272120714188,
0.04315021261572838,
0.024307923391461372,
0.03789237514138222,
-0.019303398206830025,
0.029717274010181427,
0.043642591685056686,
0.0796893984079361,
-0.018583131954073906,
0.038079116493463516,
0.04473796859383583,
-0.010229269973933697,
0.040080588310956955,
-0.01089757215231657,
-0.030228376388549805,
0.05147441849112511,
0.009501399472355843,
0.05217571556568146,
0.002720081713050604,
-0.015929842367768288,
0.04772187024354935,
0.025698313489556313,
0.016418978571891785,
-0.0033036305103451014,
-0.027192339301109314,
-0.021479757502675056,
0.021776996552944183,
0.030056646093726158,
-0.0020924804266542196,
0.012025215663015842,
0.014597747474908829,
0.013720080256462097,
-0.015609431080520153,
0.029581906273961067,
-0.001862982870079577,
-0.04508981108665466,
-0.005346524529159069,
-0.053448960185050964,
-0.07245633006095886,
0.03504597768187523,
0.0058287340216338634,
-0.025532513856887817,
-0.019495662301778793,
-0.04191276803612709,
0.015502678230404854,
0.01691107079386711,
0.022151758894324303,
0.013044466264545918,
0.04334226995706558,
-0.02153036557137966,
0.022505905479192734,
-0.005516966804862022,
-0.006111922673881054,
0.1052182987332344,
0.050868745893239975,
0.007045175414532423,
-0.0965329259634018,
0.012631185352802277,
-0.02836698852479458,
0.009472068399190903,
-0.019473634660243988,
0.019814763218164444,
-0.023433402180671692,
-0.002773093292489648,
0.019009515643119812,
0.06985943019390106,
-0.020420312881469727,
0.00020295042486395687,
0.05206244811415672,
-0.03939763456583023,
-0.053898729383945465,
0.018640851601958275,
0.004531756043434143,
0.019426660612225533,
-0.004709519911557436,
-0.029501020908355713,
0.019587190821766853,
-0.009393816813826561,
-0.007209598086774349,
-0.03892390802502632,
-0.029309453442692757,
0.03189529851078987,
0.04287070780992508,
-0.03739382326602936,
-0.004573355428874493,
-0.020141785964369774,
-0.009693500585854053,
-0.030554136261343956,
0.0050266641192138195,
0.021221261471509933,
-0.02050097845494747,
0.038660526275634766,
0.030735820531845093,
0.03621182590723038,
0.00529835931956768,
0.04961681738495827,
-0.018144385889172554,
-0.026511864736676216,
0.05330417677760124,
-0.025939883664250374,
0.04649434983730316,
-0.017479809001088142,
0.016589462757110596,
-0.0011968206381425261,
-0.015517745167016983,
-0.0028403080068528652,
-0.0790829285979271,
-0.01822759583592415,
-0.012009292840957642,
-0.001169270952232182,
-0.007792336866259575,
0.006277814507484436,
-0.018991980701684952,
0.009399080649018288,
-0.013379541225731373,
0.009323345497250557,
-0.04520093649625778,
-0.009947706013917923,
0.008264541625976562,
-0.031112849712371826,
0.03952591493725777,
-0.0053880056366324425,
-0.02425612136721611,
0.004734441637992859,
-0.048306673765182495,
-0.05277440324425697,
-0.011415723711252213,
0.0019214869244024158,
0.013212398625910282,
0.019409876316785812,
-0.011914819478988647,
-0.016624221578240395,
-0.036865897476673126,
-0.04820488020777702,
0.017747024074196815,
-0.030979719012975693,
-0.006632926408201456,
-0.006325596943497658,
-0.012643272988498211,
0.02556661143898964,
0.048254482448101044,
-0.03122054412961006,
-0.019917014986276627,
-0.020543713122606277,
0.014299101196229458,
0.028446152806282043,
-0.041439078748226166,
-0.012007671408355236,
0.011814710684120655,
-0.03235549479722977,
-0.02710455283522606,
-0.001683963229879737,
0.022062575444579124,
0.023667195811867714,
0.0029054642654955387,
-0.013925652019679546,
0.014888041652739048,
0.0004687757755164057,
-0.02674352563917637,
0.0070650819689035416,
-0.007665792014449835,
0.015722380951046944,
-0.01792573556303978,
0.02994764782488346,
-0.02732323668897152,
-0.004926259163767099,
0.0005052480264566839,
-0.010006695985794067,
-0.0020878969226032495,
0.06940683722496033,
-0.05780419707298279,
0.014259805902838707,
-0.02502041682600975,
0.011420220136642456,
-0.028821401298046112,
-0.003067502984777093,
-0.046040743589401245,
0.025884058326482773,
0.016886044293642044,
0.009452855214476585,
-0.016738571226596832,
0.0204833522439003,
0.009736265987157822,
-0.0057865590788424015,
0.004445923492312431,
0.007760658860206604,
-0.04420657083392143,
0.01841028779745102,
0.030553903430700302,
-0.015689006075263023,
0.05541544780135155,
-0.012984275817871094,
-0.02389136701822281,
0.022385893389582634,
-0.04102310165762901,
-0.027792256325483322,
0.037529777735471725,
0.0015423395670950413,
0.03245948255062103,
0.03579901531338692,
-0.03381308540701866,
-0.019568638876080513,
0.04345337674021721,
-0.031712766736745834,
-0.03796539455652237,
0.02983204275369644,
-0.05397876352071762,
-0.025997130200266838,
-0.017451876774430275,
-0.01774090714752674,
0.010670019313693047,
-0.046554602682590485,
0.015554260462522507,
0.03160088136792183,
-0.03973853215575218,
-0.04055154696106911,
0.0198409054428339,
0.016436589881777763,
0.015593885444104671,
0.038037415593862534,
-0.02613389492034912,
-0.012771427631378174,
0.03190620243549347,
-0.05654434859752655,
0.006967016030102968,
0.008235610090196133,
0.012488947249948978,
-0.06682050228118896,
0.006707967724651098,
-0.015891700983047485,
0.037278350442647934,
0.05218559876084328,
-0.028234083205461502,
0.06081313639879227,
0.03536529466509819,
-0.04111723229289055,
0.022711075842380524,
-0.010797915980219841,
-0.007044762838631868,
-0.008810577914118767,
0.013742927461862564,
0.017909448593854904,
0.06922971457242966,
0.01600901409983635,
0.04505737125873566,
0.042025208473205566,
0.00490935193374753,
-0.03477121889591217,
-0.031549032777547836,
0.002221302594989538,
0.008388926275074482,
0.010967597365379333,
-0.016368795186281204,
0.047676753252744675,
-0.012284389697015285,
-0.022188866510987282,
0.05968016758561134,
0.014240901917219162,
-0.009771684184670448,
-0.009435205720365047,
0.04491640254855156,
-0.005820106714963913,
0.028911439701914787,
0.017877671867609024,
-0.008165356703102589,
-0.003339373506605625,
0.012886629439890385,
0.001184134860523045,
0.04784450680017471,
-0.010555937886238098,
-0.0012887619668617845,
-0.010141368955373764,
-0.019800059497356415,
0.005699139554053545,
0.059484824538230896,
-0.02919570542871952,
-0.07050653547048569,
-0.05982646718621254,
-0.034754373133182526,
-0.017288414761424065,
-0.022789891809225082,
0.009154233150184155,
-0.028176018968224525,
0.04713394492864609,
0.018699998036026955,
-0.019660860300064087,
-0.008551262319087982,
0.040539901703596115,
0.020425928756594658,
0.003185688052326441,
0.022721851244568825,
0.038078371435403824,
-0.021936392411589622,
-0.025200674310326576,
-0.03631417080760002,
0.03134983777999878,
0.035975370556116104,
0.015242478810250759,
-0.05584273487329483,
-0.061927665024995804,
0.020273800939321518,
-0.010701826773583889,
0.01358700916171074,
0.024809282273054123,
-0.03332340344786644,
0.03257592022418976,
-0.05569153279066086,
0.0355803482234478,
0.022832853719592094,
0.023272331804037094,
-0.010579891502857208,
-0.03096221759915352,
0.003141282591968775,
-0.020518239587545395,
0.06707547605037689,
0.004677234683185816,
-0.04250161349773407,
0.03545840084552765,
-0.0011849956354126334,
-0.0011259872699156404,
-0.0009279540972784162,
0.011945375241339207,
-0.008599737659096718,
-0.019144978374242783,
-0.03404977172613144,
0.01972240023314953,
-0.00788175594061613,
0.02370326779782772,
0.023404842242598534,
0.03438157960772514,
0.027206990867853165,
-0.016186140477657318,
-0.06760800629854202,
0.0619673877954483,
0.02329839952290058,
-0.006958518642932177,
0.07158562541007996,
-0.012001085095107555,
0.009920801967382431,
0.04661736264824867,
-0.045104339718818665,
-0.02525831013917923,
0.005732873920351267,
-0.05857492610812187,
-0.04894157126545906,
-0.00024027614563237876,
0.0008014547056518495,
0.01252658199518919,
-0.04009486734867096,
0.01267782598733902,
0.031092386692762375,
-0.03406120464205742,
-0.03669123724102974,
0.04394419863820076,
0.01959359459578991,
0.03488050028681755,
-0.006597542203962803,
0.03378412127494812,
0.01633480377495289,
0.023439569398760796,
0.03459249436855316,
0.08477912098169327,
0.026233747601509094,
-0.011318431235849857,
-0.029059380292892456,
0.000596356694586575,
-0.009905550628900528,
-0.0037848406936973333,
0.03437018394470215,
0.05348219349980354,
-0.014564217999577522,
0.0020552456844598055,
0.01384697388857603,
-0.029187195003032684,
0.030023960396647453,
-0.013704875484108925,
-0.032853398472070694,
0.09886717796325684,
-0.02138720266520977,
0.031561896204948425,
-0.0050032432191073895,
0.04865581914782524,
-0.03028668649494648,
-0.029034575447440147,
0.005499606020748615,
0.03969578817486763,
-0.014202464371919632,
-0.05266358703374863,
-0.00047178834211081266,
-0.019788943231105804,
-0.015808045864105225,
-0.06719695031642914,
0.0027071067597717047,
0.0296013280749321,
-0.005265595391392708,
-0.00337796239182353,
-0.007071556989103556,
0.0004656403907574713,
0.009220713749527931,
0.007069690153002739,
0.0005709261167794466,
0.018735075369477272,
-0.016085436567664146,
0.007007494568824768,
-0.03470238670706749,
0.04078720510005951,
-0.057866983115673065,
-0.02588612586259842,
0.0019158810609951615,
0.03655780106782913,
-0.06386319547891617,
0.0026469267904758453
] |
<p>Let a person of mass ( m ) = 10kg. then his weight will be 98N. Now, when he jumps from 1m height on the ground, the impact force becomes 9800N ( considering deflection of ground after impact is 1cm ). 100 times. But i am highly confused. 100 times force should simply crush a human! how the force is neutralized?</p>
<p>for calculating impact force:
<a href="http://hyperphysics.phy-astr.gsu.edu/hbase/flobi.html" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/flobi.html</a></p>
| 10,813 |
[
-0.04882783442735672,
-0.029887685552239418,
-0.0375649631023407,
-0.031025409698486328,
0.049416106194257736,
0.02257459983229637,
-0.015380613505840302,
-0.05361275374889374,
0.03187263384461403,
-0.027101876214146614,
0.037956129759550095,
0.040194373577833176,
0.03282647579908371,
0.017667794600129128,
0.018531236797571182,
-0.02303457073867321,
-0.04205502197146416,
0.010679231956601143,
0.01841801218688488,
-0.0529806949198246,
-0.028282782062888145,
-0.018925486132502556,
0.02874680608510971,
0.00553694786503911,
-0.015623863786458969,
0.0072106849402189255,
0.028064150363206863,
-0.024085648357868195,
0.036999236792325974,
0.051127467304468155,
0.006998990662395954,
-0.03105028346180916,
0.021160557866096497,
-0.022436760365962982,
-0.014651601202785969,
0.04551796242594719,
-0.05041365697979927,
-0.018214354291558266,
-0.05016243830323219,
0.02807343564927578,
0.013323279097676277,
-0.02191455289721489,
-0.0006758676609024405,
0.06963443011045456,
-0.03801165521144867,
0.03286450356245041,
-0.0071373446844518185,
0.0022338642738759518,
0.06360556930303574,
-0.06809782981872559,
0.04975816234946251,
0.007701990660279989,
0.06629900634288788,
0.011441324837505817,
0.011008642613887787,
-0.019079387187957764,
0.0648425966501236,
0.05505696311593056,
-0.04146518185734749,
-0.047887492924928665,
0.00312308082357049,
-0.06504225730895996,
-0.04629254341125488,
-0.005661036819219589,
0.04077112674713135,
0.0648924857378006,
-0.02971295826137066,
-0.01927848719060421,
0.04516321048140526,
0.019246121868491173,
0.017595048993825912,
-0.007323001977056265,
0.010819443501532078,
-0.04449813812971115,
0.016946127638220787,
-0.032485440373420715,
0.04754703491926193,
0.004063265863806009,
0.04668542742729187,
0.05556844174861908,
-0.012118618935346603,
0.027300935238599777,
0.05608237162232399,
0.041937924921512604,
0.014934300445020199,
-0.05445317178964615,
0.07866214960813522,
0.011849850416183472,
0.013771574944257736,
0.04470611736178398,
-0.018289456143975258,
-0.013472113758325577,
0.01806890219449997,
-0.016878865659236908,
0.005699056200683117,
0.048311538994312286,
0.012626240961253643,
0.06363540887832642,
0.0008569685160182416,
-0.027675755321979523,
-0.010744448751211166,
0.004395518451929092,
0.038338735699653625,
0.03462529927492142,
0.007110964972525835,
-0.02129155583679676,
-0.035554613918066025,
-0.010019170120358467,
-0.02048119716346264,
0.015196158550679684,
-0.020953364670276642,
-0.009053199551999569,
-0.00956834014505148,
-0.03220105916261673,
0.024671897292137146,
-0.036165397614240646,
-0.0027681977953761816,
0.008608043193817139,
0.030814170837402344,
0.005712464451789856,
-0.0040070489048957825,
-0.003561465535312891,
0.04160396754741669,
-0.008178063668310642,
-0.023010749369859695,
0.012751691974699497,
0.020436817780137062,
0.014709803275763988,
0.002896017860621214,
0.018535368144512177,
-0.008974564261734486,
-0.0026875713374465704,
0.008161235600709915,
0.02361241914331913,
0.054640136659145355,
-0.03745720908045769,
-0.09839487820863724,
-0.0428595133125782,
0.055551595985889435,
-0.019433869048953056,
0.008558331988751888,
-0.07818151265382767,
0.03322670981287956,
-0.002224047901108861,
0.05147503688931465,
0.03689797967672348,
-0.0036783653777092695,
0.014867964200675488,
-0.023010361939668655,
0.014532096683979034,
0.01234450377523899,
-0.012180390767753124,
-0.02004767209291458,
0.0017658305587247014,
-0.006338431965559721,
-0.0672086849808693,
0.042214468121528625,
0.027054207399487495,
0.01266215369105339,
-0.030868111178278923,
0.019881771877408028,
-0.006823979318141937,
-0.004297118633985519,
-0.01599930040538311,
-0.019134318456053734,
-0.005983404815196991,
0.0967506691813469,
-0.0015176980523392558,
-0.0008034922066144645,
0.04848580062389374,
0.012026780284941196,
0.01693766750395298,
-0.011807476170361042,
0.028343327343463898,
0.03826684504747391,
-0.041360583156347275,
-0.002746548503637314,
-0.0553697869181633,
0.037161458283662796,
-0.013726672157645226,
-0.050176411867141724,
-0.029873734340071678,
0.01579282060265541,
0.010255600325763226,
0.019474739208817482,
0.047490932047367096,
0.000750551640521735,
0.010911432094871998,
0.016460992395877838,
-0.02344502881169319,
-0.05347282066941261,
-0.0835249200463295,
0.05293631553649902,
0.00044400320621207356,
0.031877968460321426,
0.023937026038765907,
-0.00829137209802866,
0.028824351727962494,
-0.0412365160882473,
-0.0030149274971336126,
-0.012914535589516163,
0.027786893770098686,
0.025383243337273598,
-0.005017814226448536,
-0.009159031324088573,
0.047615550458431244,
0.024683358147740364,
0.005089906044304371,
0.01036391407251358,
-0.0028035296127200127,
0.004201803356409073,
0.006615125574171543,
-0.04642614722251892,
-0.014190101996064186,
-0.012090031988918781,
-0.015273301862180233,
0.05096480995416641,
0.014460764825344086,
-0.009497497230768204,
0.027878591790795326,
-0.02019573748111725,
0.08458399027585983,
0.05248110741376877,
0.02728375233709812,
0.00208244938403368,
0.024705704301595688,
0.005306105595082045,
-0.03229736536741257,
0.020328562706708908,
-0.03350725769996643,
-0.02592127025127411,
-0.011504988186061382,
-0.008300893940031528,
0.02721908874809742,
-0.012984797358512878,
-0.019553035497665405,
0.015429157763719559,
0.022407742217183113,
0.040579769760370255,
0.016016444191336632,
-0.02141980640590191,
-0.058783214539289474,
0.03022065944969654,
0.02714383602142334,
-0.026820441707968712,
-0.006380923092365265,
0.015419029630720615,
0.027380790561437607,
-0.018177663907408714,
-0.032433610409498215,
-0.005435367580503225,
0.012524549849331379,
-0.00444561243057251,
0.016981342807412148,
0.01268845796585083,
-0.03773631900548935,
0.03846052661538124,
-0.020541386678814888,
0.02376088872551918,
0.039067599922418594,
-0.023771991953253746,
-0.015894534066319466,
-0.08303527534008026,
0.00166054698638618,
0.04107912629842758,
0.010540506802499294,
-0.007503380998969078,
-0.011934202164411545,
0.024035418406128883,
-0.038382235914468765,
-0.017987636849284172,
0.022496173158288002,
0.005093398038297892,
-0.05884309858083725,
0.002625673310831189,
0.011400304734706879,
-0.007484320551156998,
0.028716783970594406,
-0.02443203516304493,
-0.005874956492334604,
-0.008775479160249233,
-0.0669475793838501,
-0.01641736552119255,
-0.012286835350096226,
-0.032296568155288696,
-0.005727675277739763,
-0.04362763464450836,
0.005496364552527666,
0.0713079422712326,
0.0039770039729774,
-0.008244164288043976,
0.04508345574140549,
-0.005362598691135645,
-0.02895638346672058,
-0.007345713209360838,
-0.019516397267580032,
0.015295691788196564,
0.00630733510479331,
-0.02505132183432579,
0.03899078816175461,
0.01246175728738308,
-0.00008835277549223974,
0.03317245841026306,
-0.04947812110185623,
-0.022671286016702652,
-0.036003533750772476,
0.0024953021202236414,
0.013469827361404896,
-0.0315229669213295,
-0.014383325353264809,
0.011215727776288986,
-0.010104757733643055,
0.002695168135687709,
-0.04116382822394371,
-0.03834296390414238,
-0.022835491225123405,
-0.009549496695399284,
0.04110127314925194,
0.0026462909299880266,
-0.031464140862226486,
0.08201336115598679,
0.010868040844798088,
-0.03141795098781586,
-0.050067733973264694,
-0.014072100631892681,
-0.0038166744634509087,
-0.02042723260819912,
0.020030738785862923,
0.03032287210226059,
-0.05194747820496559,
-0.007773664779961109,
0.014054371044039726,
0.002381016267463565,
0.05763294920325279,
0.0012403464643284678,
0.002756360685452819,
-0.05292261391878128,
-0.008907580748200417,
-0.004822998307645321,
0.04467907175421715,
-0.0029275058768689632,
-0.047045428305864334,
0.02050067111849785,
-0.014409004710614681,
0.036968253552913666,
0.006489617750048637,
-0.03541788458824158,
0.057411812245845795,
0.007952210493385792,
-0.008223551325500011,
-0.05122058093547821,
0.020659925416111946,
-0.019692866131663322,
-0.032819442451000214,
0.029402971267700195,
0.01078019943088293,
0.0558379590511322,
-0.05130329355597496,
0.004674107767641544,
0.022033384069800377,
0.05556240677833557,
-0.023815101012587547,
-0.05741481855511665,
0.005232484079897404,
0.028912143781781197,
0.025833090767264366,
-0.0335133895277977,
0.02565312758088112,
0.018977636471390724,
0.03778368979692459,
0.06392982602119446,
0.0329848937690258,
-0.022904222831130028,
-0.004439452663064003,
-0.00905064307153225,
-0.028354991227388382,
0.03030974417924881,
0.05455506220459938,
-0.016225704923272133,
0.0496029295027256,
0.01652619242668152,
0.01964959129691124,
0.029068324714899063,
0.013820575550198555,
-0.0801803469657898,
0.033772584050893784,
-0.04885903373360634,
-0.025596924126148224,
0.005917965900152922,
-0.028046898543834686,
-0.01772969216108322,
-0.012517226859927177,
0.01050639245659113,
0.02789246290922165,
0.043339818716049194,
-0.04904227703809738,
-0.01217605359852314,
-0.026212481781840324,
-0.015896787866950035,
-0.001498921075835824,
0.01227959617972374,
0.02812945656478405,
-0.00976112112402916,
-0.006057161372154951,
0.04172218218445778,
-0.00684817461296916,
0.010833836160600185,
-0.011909935623407364,
-0.002556679304689169,
0.016510924324393272,
0.04279053211212158,
-0.011411883868277073,
0.022128146141767502,
0.006014387123286724,
0.01176793035119772,
0.0026498192455619574,
0.021906567737460136,
0.02640383131802082,
0.022577360272407532,
-0.02062826417386532,
-0.07271146774291992,
-0.025307731702923775,
-0.026419615373015404,
-0.0023361591156572104,
-0.0034998927731066942,
0.008353950455784798,
0.023237526416778564,
0.030002936720848083,
0.005995193030685186,
0.0561939999461174,
0.062455397099256516,
0.0066619194112718105,
-0.009510098956525326,
-0.040651604533195496,
-0.010898429900407791,
-0.06237579509615898,
-0.010794666595757008,
0.00045467662857845426,
0.025725258514285088,
-0.026964787393808365,
0.03000398352742195,
0.07246515154838562,
0.014399311505258083,
-0.013878006488084793,
0.022157792001962662,
0.02125273458659649,
0.026419425383210182,
-0.06001198664307594,
-0.007997596636414528,
-0.013741391710937023,
0.018925877287983894,
0.045503418892621994,
-0.012036573141813278,
-0.027553703635931015,
-0.05828797072172165,
-0.01018211618065834,
0.007455452810972929,
0.035242266952991486,
-0.03871987760066986,
0.00005057783346273936,
-0.04114905372262001,
-0.006316945888102055,
0.028373992070555687,
-0.046669214963912964,
0.02928939275443554,
-0.003602800890803337,
0.06891115754842758,
-0.022166822105646133,
0.004020006861537695,
-0.002359750447794795,
0.00007077305053826421,
-0.020822914317250252,
0.01892697811126709,
-0.030868718400597572,
0.010736792348325253,
0.00854215957224369,
0.02954249270260334,
0.008763035759329796,
0.034474797546863556,
0.004940730053931475,
0.0000740814721211791,
-0.02485480159521103,
0.006386526394635439,
-0.05945662409067154,
-0.0593486912548542,
-0.004116926807910204,
0.022461282089352608,
0.011554296128451824,
0.0018691932782530785,
-0.025719843804836273,
-0.04759562760591507,
0.02039913833141327,
0.04107550159096718,
0.004642686806619167,
-0.020215315744280815,
-0.01920376718044281,
0.024415263906121254,
0.048995159566402435,
-0.010331030935049057,
0.03680234029889107,
0.01637604460120201,
-0.004354707431048155,
0.0056828646920621395,
-0.009319666773080826,
0.034646082669496536,
-0.0025302055291831493,
-0.03426330164074898,
-0.030863914638757706,
0.036117132753133774,
-0.0462300144135952,
0.03288555145263672,
-0.0033233242575079203,
0.029076267033815384,
-0.017399460077285767,
-0.029889993369579315,
-0.01450977474451065,
0.03549753874540329,
0.029010340571403503,
0.030815495178103447,
0.0043878029100596905,
-0.009521679021418095,
0.022451281547546387,
-0.0008949307375587523,
-0.014509951695799828,
0.021480852738022804,
0.004825423937290907,
-0.02577216923236847,
-0.017408549785614014,
-0.0005910660838708282,
-0.019327042624354362,
-0.044405728578567505,
0.019408240914344788,
-0.05885893851518631,
0.03215300291776657,
-0.016378337517380714,
-0.004870106931775808,
0.03914647921919823,
-0.06765934079885483,
-0.029240544885396957,
0.00041309642256237566,
-0.020442696288228035,
0.03040689416229725,
-0.053020816296339035,
0.035188328474760056,
0.01136393565684557,
0.025019051507115364,
-0.036076582968235016,
-0.008618062362074852,
0.04893214628100395,
-0.024479135870933533,
0.004422128200531006,
-0.028471140190958977,
0.002557908184826374,
-0.005952121689915657,
-0.020381638780236244,
-0.010174567811191082,
0.04599073529243469,
-0.020046304911375046,
0.010233514942228794,
0.017371144145727158,
-0.009486502036452293,
0.038190245628356934,
0.029773438349366188,
-0.0028556932229548693,
-0.02203804813325405,
-0.00382741610519588,
0.0013259956613183022,
-0.001972887199372053,
0.05276759713888168,
-0.004526484292000532,
-0.007284552324563265,
-0.03219198063015938,
-0.0444851778447628,
0.020244594663381577,
0.01089091133326292,
0.06358091533184052,
0.024214129894971848,
0.028533756732940674,
0.003069920465350151,
-0.01155606284737587,
0.01956232264637947,
0.03366177901625633,
0.07031788676977158,
0.02738902159035206,
0.00459683034569025,
-0.04967861250042915,
-0.004648551810532808,
0.052937258034944534,
-0.00010973384632961825,
0.04101468250155449,
-0.005761078558862209,
0.060375090688467026,
-0.026140602305531502,
-0.017542622983455658,
-0.0011414116015657783,
-0.030052870512008667,
0.05819481611251831,
-0.016339262947440147,
-0.04941898211836815,
0.04708285257220268,
0.015906142070889473,
-0.005063268821686506,
-0.03267838805913925,
-0.035573627799749374,
0.011791758239269257,
0.022890498861670494,
-0.05111170560121536,
0.05646815896034241,
0.015707166865468025,
0.02640903741121292,
-0.011494805105030537,
-0.001707598683424294,
0.0059852153062820435,
-0.004032204858958721,
0.034162405878305435,
0.0170764047652483,
0.005285023711621761,
0.029622577130794525,
0.05151379853487015,
0.04203330725431442,
-0.010330181568861008,
0.008267240598797798,
0.026744147762656212,
0.0038907350972294807,
0.008423580788075924,
-0.01629166677594185,
0.011527431197464466,
0.052349843084812164,
-0.017826955765485764,
0.02258099801838398,
-0.0007364024640992284,
-0.04033162072300911,
0.04527071863412857,
0.0033556942362338305,
0.005406294483691454,
-0.038747165352106094,
-0.01316413376480341,
-0.022863242775201797,
-0.005151163786649704,
-0.007307944353669882,
0.002172244479879737,
0.010295718908309937,
-0.001711511635221541,
0.015837905928492546,
0.026374630630016327,
0.026043230667710304,
-0.006204681005328894,
-0.03024122305214405,
-0.049137480556964874,
-0.015796363353729248,
-0.04123005270957947,
0.009564658626914024,
0.010938436724245548,
-0.01964530721306801,
0.042278409004211426,
-0.05493505299091339,
0.0405883714556694,
-0.015480020083487034,
-0.009068207815289497,
0.0009526797221042216,
0.08035877346992493,
0.01694299839437008,
0.028248650953173637,
-0.0010768043575808406,
0.020971132442355156,
0.0962744876742363,
0.04535313695669174,
0.012760958634316921,
-0.027768243104219437,
-0.04775173217058182,
-0.01895936392247677,
0.0003409750934224576,
-0.03136327490210533,
0.01634843274950981,
0.04388096183538437,
-0.002493631560355425,
0.026095515117049217,
0.04216774180531502,
0.01340779010206461,
-0.043708618730306625,
0.027701161801815033,
-0.007464141584932804,
-0.04181760177016258,
0.008452377282083035,
-0.021051444113254547,
-0.04530314728617668,
-0.02571839652955532,
-0.027157330885529518,
0.04999065771698952,
-0.010427440516650677,
-0.019781459122896194,
-0.027401305735111237,
-0.0219818614423275,
0.035220418125391006,
0.01575971022248268,
-0.03223677724599838,
0.009358502924442291,
-0.008996263146400452,
-0.061494871973991394,
-0.04081593453884125,
0.02932986430823803,
0.0029030148871243,
-0.0023647346533834934,
0.003325178986415267,
0.035070594400167465,
0.034929532557725906,
0.009075857698917389,
-0.006423593033105135,
0.025698112323880196,
-0.05326750874519348,
0.0031340462155640125,
-0.02239092066884041,
0.044134270399808884,
-0.011486947536468506,
0.008580299094319344,
0.01960819587111473,
0.006956383585929871,
-0.0036011801566928625,
-0.030659638345241547,
-0.007039585150778294,
0.008402876555919647,
0.04341554269194603,
0.006204828154295683,
-0.027152808383107185,
-0.027209270745515823,
0.014553908258676529,
-0.03245444595813751,
0.009714947082102299,
-0.016347380355000496,
0.03043605014681816,
-0.017972001805901527,
-0.018300404772162437,
0.010477917268872261,
-0.023453500121831894,
0.0003393969382159412,
-0.038268860429525375,
-0.0210260022431612,
-0.04275932535529137,
-0.04005996137857437,
-0.006847490090876818,
0.045202549546957016,
0.029556648805737495,
-0.021513795480132103,
-0.01153656467795372,
-0.07190365344285965,
-0.011326776817440987,
0.06546960026025772,
-0.011818040162324905,
-0.004365488421171904,
-0.03972090035676956,
-0.04700182378292084,
-0.01578650437295437,
0.024019280448555946,
-0.015403852798044682,
0.026589205488562584,
-0.049619365483522415,
-0.009694236330688,
0.022472040727734566,
-0.061206892132759094,
-0.042342375963926315,
0.013894403353333473,
-0.004370919428765774,
0.02579823136329651,
-0.023666072636842728,
0.03912999480962753,
0.019119108095765114,
-0.004082216415554285,
0.04644565284252167,
0.02929096110165119,
-0.030420323833823204,
-0.009748115204274654,
0.01494462788105011,
-0.032437846064567566,
-0.006622034590691328,
0.01629466749727726,
0.04539715126156807,
-0.014576461166143417,
-0.01156089548021555,
-0.006302263587713242,
-0.037347059696912766,
-0.001267978805117309,
0.021304357796907425,
-0.02023746632039547,
0.006758449133485556,
-0.009099467657506466,
0.025999493896961212,
-0.022672809660434723,
0.007597378920763731,
-0.036252882331609726,
0.047335781157016754,
-0.0059773423708975315,
-0.03249160572886467,
-0.04081945866346359,
0.010684880428016186,
-0.03822669759392738,
0.021495748311281204,
0.009052349254488945,
0.008292955346405506,
0.0011476598447188735,
-0.02460704743862152,
0.0250056404620409,
-0.017334461212158203,
0.03622874617576599,
-0.013031021691858768,
0.014177433215081692,
0.049985747784376144,
-0.08697231113910675,
-0.09166987240314484,
0.030276119709014893,
-0.0037555699236691,
0.04830082505941391,
0.003958437126129866,
-0.04142279177904129,
-0.028852712363004684,
0.08766952157020569,
-0.024801066145300865,
-0.0235013198107481,
-0.0034195310436189175,
-0.03753644973039627,
-0.021301118656992912,
0.021968059241771698,
-0.04483059421181679,
-0.03989346697926521,
-0.0016785531770437956,
0.04252062737941742,
0.04814932867884636,
-0.0008040432585403323,
0.019644159823656082,
-0.0047990079037845135,
-0.01092102937400341,
0.002680702367797494,
0.04726742208003998,
-0.010154442861676216,
0.0013012007111683488,
0.06952407211065292,
-0.021593287587165833,
-0.00417208531871438,
-0.05294061824679375,
0.02597290277481079,
-0.11657065153121948,
-0.016766997054219246,
-0.01221926137804985,
0.01912786439061165,
0.06698017567396164,
-0.04949502646923065,
0.01573006808757782,
0.01391978282481432,
-0.08607536554336548,
-0.012977545149624348,
-0.02133227325975895,
0.011795064434409142,
0.016894103959202766,
0.005029104184359312,
-0.006109859794378281,
0.026228222995996475,
-0.002134122420102358,
0.026882918551564217,
0.028045054525136948,
-0.012156366370618343,
0.002178088529035449,
-0.017033563926815987,
-0.015552455559372902,
0.02344316802918911,
-0.007565992418676615,
-0.009244256652891636,
0.07103509455919266,
-0.04006928950548172,
-0.04599570855498314,
0.05906252562999725,
-0.016779564321041107,
0.01227029599249363,
0.041840050369501114,
0.041602663695812225,
0.024711037054657936,
0.024350028485059738,
-0.03492828458547592,
-0.01843687891960144,
-0.010523173958063126,
0.05590735003352165,
-0.005456120241433382,
0.03685745596885681,
-0.006986862048506737,
0.016899874433875084,
0.029489438980817795,
-0.05353871360421181,
-0.03187540918588638,
-0.008130048401653767,
0.005262371618300676,
-0.011033544316887856,
-0.004833425395190716,
-0.02752946875989437,
0.013788550160825253,
-0.029531212523579597,
-0.012406919151544571,
-0.04380551353096962,
0.009066657163202763,
0.03592724725604057,
-0.05382433906197548,
0.018456533551216125,
0.02728726528584957,
-0.007143451366573572,
0.007761375978589058,
-0.026600848883390427,
-0.016781942918896675,
-0.06047843396663666,
-0.03347848728299141,
0.002792339539155364,
0.030942201614379883,
-0.016522880643606186,
-0.006807573605328798,
-0.05400126799941063,
-0.03154728561639786,
0.03404951095581055,
-0.013752070255577564,
-0.00441088667139411,
0.006073720753192902,
-0.04045798256993294,
-0.008794364519417286,
-0.10749638825654984,
0.006076213903725147,
-0.01668528839945793,
-0.058975428342819214,
-0.06645964831113815,
-0.01046496070921421,
0.01439218781888485,
-0.00033439253456890583,
0.036444276571273804,
-0.03212623670697212,
-0.015393760986626148,
-0.008573333732783794,
-0.016591034829616547,
-0.0016567305428907275,
-0.02518879994750023,
-0.0009623090154491365,
-0.006578739266842604,
-0.03139631822705269,
0.010518612340092659,
-0.005316917784512043,
0.012080326676368713,
0.011425962671637535,
0.004369183909147978,
-0.008188068866729736,
0.007211507763713598,
-0.030219383537769318,
-0.03023618273437023,
0.011894403025507927,
0.026448773220181465,
-0.0010516369948163629,
0.05128387361764908,
-0.0024914771784096956,
-0.002617355203256011,
0.041082803159952164,
-0.015365480445325375,
-0.02301935665309429,
0.021100964397192,
-0.005435234867036343,
0.03781403973698616,
-0.04820651561021805,
0.0002063694701064378,
0.03334426507353783,
-0.05372520163655281,
0.012973573990166187,
0.006446976214647293,
-0.0014011571183800697,
-0.01868397556245327,
0.03763219714164734,
0.05665330961346626,
0.021270766854286194,
0.02454376593232155,
0.030014146119356155,
0.008789818733930588,
0.0013666899176314473,
0.011186128482222557,
0.019997205585241318,
-0.0016270489431917667,
-0.014687882736325264,
-0.0011813725577667356,
0.045067720115184784,
0.033603236079216,
0.03535153716802597,
0.04687533527612686,
0.06058555096387863,
0.001585304969921708,
-0.005015198141336441,
-0.019185958430171013,
-0.01689346507191658,
0.014913316816091537,
0.037060465663671494,
-0.015702182427048683,
0.07308706641197205,
-0.04876324534416199,
0.02763049304485321,
0.023503640666604042,
-0.04243377596139908,
-0.032760318368673325,
-0.011946866288781166,
-0.010990473441779613,
0.05161748453974724,
-0.02695602923631668,
-0.031491734087467194,
0.00034889523521997035,
0.023951690644025803,
0.050195299088954926,
0.0076821912080049515,
0.030049672350287437,
-0.02411886677145958,
-0.0026237356942147017,
-0.020803261548280716,
-0.01621541939675808,
0.0017517261439934373,
-0.018608301877975464,
0.052720218896865845,
0.03687620535492897,
0.035000868141651154,
0.005872212816029787,
0.00164255709387362,
-0.019425835460424423,
0.050467681139707565,
-0.0390017144382,
-0.04067782685160637,
-0.042329441756010056,
0.03238249570131302,
-0.0055241514928638935,
-0.002833771053701639
] |
<p>What is the <a href="http://en.wikipedia.org/wiki/Pseudotensor" rel="nofollow">pseudo tensor</a> in relativity?
How do we transform tensor and pseudo tensor under parity?</p>
| 10,814 |
[
-0.0208200141787529,
-0.012422994710505009,
-0.02919868938624859,
-0.07340320199728012,
0.06210961937904358,
0.03241109102964401,
-0.026420336216688156,
-0.024676010012626648,
-0.007149807643145323,
-0.024108700454235077,
0.02519582211971283,
0.018012601882219315,
0.0031243953853845596,
-0.009813270531594753,
0.02059256285429001,
0.03372880443930626,
0.0312429778277874,
0.01727238856256008,
-0.01322326809167862,
-0.04903321713209152,
0.047807421535253525,
0.009600487537682056,
-0.014284288510680199,
-0.00038412725552916527,
-0.026683785021305084,
0.021914489567279816,
0.015735825523734093,
-0.01694772019982338,
0.02625187300145626,
0.049729593098163605,
-0.021834533661603928,
-0.0030605453066527843,
0.004081792198121548,
-0.020875442773103714,
-0.007091827690601349,
-0.007275320123881102,
-0.0007926844991743565,
-0.029481198638677597,
0.051256660372018814,
0.030957350507378578,
-0.039346978068351746,
-0.011315304785966873,
-0.023090388625860214,
0.07047274708747864,
-0.022478684782981873,
0.028615225106477737,
0.003640573238953948,
-0.028049636632204056,
0.052381567656993866,
-0.054798584431409836,
0.09132986515760422,
0.010583033785223961,
0.019304217770695686,
-0.013409032486379147,
-0.03472404181957245,
0.021397139877080917,
0.10163731873035431,
0.07885634154081345,
-0.03513817861676216,
-0.08122974634170532,
-0.016789264976978302,
-0.008370946161448956,
0.0029658556450158358,
-0.02563139609992504,
-0.014583814889192581,
0.050004780292510986,
0.009416483342647552,
-0.012333579361438751,
0.026914823800325394,
-0.02335839346051216,
0.0035364702343940735,
-0.01132210809737444,
0.023103946819901466,
-0.019107265397906303,
0.01692650094628334,
-0.028918975964188576,
0.017061976715922356,
-0.004260890651494265,
0.059221770614385605,
0.0339633971452713,
0.013003586791455746,
-0.0012362380512058735,
-0.017211584374308586,
0.01845570094883442,
-0.01675591617822647,
-0.026174161583185196,
0.052991658449172974,
0.017661208286881447,
0.006762344390153885,
0.032538123428821564,
-0.0003729013551492244,
-0.028514906764030457,
0.018543817102909088,
-0.010438690893352032,
-0.010589580982923508,
0.047631461173295975,
0.020924832671880722,
0.04935341700911522,
0.0015343454433605075,
-0.004603198729455471,
0.022649480029940605,
-0.016419511288404465,
0.0005547535256482661,
0.05511415749788284,
0.0389958918094635,
-0.0059865922667086124,
-0.05245305597782135,
0.0033791332971304655,
-0.011463738046586514,
0.023834040388464928,
0.005563087295740843,
-0.005723017733544111,
-0.02848581038415432,
0.010412252508103848,
0.0304280873388052,
-0.03517155349254608,
0.011441017501056194,
-0.010011933743953705,
0.014675631187856197,
0.05425649136304855,
0.006839504931122065,
-0.015054544433951378,
0.038202475756406784,
-0.022334476932883263,
-0.036359526216983795,
0.007303475867956877,
0.04686887189745903,
-0.005406323820352554,
-0.020298026502132416,
0.028888562694191933,
0.016220401972532272,
-0.05583585798740387,
0.01920437254011631,
0.01735375076532364,
0.02410581149160862,
-0.036752745509147644,
-0.10776861011981964,
-0.09392720460891724,
0.01809506118297577,
-0.013377674855291843,
-0.028458371758461,
-0.08086498826742172,
0.05510883033275604,
0.01147770881652832,
0.0675804540514946,
-0.003754665609449148,
0.030396096408367157,
0.036588478833436966,
0.010309448465704918,
-0.004213064908981323,
0.0036196683067828417,
-0.012341936118900776,
-0.03683454170823097,
-0.032570719718933105,
-0.02136368863284588,
-0.08008463680744171,
-0.022416837513446808,
0.017531730234622955,
-0.020201705396175385,
-0.027092982083559036,
0.07526730746030807,
0.007692481391131878,
-0.012414468452334404,
0.019183866679668427,
-0.03305407613515854,
-0.013057315722107887,
0.08604059368371964,
0.031431715935468674,
-0.0025651976466178894,
0.05813061073422432,
-0.018040357157588005,
0.032710373401641846,
-0.00464592594653368,
0.07619000226259232,
0.02414836548268795,
-0.020493080839514732,
-0.005795639008283615,
-0.005828530993312597,
-0.0013981243828311563,
-0.0010890638222917914,
-0.0490514300763607,
-0.017871148884296417,
0.002301520202308893,
0.020440328866243362,
0.01168583519756794,
0.03648301213979721,
0.009322067722678185,
-0.01712045632302761,
0.03608730435371399,
-0.0755314752459526,
-0.021246984601020813,
-0.05253634229302406,
-0.011334974318742752,
0.013341402634978294,
-0.005312825087457895,
0.02034212462604046,
0.05499890819191933,
0.02665662206709385,
-0.03172304481267929,
-0.004435333423316479,
-0.007906094193458557,
0.06232791766524315,
0.019666612148284912,
0.007274283561855555,
0.010311387479305267,
0.0354529544711113,
0.04455927759408951,
-0.040039390325546265,
-0.009891936555504799,
-0.003990041557699442,
0.00640730420127511,
0.029436642304062843,
0.020373903214931488,
0.019537823274731636,
-0.038066912442445755,
-0.0037967581301927567,
-0.009196165949106216,
-0.0011434451444074512,
0.017996011301875114,
0.014309949241578579,
-0.03935098648071289,
0.05894096568226814,
0.032780855894088745,
-0.003132809419184923,
0.0020117706153541803,
0.009844130836427212,
0.0357799157500267,
0.031799398362636566,
0.0064725931733846664,
-0.015267016366124153,
-0.01735728792846203,
0.002332476433366537,
0.044648896902799606,
0.036045923829078674,
-0.043820206075906754,
0.013287093490362167,
0.022067343816161156,
0.03571821749210358,
0.020171532407402992,
0.01659511774778366,
0.0010002775816246867,
-0.04542120173573494,
-0.001555129885673523,
-0.017830872908234596,
0.03045002929866314,
0.020398739725351334,
0.01532314158976078,
0.009177297353744507,
0.032629430294036865,
-0.024245593696832657,
-0.016569681465625763,
0.027073951438069344,
0.01875852793455124,
0.000054694584832759574,
0.006559917703270912,
-0.034645337611436844,
0.04970020800828934,
-0.010140255093574524,
0.03973570838570595,
0.036550041288137436,
-0.0031242109835147858,
0.02052377164363861,
-0.03188679367303848,
-0.02586944028735161,
-0.0049988036043941975,
-0.005395835265517235,
-0.01542502362281084,
-0.0200516264885664,
0.011140059679746628,
-0.029167497530579567,
0.011452452279627323,
-0.045653048902750015,
-0.0006542989867739379,
-0.020528212189674377,
-0.010555628687143326,
0.026041721925139427,
-0.0009739085799083114,
0.045228101313114166,
-0.015567557886242867,
-0.040344350039958954,
0.0017394510796293616,
-0.00953457597643137,
0.01633591763675213,
0.00792653113603592,
-0.07098492980003357,
0.0635104775428772,
-0.05895186960697174,
-0.03342371806502342,
0.041788991540670395,
-0.012619241140782833,
0.03634059056639671,
0.029962411150336266,
-0.025585010647773743,
-0.04976212605834007,
-0.050239864736795425,
-0.02870456501841545,
0.006865119561553001,
-0.04264400154352188,
-0.0051127709448337555,
0.06608965247869492,
-0.026879630982875824,
-0.03341512754559517,
-0.0070282090455293655,
-0.06535106897354126,
-0.02819291688501835,
0.007778972387313843,
-0.0015375256771221757,
0.029350165277719498,
-0.028171923011541367,
0.03322145342826843,
0.02003360539674759,
-0.054498203098773956,
0.03310263901948929,
-0.0372147373855114,
-0.03280787542462349,
0.000948350119870156,
-0.015805574133992195,
0.048491839319467545,
0.001472220872528851,
-0.06800702214241028,
0.07913623750209808,
0.012298963963985443,
-0.03130415454506874,
-0.029167581349611282,
0.020805256441235542,
0.01502477377653122,
-0.04821016266942024,
0.021655257791280746,
0.03256069868803024,
-0.01209039706736803,
0.019511260092258453,
0.04451112449169159,
0.036107614636421204,
0.056359946727752686,
0.04354307800531387,
-0.04105374962091446,
-0.029073061421513557,
0.009370478801429272,
-0.035445887595415115,
0.03598347678780556,
0.006534989457577467,
-0.030028199777007103,
0.01930159144103527,
-0.006179377902299166,
0.018510039895772934,
-0.013646694831550121,
-0.032599009573459625,
0.056072596460580826,
0.016187934204936028,
0.020276613533496857,
-0.020627448335289955,
0.0517006516456604,
0.0019036870216950774,
0.0027615809813141823,
-0.015841664746403694,
0.04604653641581535,
0.006987545173615217,
-0.01497610379010439,
-0.008128710091114044,
0.019205376505851746,
0.020324502140283585,
-0.023024694994091988,
0.002497280016541481,
0.004561728332191706,
-0.032233454287052155,
0.03789083659648895,
-0.033751316368579865,
0.008013730868697166,
0.058288246393203735,
0.018561355769634247,
0.004020041320472956,
0.026109270751476288,
0.005144388414919376,
0.03404473885893822,
-0.0430738665163517,
0.011403773911297321,
-0.022866588085889816,
0.024376552551984787,
-0.008993245661258698,
0.06365954875946045,
0.027423135936260223,
0.01672479696571827,
-0.0010812601540237665,
0.003674544859677553,
-0.07416679710149765,
0.020146364346146584,
-0.016292516142129898,
0.0036670449189841747,
-0.03417050093412399,
0.001338909612968564,
0.017698122188448906,
-0.06435615569353104,
-0.02956228516995907,
-0.039623428136110306,
0.019445547834038734,
-0.04376116767525673,
0.027826039120554924,
0.011324137449264526,
-0.034165650606155396,
-0.02215808629989624,
0.04314210265874863,
0.06441780179738998,
-0.005010802298784256,
0.03384227305650711,
0.03684893250465393,
-0.018621711060404778,
-0.007629703730344772,
0.022362973541021347,
0.017320852726697922,
0.025811512023210526,
0.020090214908123016,
0.022737964987754822,
0.006139460019767284,
-0.05031082034111023,
0.001303945784457028,
0.018561484292149544,
0.06082528829574585,
0.03691171482205391,
-0.015367120504379272,
-0.016203386709094048,
-0.03561793267726898,
-0.022524487227201462,
-0.03130917251110077,
0.04451606050133705,
-0.0035171855706721544,
0.02162487432360649,
0.02055860497057438,
0.044933807104825974,
-0.00664031645283103,
0.019061338156461716,
0.07492600381374359,
-0.005293007008731365,
-0.014351080171763897,
-0.06117400527000427,
-0.03777492046356201,
-0.011582860723137856,
0.010539700277149677,
0.011754111386835575,
-0.0019059523474425077,
-0.03157716244459152,
-0.000025300454581156373,
0.0218203142285347,
0.02015538327395916,
-0.004545386414974928,
-0.002095048315823078,
-0.028421837836503983,
-0.006783232558518648,
-0.002803187118843198,
0.02969334088265896,
-0.017710760235786438,
0.04932890087366104,
0.07105176150798798,
0.0031664662528783083,
-0.016432996839284897,
-0.07899414747953415,
-0.008546441793441772,
0.029122214764356613,
0.050130005925893784,
-0.007508168928325176,
-0.03006817400455475,
-0.04890597611665726,
-0.008546982891857624,
0.06908286362886429,
-0.042419858276844025,
0.008096201345324516,
0.009490910917520523,
0.00268184719607234,
-0.012406140565872192,
-0.010182737372815609,
-0.009209280833601952,
0.042407549917697906,
-0.022302256897091866,
0.0012144739739596844,
-0.04375050961971283,
0.026550307869911194,
-0.01539220567792654,
-0.005311497021466494,
-0.003422018140554428,
0.03331613540649414,
0.02312237210571766,
0.019999464973807335,
-0.0002413838665233925,
0.06490730494260788,
-0.02919870801270008,
-0.06930927187204361,
-0.009554736316204071,
0.048002369701862335,
-0.03296896070241928,
0.029299771413207054,
-0.03256700932979584,
-0.02120206691324711,
0.013350361958146095,
-0.021078364923596382,
-0.001861745840869844,
0.028085501864552498,
-0.07311569899320602,
0.02184825949370861,
0.01081754919141531,
-0.012705703265964985,
0.046788159757852554,
0.0013995049521327019,
-0.05069877952337265,
-0.026799283921718597,
-0.024785397574305534,
0.030278371647000313,
-0.04227730631828308,
0.028581904247403145,
-0.023204509168863297,
-0.016523968428373337,
-0.056392695754766464,
0.06419643014669418,
-0.03243504464626312,
0.0119355833157897,
0.0141886742785573,
0.00969952903687954,
-0.00011430931044742465,
0.07067787647247314,
0.018264347687363625,
-0.02203095331788063,
0.003319795010611415,
-0.020390262827277184,
0.0009788599563762546,
-0.031068069860339165,
0.029031237587332726,
-0.005693485494703054,
-0.021020622923970222,
0.024664027616381645,
0.0019468244863674045,
0.015529518015682697,
0.02289651520550251,
-0.03492189943790436,
0.026242002844810486,
-0.05785603076219559,
0.018884485587477684,
0.003665407421067357,
-0.02533264458179474,
0.012192856520414352,
-0.034841615706682205,
-0.01609833911061287,
0.016445979475975037,
-0.011358963325619698,
0.031220361590385437,
-0.03851744905114174,
0.011540631763637066,
0.01690858043730259,
0.04206019267439842,
-0.061441387981176376,
-0.020335471257567406,
0.05170947313308716,
-0.030270492658019066,
-0.03243068978190422,
-0.01323944702744484,
0.0032695492263883352,
-0.020187189802527428,
-0.05217999219894409,
-0.011081814765930176,
0.07324837148189545,
-0.039707813411951065,
-0.03721676021814346,
-0.029652105644345284,
-0.010405070148408413,
0.02487344853579998,
-0.04470588266849518,
-0.01843370497226715,
0.001003564684651792,
-0.0010102029191330075,
-0.014325321651995182,
0.004825202282518148,
0.0417003370821476,
-0.018225383013486862,
-0.014619969762861729,
-0.027407318353652954,
-0.025189198553562164,
-0.007494860328733921,
-0.018397171050310135,
0.017779681831598282,
-0.0015178294852375984,
0.029964176937937737,
-0.04090369492769241,
-0.030321355909109116,
0.02871064655482769,
0.013083726167678833,
0.043460726737976074,
-0.0120235038921237,
0.009096344001591206,
-0.0551200807094574,
-0.030317427590489388,
0.026583781465888023,
0.0016457801684737206,
0.006237150169909,
-0.020708564668893814,
0.05875452980399132,
-0.015460627153515816,
0.01535631064325571,
0.002560738241299987,
-0.02261287346482277,
0.0019207332516089082,
0.02753530442714691,
-0.0006953005795367062,
0.015614034608006477,
0.003118783002719283,
-0.04944775626063347,
0.005150817334651947,
-0.002880098531022668,
-0.018599044531583786,
0.07971498370170593,
-0.022516367956995964,
0.04359103739261627,
0.01716524176299572,
-0.04001925140619278,
0.00819990411400795,
0.017430387437343597,
-0.0063563245348632336,
0.02736826427280903,
-0.02653610147535801,
0.025105727836489677,
-0.032525599002838135,
0.004598380997776985,
0.008935859426856041,
0.06517219543457031,
-0.028160344809293747,
0.017917409539222717,
0.018687989562749863,
0.014546297490596771,
0.020140763372182846,
-0.02350424788892269,
-0.048408590257167816,
0.06016671657562256,
-0.02073119953274727,
0.03062593564391136,
0.002834260230883956,
0.012825848534703255,
0.053876426070928574,
0.024510249495506287,
0.017909955233335495,
-0.04479483887553215,
-0.01135678868740797,
-0.031255826354026794,
0.0011229231022298336,
0.02217240072786808,
0.00418638251721859,
-0.028713012114167213,
0.011210431344807148,
0.03665042296051979,
-0.00605729641392827,
0.02526267059147358,
-0.013590485788881779,
-0.06755343824625015,
-0.021421073004603386,
-0.05782609060406685,
-0.022257890552282333,
0.049536652863025665,
-0.028188899159431458,
-0.019021134823560715,
-0.004217108245939016,
-0.05217614024877548,
0.013483748771250248,
0.006342420354485512,
0.028106482699513435,
-0.03793566673994064,
0.04992835968732834,
-0.02818324975669384,
0.022878389805555344,
-0.0034968468826264143,
-0.04624935984611511,
0.11992393434047699,
0.04600215703248978,
0.015290971845388412,
-0.08339042961597443,
0.0358155183494091,
-0.015920231118798256,
0.021050874143838882,
-0.032590217888355255,
0.027980489656329155,
-0.03509686514735222,
0.025942038744688034,
0.009252391755580902,
0.04817353934049606,
0.0011327099055051804,
-0.009820790961384773,
0.05349326133728027,
-0.04576391354203224,
-0.015564792789518833,
-0.02211548201739788,
-0.0022066193632781506,
-0.017359063029289246,
-0.01731264591217041,
-0.0010380903258919716,
0.02350255660712719,
-0.031042469665408134,
0.038515157997608185,
-0.06701501458883286,
-0.023607660084962845,
0.00040255492785945535,
0.014225720427930355,
-0.03810512647032738,
0.011733761057257652,
0.01924804225564003,
0.0010657260427251458,
-0.026517244055867195,
0.014555876143276691,
0.005821562837809324,
0.0022287031169980764,
0.030722789466381073,
0.03575979545712471,
0.007181190885603428,
-0.003094787010923028,
0.02987193688750267,
0.014508960768580437,
-0.0682298094034195,
0.035197801887989044,
-0.023227108642458916,
0.04561503604054451,
-0.012093913741409779,
-0.019315754994750023,
0.02093503065407276,
-0.004757281858474016,
0.01844560168683529,
-0.036577221006155014,
-0.0410374253988266,
0.02418537810444832,
-0.002796694403514266,
0.013208718039095402,
-0.014291915111243725,
-0.027939973399043083,
0.011750273406505585,
0.0018385701114311814,
0.05211437866091728,
-0.026462538167834282,
0.0014453318435698748,
0.0073835719376802444,
-0.01807919330894947,
0.028376784175634384,
-0.018362982198596,
-0.01259378157556057,
-0.026917079463601112,
-0.011950491927564144,
0.0020523632410913706,
-0.001931510167196393,
0.02214154042303562,
-0.016504865139722824,
0.04349130764603615,
-0.0083792544901371,
-0.009669627994298935,
-0.023506170138716698,
-0.020490329712629318,
0.019709819927811623,
-0.029377570375800133,
-0.025938449427485466,
-0.026755474507808685,
0.01146960724145174,
0.04829849675297737,
0.04573497921228409,
-0.020476236939430237,
0.006918102037161589,
-0.020639050751924515,
-0.0025744831655174494,
0.019987113773822784,
-0.015101859346032143,
-0.014647331088781357,
-0.006258848588913679,
0.02403089962899685,
-0.01904202252626419,
-0.0378597266972065,
0.025108421221375465,
0.06814379245042801,
0.013680553995072842,
-0.018026748672127724,
0.013106686994433403,
-0.03833521157503128,
-0.01152094453573227,
0.017961546778678894,
-0.020470069721341133,
-0.008858236484229565,
0.005611968692392111,
0.0076508913189172745,
-0.049701981246471405,
-0.012148694135248661,
-0.0043471320532262325,
-0.03729650378227234,
0.02298308163881302,
0.04636477679014206,
-0.03049062378704548,
-0.0057067605666816235,
0.010911879129707813,
0.029210524633526802,
-0.045852962881326675,
-0.01591813750565052,
-0.013890077359974384,
0.026381436735391617,
-0.003944435156881809,
-0.03368574008345604,
-0.00741957314312458,
0.03755376115441322,
-0.002949240617454052,
-0.018000338226556778,
0.035209182649850845,
0.008169096894562244,
-0.028171181678771973,
0.007179178297519684,
0.053663767874240875,
0.005192621145397425,
0.037636660039424896,
0.003253866219893098,
-0.021326972171664238,
0.021810490638017654,
-0.049881916493177414,
-0.0321248434484005,
0.055965594947338104,
-0.010250672698020935,
0.03449179232120514,
-0.005701957270503044,
-0.02569141983985901,
-0.014540829695761204,
0.0625889003276825,
-0.03367272764444351,
-0.03032853826880455,
-0.01383171696215868,
-0.04208153113722801,
-0.001843320787884295,
-0.0020312718115746975,
0.009304240345954895,
-0.034696709364652634,
-0.0350429005920887,
0.030587567016482353,
0.03845788910984993,
-0.020456459373235703,
-0.0014032409526407719,
-0.008964764885604382,
0.02833094447851181,
0.0027949323412030935,
-0.0024096921551972628,
0.010667914524674416,
-0.013145418837666512,
0.0300871841609478,
0.004820449743419886,
0.010224085301160812,
0.019530583173036575,
0.0067972601391375065,
-0.09870734810829163,
0.0006031733355484903,
-0.012505403719842434,
-0.016522690653800964,
0.04233084246516228,
-0.08137887716293335,
0.017051324248313904,
0.02236301079392433,
-0.04531383141875267,
0.0702173113822937,
-0.01283023040741682,
-0.04887400567531586,
0.01595715433359146,
0.012297321110963821,
-0.04335980862379074,
0.08880661427974701,
0.03380556404590607,
0.027418451383709908,
0.026949921622872353,
-0.01805453933775425,
-0.019442880526185036,
-0.05524187907576561,
-0.02907879650592804,
-0.010450168512761593,
-0.014072587713599205,
-0.024899009615182877,
0.07663979381322861,
0.008614035323262215,
-0.04713044315576553,
0.0528884120285511,
-0.018755249679088593,
-0.015282643027603626,
-0.006855198182165623,
0.0029320777393877506,
-0.0022566940169781446,
-0.010314631275832653,
0.015558307990431786,
0.0023717458825558424,
-0.03833542764186859,
0.00648152083158493,
0.010247116908431053,
0.046288639307022095,
-0.006877231411635876,
-0.012045525014400482,
-0.0035959589295089245,
-0.03182156756520271,
0.0014455325435847044,
0.0360632948577404,
-0.024539342150092125,
-0.023929519578814507,
-0.0006161542260088027,
-0.0004405801882967353,
-0.007949363440275192,
-0.031208094209432602,
0.020442908629775047,
-0.026955489069223404,
0.002253846265375614,
0.0363873727619648,
-0.016914859414100647,
-0.0019505665404722095,
0.04403866454958916,
-0.025417668744921684,
-0.02309403009712696,
0.042853858321905136,
0.0004320253792684525,
0.010118181817233562,
-0.06056605651974678,
-0.020594730973243713,
0.015402326360344887,
-0.011187341064214706,
-0.011486675590276718,
-0.01632102020084858,
-0.02027859166264534,
0.03347240760922432,
0.04555438086390495,
0.03686334565281868,
0.012931385077536106,
-0.02108297124505043,
-0.0260010976344347,
-0.06464949995279312,
0.015283025801181793,
-0.03255855664610863,
-0.018659723922610283,
-0.033892981708049774,
-0.02272047847509384,
-0.037044595927000046,
0.025407865643501282,
0.05119365081191063,
0.0045149000361561775,
-0.008967716246843338,
0.0005495062214322388,
-0.021839521825313568,
-0.01052992232143879,
-0.044244468212127686,
-0.02816438116133213,
0.012695529498159885,
-0.022460853680968285,
0.01522955484688282,
-0.00610653031617403,
-0.009813696146011353,
0.03273994103074074,
-0.013152340427041054,
0.001492659212090075,
0.040031589567661285,
0.018322188407182693,
-0.01779789850115776,
0.028160735964775085,
0.023129815235733986,
0.008726857602596283,
0.05722300708293915,
0.022969985380768776,
0.01641557551920414,
0.018122194334864616,
-0.00462472066283226,
-0.03408905118703842,
-0.024678194895386696,
-0.04979674145579338,
-0.020553654059767723,
-0.03230174630880356,
0.005919229239225388,
0.03898660093545914,
-0.023605184629559517,
0.008979315869510174,
0.06957422941923141,
-0.044919952750205994,
0.013441648334264755,
0.06905686855316162,
0.03837086260318756,
0.00997783150523901,
-0.014336523599922657,
0.019439203664660454,
-0.005766109097748995,
-0.011766910552978516,
0.013142435811460018,
0.036879464983940125,
-0.0002715886221267283,
-0.019570544362068176,
0.006895928643643856,
0.009131201542913914,
-0.009249255992472172,
0.01751176454126835,
0.006793868727982044,
0.08160378038883209,
-0.03575342521071434,
0.021964864805340767,
0.007533385418355465,
-0.02832529880106449,
0.05719583109021187,
0.01683018170297146,
-0.007971570827066898,
0.06542286276817322,
-0.014771008864045143,
0.004636884201318026,
-0.01612166315317154,
-0.00008271732076536864,
-0.014538939110934734,
0.01718699187040329,
-0.001398625667206943,
0.03760521113872528,
-0.015625059604644775,
-0.01962815411388874,
-0.03572038561105728,
-0.013493383303284645,
0.0287712924182415,
-0.011672143824398518,
0.013283485546708107,
-0.005031506065279245,
-0.013972518034279346,
0.04717615246772766,
-0.020430779084563255,
-0.0036961333826184273,
-0.012490556575357914,
0.00393972871825099,
0.015542501583695412,
0.03864731639623642,
-0.034755889326334,
0.0006826678873039782,
-0.016259605064988136,
0.02791639231145382,
-0.0988200306892395,
-0.0015542061300948262,
0.003498893929645419,
0.022784797474741936,
-0.01756616309285164,
-0.020126722753047943
] |
<p>Suppose I have an empty room of $24 m^3$ and I want to heat it to 50 °C, assuming the current room is well isolated and the current temperature is 20 °C. </p>
<ul>
<li>How much power (in Watts) would a single heating element need to produce in order to reach the 50°C? </li>
</ul>
<p>Having googled around I found this <a href="http://www.deltat.com/pdf/Quick%20estimates%20for%20wattage%20requirements.pdf" rel="nofollow">chart</a>, specifically figure 34T seems to be of interest.</p>
<p>I was looking at a heating element that provides $3 kW$ and an air displacement of $127 f^3/m$. If I'm reading the figure correctly it specifies for increases of 50 degrees. But I assume more factors are of importance, specifically the room size.</p>
<blockquote>
<p>Note:
Initially I asked this question on the general chat channel because I thought
it would be too localised and simple but It was not deemed so.</p>
<p>Edit #1: Removed the time needed subquestion, instead assume the heating element is powered on for a period of one hour time.</p>
</blockquote>
| 10,815 |
[
-0.03703770041465759,
-0.03021165356040001,
-0.02458364889025688,
0.004889227915555239,
0.06836532801389694,
-0.015027366578578949,
-0.06432309746742249,
-0.051455918699502945,
0.01746109500527382,
-0.026842180639505386,
0.05082028731703758,
0.03606949746608734,
0.05509514361619949,
0.004237685352563858,
-0.007532369811087847,
0.00871824100613594,
-0.006473364774137735,
-0.04106729105114937,
0.007537447847425938,
-0.01955946534872055,
0.013661360368132591,
0.03642505407333374,
-0.034386392682790756,
0.00633428106084466,
-0.040896106511354446,
0.046386320143938065,
0.046060048043727875,
0.03509768471121788,
-0.014684607274830341,
0.01691649667918682,
-0.014856690540909767,
-0.050776395946741104,
0.03084106743335724,
0.051153771579265594,
0.07394788414239883,
-0.020166195929050446,
-0.020615912973880768,
-0.03000880964100361,
-0.02191099151968956,
0.0591646172106266,
-0.012178914621472359,
-0.03442932292819023,
0.01719127967953682,
-0.007227709982544184,
-0.022633135318756104,
0.006697295233607292,
-0.017733074724674225,
-0.0372246578335762,
0.04750308394432068,
-0.08375412970781326,
0.07325123995542526,
0.014241320081055164,
0.04743250086903572,
0.005777368322014809,
0.017922911792993546,
0.015695834532380104,
0.04691452533006668,
0.019431743770837784,
-0.006780077237635851,
-0.02546478994190693,
-0.020629985257983208,
-0.011914413422346115,
-0.02672579698264599,
-0.0289864931255579,
-0.03988607972860336,
0.004351987037807703,
-0.020304329693317413,
-0.017476238310337067,
0.02042275294661522,
-0.0020500465761870146,
0.04474659636616707,
0.03011435456573963,
0.05284908041357994,
-0.006378795951604843,
0.0009734421037137508,
-0.026352420449256897,
-0.01928931660950184,
0.03875007852911949,
0.05574407801032066,
0.04452916234731674,
-0.023837026208639145,
0.0021499122958630323,
0.05911170691251755,
0.04591751471161842,
0.0044145709834992886,
0.005601820070296526,
0.056049808859825134,
0.005461431574076414,
0.02732575684785843,
-0.010568001307547092,
-0.01564713940024376,
0.024950357154011726,
0.011540966108441353,
0.002511636819690466,
0.02980858087539673,
0.016575368121266365,
-0.024733494967222214,
0.04512539133429527,
0.010881108231842518,
-0.023020971566438675,
0.03619594871997833,
0.005787537433207035,
0.04655065760016441,
0.03618164733052254,
0.021609677001833916,
-0.018121372908353806,
-0.006718602031469345,
-0.029218310490250587,
0.03874090313911438,
-0.013603796251118183,
-0.03914465010166168,
0.023997943848371506,
-0.008005224168300629,
-0.010990701615810394,
0.00606554513797164,
-0.042642831802368164,
-0.006980128586292267,
-0.02204723283648491,
0.057693351060152054,
0.009355287998914719,
0.022570373490452766,
0.00418913783505559,
0.05228317528963089,
-0.06388421356678009,
-0.07565812021493912,
0.023557448759675026,
-0.01198670919984579,
-0.006943018175661564,
-0.0599868968129158,
0.058674637228250504,
0.005561312660574913,
-0.029556985944509506,
0.01299615204334259,
-0.030137622728943825,
0.019274180755019188,
-0.023010363802313805,
-0.0728122740983963,
-0.055450186133384705,
0.037358518689870834,
-0.013808513060212135,
-0.027871154248714447,
-0.09383531659841537,
-0.008288518525660038,
0.03351351246237755,
0.056510116904973984,
-0.009531314484775066,
0.023640679195523262,
-0.048513785004615784,
0.030778154730796814,
-0.024912141263484955,
-0.057880908250808716,
-0.006944057997316122,
0.018041791394352913,
0.002149339532479644,
0.02425016090273857,
-0.03745781630277634,
0.039619505405426025,
0.054429780691862106,
0.006224909797310829,
-0.02485998347401619,
0.053890909999608994,
0.026408232748508453,
-0.011916001327335835,
0.026888418942689896,
0.02973429672420025,
-0.031907156109809875,
0.09133870154619217,
-0.005663524381816387,
-0.003993529826402664,
0.029979832470417023,
0.02726738527417183,
-0.018640106543898582,
0.008023127913475037,
-0.013154382817447186,
0.05207459628582001,
-0.015202521346509457,
-0.010962741449475288,
-0.08528243750333786,
0.019901592284440994,
0.03789681941270828,
-0.04712047800421715,
-0.001742732827551663,
0.013910318724811077,
0.0056039257906377316,
0.0095368642359972,
0.026294108480215073,
-0.005806117784231901,
0.018005922436714172,
0.00791503582149744,
-0.012108124792575836,
-0.03664092347025871,
-0.08609287440776825,
-0.0006514489068649709,
0.000525547016877681,
0.02448420040309429,
0.016408348456025124,
0.01101786270737648,
0.050292178988456726,
-0.026846138760447502,
-0.03021467849612236,
0.016322147101163864,
-0.013551478274166584,
0.03125273808836937,
-0.011584330350160599,
0.02880266308784485,
0.05467735603451729,
0.06076521426439285,
0.0034814614336937666,
0.014431865885853767,
-0.041119955480098724,
-0.00797357875853777,
-0.03346393629908562,
-0.036662593483924866,
0.024110933765769005,
0.011873950250446796,
-0.011387432925403118,
-0.0021205067168921232,
-0.01842183992266655,
-0.023145342245697975,
0.03510722145438194,
0.006603794638067484,
0.07704039663076401,
0.037484873086214066,
0.024104665964841843,
-0.002543237991631031,
0.04430467262864113,
0.002922608284279704,
-0.006090330425649881,
-0.04164639860391617,
-0.0437198244035244,
-0.057541754096746445,
0.0027212915010750294,
0.009339687414467335,
0.011739549227058887,
-0.030279982835054398,
0.0065429420210421085,
0.03771567344665527,
0.025705067440867424,
0.059964463114738464,
0.030365414917469025,
0.005280874669551849,
0.004917622543871403,
0.018521957099437714,
0.0150571558624506,
0.007373744156211615,
0.007608228363096714,
-0.019947893917560577,
0.028918275609612465,
0.008836942724883556,
0.020190298557281494,
0.030223358422517776,
0.034143686294555664,
0.008156188763678074,
0.008385718800127506,
-0.01618249900639057,
-0.0068908752873539925,
0.0233476459980011,
-0.0404115691781044,
0.010809352621436119,
-0.009092775173485279,
0.02259271778166294,
0.047260452061891556,
-0.00020724916248582304,
-0.0425594188272953,
0.0042373803444206715,
-0.010162840597331524,
0.018432045355439186,
-0.008991394191980362,
0.026894856244325638,
-0.03311331942677498,
0.010217104107141495,
-0.04066704213619232,
0.030348200350999832,
0.006228824146091938,
-0.029519302770495415,
0.009329481050372124,
0.014040403068065643,
0.04319596290588379,
-0.05038861557841301,
-0.01751716621220112,
-0.016395902261137962,
-0.029764449223876,
0.016749553382396698,
-0.004960405640304089,
-0.032565999776124954,
0.018398413434624672,
-0.010319393128156662,
-0.04288988932967186,
0.05011313781142235,
-0.014927921816706657,
-0.01979788951575756,
0.033609598875045776,
-0.005718556698411703,
-0.06105469912290573,
-0.003283035010099411,
-0.01753765158355236,
0.04658634960651398,
-0.030262617394328117,
0.0026281392201781273,
0.03212257847189903,
-0.013960257172584534,
-0.04323388636112213,
0.030017223209142685,
-0.059090256690979004,
-0.008504645898938179,
-0.007186261937022209,
-0.013874483294785023,
0.02964112162590027,
-0.02503904141485691,
0.006574659608304501,
0.04531648010015488,
-0.04936796799302101,
0.00424394803121686,
-0.03784523904323578,
-0.044155389070510864,
-0.005757419392466545,
0.003710090648382902,
0.03908681124448776,
-0.0007111591403372586,
-0.026055999100208282,
0.0357360765337944,
-0.005481933243572712,
-0.04864165559411049,
-0.007853619754314423,
-0.06246979534626007,
-0.008055323734879494,
-0.0273157749325037,
-0.011645144782960415,
0.010830880142748356,
-0.03024841472506523,
0.03447745367884636,
0.005696755833923817,
-0.00037319830153137445,
0.04259354993700981,
0.05569538474082947,
-0.015049084089696407,
0.0062453714199364185,
-0.005440225824713707,
0.01624344289302826,
0.061012934893369675,
-0.002370202448219061,
-0.016474924981594086,
0.008327553980052471,
-0.004890087526291609,
0.043994929641485214,
0.03888244554400444,
-0.06549159437417984,
0.020520176738500595,
0.011131136678159237,
0.02815297618508339,
-0.0757729783654213,
0.023155340924859047,
-0.017584282904863358,
-0.011475102044641972,
-0.020671110600233078,
0.06747627258300781,
0.05138973146677017,
-0.016265463083982468,
-0.01710275560617447,
0.038635339587926865,
0.04054327681660652,
0.03906622529029846,
-0.031085826456546783,
0.007379928603768349,
0.01131937000900507,
-0.02336064539849758,
0.018676305189728737,
-0.009447458200156689,
0.025277450680732727,
0.007554071489721537,
0.04944339394569397,
0.01338327955454588,
-0.002186921425163746,
0.013246385380625725,
-0.056220877915620804,
-0.02669326588511467,
0.008474226109683514,
0.08623354882001877,
-0.01792619191110134,
0.029436051845550537,
-0.0011144628515467048,
-0.0016504196682944894,
0.02550523355603218,
-0.037747059017419815,
-0.06326628476381302,
0.058209128677845,
-0.024098273366689682,
-0.0009437953121960163,
0.03317342326045036,
-0.00696847727522254,
-0.009591002948582172,
-0.0026087749283760786,
0.010575643740594387,
0.004818607121706009,
0.019592437893152237,
-0.02090664766728878,
0.03565692901611328,
0.0024537858553230762,
-0.014996281825006008,
0.00390107580460608,
0.018027933314442635,
0.055335983633995056,
-0.06865628808736801,
0.004187115002423525,
0.03761853277683258,
-0.012053263373672962,
-0.003359398804605007,
-0.004991086665540934,
0.046401504427194595,
-0.007503258064389229,
0.0240496676415205,
0.044040363281965256,
0.021411743015050888,
-0.043271105736494064,
0.01720111444592476,
-0.009409379214048386,
0.026292437687516212,
-0.0001479594939155504,
-0.014130600728094578,
0.00849009957164526,
-0.01331108808517456,
-0.009909161366522312,
0.036918140947818756,
0.016721520572900772,
-0.010463953949511051,
0.045522358268499374,
0.021591516211628914,
-0.005827926564961672,
-0.03059522435069084,
0.020516520366072655,
0.052844662219285965,
-0.001974786864593625,
-0.014385783113539219,
-0.042407795786857605,
-0.009994999505579472,
-0.022584889084100723,
0.003629387589171529,
0.020351042971014977,
-0.001540510798804462,
-0.005386327393352985,
0.002097537973895669,
0.007849370129406452,
-0.0014706030488014221,
-0.01832526922225952,
0.05891096591949463,
0.029979096725583076,
0.04859099164605141,
0.030066747218370438,
-0.054128289222717285,
-0.012372231110930443,
0.022320138290524483,
-0.015003268606960773,
-0.021063843742012978,
0.007858212105929852,
-0.09655817598104477,
-0.03886890411376953,
0.027265267446637154,
0.06355167180299759,
-0.02599615789949894,
-0.0032452153973281384,
-0.03955496475100517,
0.011176449246704578,
0.04806406795978546,
-0.02378864958882332,
0.03944059833884239,
-0.02370607666671276,
-0.0018027223413810134,
0.0042875781655311584,
-0.04817282781004906,
-0.021987194195389748,
-0.016477499157190323,
0.01953124813735485,
0.018490217626094818,
-0.00952993892133236,
-0.03462013229727745,
0.0289413221180439,
0.026783550158143044,
0.046384427696466446,
0.012338345870375633,
-0.009291154332458973,
-0.000998927978798747,
0.0027078636921942234,
0.010329931043088436,
0.019002161920070648,
-0.061957407742738724,
-0.022410783916711807,
0.0041414424777030945,
-0.010407955385744572,
0.006396675016731024,
-0.05372403562068939,
-0.03861174359917641,
0.027188794687390327,
0.03027227520942688,
-0.038312382996082306,
-0.02063910849392414,
-0.051029857248067856,
0.06302478164434433,
0.030403289943933487,
0.017046263441443443,
0.059939999133348465,
0.04014088213443756,
-0.04186422377824783,
0.02276723086833954,
-0.023826515302062035,
0.029436606913805008,
-0.014159344136714935,
-0.0016246571904048324,
-0.034760165959596634,
0.019851798191666603,
-0.0037835908588021994,
0.05850100517272949,
-0.017891747877001762,
0.030805567279458046,
-0.003906198311597109,
-0.011604716069996357,
0.007488376926630735,
0.032081589102745056,
0.017691396176815033,
-0.0011814484605565667,
-0.007824080064892769,
0.03238610178232193,
-0.006408866960555315,
-0.061395566910505295,
0.014140086248517036,
-0.02863067016005516,
0.02751120552420616,
0.012463674880564213,
-0.03574991598725319,
0.001669231685809791,
-0.012864415533840656,
-0.004976511932909489,
0.01519097201526165,
-0.04526759684085846,
0.04669981449842453,
-0.04166220501065254,
0.039705682545900345,
0.014777754433453083,
-0.06570538133382797,
-0.009438390843570232,
-0.011612732894718647,
0.03234857693314552,
0.0032751711551100016,
-0.01980053260922432,
0.02777843177318573,
-0.025997573509812355,
0.013319825753569603,
-0.04685484990477562,
-0.021550333127379417,
0.019902579486370087,
0.01453319936990738,
-0.017818506807088852,
-0.0494055300951004,
-0.044206634163856506,
-0.027099885046482086,
-0.05480450764298439,
-0.016107000410556793,
0.047915227711200714,
-0.012747402302920818,
-0.01652919128537178,
-0.013686363585293293,
0.03581056743860245,
0.02680429071187973,
0.0332321934401989,
-0.029563581570982933,
0.001398721942678094,
-0.027915367856621742,
-0.0398121140897274,
-0.01749841868877411,
0.05618913471698761,
-0.028337882831692696,
0.0027748344000428915,
0.012622511945664883,
-0.011980261653661728,
0.05024871975183487,
0.013096273876726627,
-0.027571987360715866,
0.02840997464954853,
0.051019832491874695,
0.004448515363037586,
-0.0028731038328260183,
0.06733833998441696,
0.026421286165714264,
0.022100146859884262,
-0.009022615849971771,
-0.008463775739073753,
-0.029496673494577408,
0.00015292224998120219,
0.019254012033343315,
-0.0026688219513744116,
0.01773475483059883,
-0.00801271665841341,
0.05534715950489044,
0.0010245731100440025,
0.013785593211650848,
0.040871262550354004,
-0.011435565538704395,
0.010101723484694958,
-0.019117189571261406,
0.00895623117685318,
-0.001295388676226139,
-0.031847987323999405,
-0.0013477432075887918,
-0.0248009841889143,
-0.03301846608519554,
0.016045808792114258,
0.02882387675344944,
-0.014777054078876972,
0.028492247685790062,
0.002787607489153743,
-0.018191950395703316,
0.047129955142736435,
0.026583822444081306,
-0.003792218631133437,
0.008505711331963539,
0.0027734602335840464,
0.006513205356895924,
0.008401632308959961,
-0.03434688225388527,
0.030049262568354607,
0.00869606900960207,
0.022430503740906715,
0.0010223097633570433,
0.036563690751791,
0.008714116178452969,
0.01647549495100975,
-0.057124000042676926,
-0.034545499831438065,
0.00484849326312542,
-0.020221378654241562,
0.01814720593392849,
-0.02321273647248745,
0.006458084564656019,
0.032821252942085266,
0.003688863944262266,
-0.02117619477212429,
-0.041736915707588196,
0.010595559142529964,
-0.03944208472967148,
0.015647634863853455,
0.03108837641775608,
-0.02757047489285469,
-0.0036037894897162914,
0.009699540212750435,
0.013615970499813557,
-0.03335846588015556,
0.012237664312124252,
-0.02297993376851082,
-0.05341312661767006,
-0.008596406318247318,
-0.024208376184105873,
-0.04022097960114479,
0.032775744795799255,
-0.013368376530706882,
-0.03901621326804161,
0.009689715690910816,
-0.029265599325299263,
0.004939812235534191,
-0.018869346007704735,
0.03436807915568352,
0.021753588691353798,
0.06664470583200455,
-0.017429107800126076,
-0.008630591444671154,
-0.026196181774139404,
0.030811544507741928,
0.11849238723516464,
0.058104824274778366,
-0.0179377943277359,
-0.040371593087911606,
0.004494117572903633,
-0.018984654918313026,
-0.05684102326631546,
-0.015254460275173187,
0.003778316779062152,
-0.030783336609601974,
-0.0191966462880373,
0.023092662915587425,
0.06087857112288475,
-0.02543712966144085,
0.03610625118017197,
0.053922634571790695,
-0.023569632321596146,
-0.01994103565812111,
0.01747189275920391,
0.0009531234391033649,
-0.019562924280762672,
0.007150632329285145,
-0.009909539483487606,
-0.0008458177908323705,
-0.03525987267494202,
0.002901994390413165,
0.009387265890836716,
-0.03829184174537659,
0.04098299890756607,
-0.004533701576292515,
-0.04752574488520622,
-0.04405278339982033,
-0.020937886089086533,
-0.016562584787607193,
-0.05234025791287422,
0.010453551076352596,
0.019642949104309082,
0.00046968040987849236,
-0.008241859264671803,
0.07028522342443466,
0.021017897874116898,
0.0050319950096309185,
0.014633534476161003,
0.02392960526049137,
-0.009936463087797165,
-0.04988490417599678,
-0.031354423612356186,
-0.0148231852799654,
-0.011280013248324394,
-0.004004601389169693,
0.013148929923772812,
0.05546214058995247,
-0.0005745143862441182,
-0.03401108458638191,
-0.006727167405188084,
-0.04154079407453537,
0.05234374478459358,
-0.07210782170295715,
-0.030073704198002815,
-0.020524274557828903,
0.04410785064101219,
0.01915503852069378,
0.0067213852889835835,
0.02413540706038475,
-0.01200889702886343,
-0.002154712798073888,
0.004295166581869125,
0.06448200345039368,
0.03537219762802124,
-0.01640409044921398,
-0.03270303085446358,
-0.039453521370887756,
-0.013438781723380089,
0.024175619706511497,
0.03937054052948952,
0.024535251781344414,
0.05009390786290169,
-0.013042165897786617,
-0.03591655194759369,
-0.03718817979097366,
-0.05164709314703941,
0.025509996339678764,
0.007697769906371832,
-0.029493873938918114,
-0.02543776109814644,
-0.0052621029317379,
-0.022585440427064896,
0.06319880485534668,
0.006914323195815086,
-0.029290910810232162,
0.02812069095671177,
0.005593521054834127,
0.05189654603600502,
-0.04511064663529396,
-0.026279132813215256,
0.016895590350031853,
-0.06251703947782516,
-0.000663033570162952,
0.0031884636264294386,
0.05717102810740471,
0.006507703103125095,
-0.02509678527712822,
-0.02065730094909668,
0.023831376805901527,
-0.04812095686793327,
-0.024188918992877007,
-0.025780925527215004,
-0.046491291373968124,
-0.009550029411911964,
0.009630939923226833,
-0.02944551408290863,
-0.010769018903374672,
-0.05306386947631836,
-0.018404079601168633,
0.009644069708883762,
-0.01990065723657608,
0.018522825092077255,
-0.017539149150252342,
0.045118749141693115,
-0.009946332313120365,
0.024698713794350624,
-0.023724254220724106,
-0.0020878477953374386,
-0.026683876290917397,
-0.018458079546689987,
0.05316133424639702,
0.01044665090739727,
-0.023167062550783157,
0.02783389389514923,
-0.023771142587065697,
-0.004252152983099222,
0.0086398646235466,
0.017435111105442047,
-0.010001624003052711,
-0.062098179012537,
-0.020812254399061203,
-0.014021440409123898,
0.0330398827791214,
-0.028595319017767906,
-0.023343926295638084,
0.041795916855335236,
-0.004036667291074991,
-0.025546802207827568,
0.03182275965809822,
-0.015052246861159801,
0.026836352422833443,
0.012434643693268299,
-0.003865135135129094,
-0.022203857079148293,
0.05650500953197479,
-0.006908394396305084,
-0.006361492909491062,
0.005440779495984316,
0.0057557327672839165,
0.015325022861361504,
0.012914029881358147,
-0.014045841060578823,
-0.03932749107480049,
0.013091209344565868,
0.009793291799724102,
0.05089104548096657,
-0.009533577598631382,
-0.008508789353072643,
-0.015821142122149467,
-0.006786171346902847,
-0.007527626119554043,
0.019121233373880386,
-0.00020914261403959244,
0.018213093280792236,
0.03969240188598633,
-0.03650158643722534,
0.014971711672842503,
0.0029470522422343493,
-0.008118330501019955,
-0.10266680270433426,
-0.007975279353559017,
-0.01263604499399662,
-0.014070761390030384,
0.024825001135468483,
-0.07345530390739441,
0.03393377736210823,
0.04396650195121765,
-0.06864114105701447,
-0.009218787774443626,
-0.0007577243959531188,
-0.002240917645394802,
-0.03686455637216568,
-0.0245981365442276,
-0.01718992553651333,
0.017138885334134102,
0.022891586646437645,
0.034965213388204575,
0.027158223092556,
0.03621746599674225,
-0.014382047578692436,
-0.04814821854233742,
0.033849019557237625,
0.045241162180900574,
0.0202939473092556,
-0.02778477594256401,
0.041250839829444885,
-0.02726021036505699,
-0.014205051586031914,
0.009437399916350842,
0.0010340339504182339,
0.0013187662698328495,
-0.0350799560546875,
0.03192175552248955,
-0.03559916466474533,
0.07004183530807495,
0.044868141412734985,
0.011430353857576847,
-0.00022338132839649916,
0.03948872536420822,
0.0024204584769904613,
0.02452893741428852,
-0.030248595401644707,
-0.04149458184838295,
0.04916537553071976,
-0.013795080594718456,
-0.014950492419302464,
0.029482798650860786,
-0.016141023486852646,
-0.02176966331899166,
0.050919901579618454,
-0.014249308966100216,
0.018139256164431572,
-0.03685063496232033,
-0.012281503528356552,
-0.048210740089416504,
-0.029286425560712814,
0.02652491256594658,
-0.0376458540558815,
0.00476522883400321,
-0.03428510203957558,
-0.026792114600539207,
-0.015471932478249073,
0.04669535905122757,
-0.016287390142679214,
-0.06284385919570923,
-0.07981877028942108,
-0.01617671549320221,
0.0077460831962525845,
0.00865271594375372,
-0.027425194159150124,
-0.033428799360990524,
-0.04646529257297516,
0.019901379942893982,
0.03535507246851921,
0.03849312663078308,
0.040379855781793594,
0.0012802830897271633,
-0.024164754897356033,
-0.02795674093067646,
0.04132413491606712,
-0.0056798579171299934,
-0.0034752285573631525,
-0.034472789615392685,
-0.04004637151956558,
0.03226065635681152,
-0.01806987263262272,
0.059987325221300125,
-0.010965913534164429,
-0.03892015665769577,
0.01917063631117344,
-0.005929833743721247,
0.023976324126124382,
-0.017222024500370026,
0.045227665454149246,
0.020049041137099266,
-0.008950823917984962,
-0.01672663353383541,
-0.018229855224490166,
-0.01840086840093136,
0.013045164756476879,
0.05962944030761719,
-0.002788476413115859,
-0.001829732907935977,
-0.02156531997025013,
0.020609891042113304,
0.009934229776263237,
0.024388452991843224,
-0.0006618026527576149,
0.046167802065610886,
0.010514618828892708,
0.003237325930967927,
0.032638486474752426,
-0.0010703508742153645,
-0.057836733758449554,
0.016723385080695152,
-0.034079961478710175,
0.048884548246860504,
-0.0126206548884511,
-0.02871224656701088,
0.036662474274635315,
-0.07550603151321411,
-0.008127724751830101,
0.02950705960392952,
-0.02595236711204052,
0.006783514749258757,
0.005861481186002493,
0.011164261028170586,
0.007570193149149418,
-0.03436547517776489,
0.01343426015228033,
-0.0024369233287870884,
0.02293492667376995,
-0.004638535436242819,
0.033652909100055695,
0.027957772836089134,
-0.013775081373751163,
0.023264287039637566,
-0.001498199300840497,
0.007500685751438141,
0.03325382247567177,
0.03221043944358826,
-0.01198435015976429,
-0.008154194802045822,
-0.05040586739778519,
0.016039686277508736,
0.008820347487926483,
-0.03622680529952049,
0.022475339472293854,
-0.03216466307640076,
0.051400791853666306,
0.01784614659845829,
0.008142286911606789,
-0.01779118925333023,
0.00254513556137681,
0.005495022051036358,
0.003404565853998065,
0.05459507927298546,
0.06619998067617416,
-0.058730125427246094,
0.007984856143593788,
0.014269949868321419,
-0.0353037491440773,
0.03655069321393967,
-0.05718293786048889,
0.022237466648221016,
0.01994936168193817,
0.008499589748680592,
-0.05210310220718384,
-0.03129945322871208,
-0.012940168380737305,
-0.005347839556634426,
0.023847850039601326,
0.04690132290124893,
0.008946736343204975,
0.007453767117112875,
-0.04317626357078552,
0.008453955873847008,
0.07057878375053406,
-0.0625038743019104,
0.004849057644605637,
0.005743511952459812,
0.0011789848795160651,
-0.022930102422833443,
0.0010755294933915138
] |
<p>we know that for a one component system</p>
<p>$$U= TS - PV + N \mu$$</p>
<p>Now all terms on the right hand side have well defined zeros, but the internal energy is known to be a relative quantity, with no unique zero. What's going on?</p>
<p>Similarly, we derive the above from the fact that:</p>
<p>$$U(kS, kV, kN)= kU(S,V,N)$$</p>
<p>And it seems to me that taking $k=0$ gives us $U(0,0,0)=0$ - the internal energy of an empty system is the uniquely defined zero of energy.</p>
| 10,816 |
[
-0.008792520500719547,
-0.018509404733777046,
-0.015776902437210083,
0.014724299311637878,
0.03573732450604439,
-0.010982628911733627,
-0.021527012810111046,
-0.01602444425225258,
0.00045722280628979206,
-0.045102622359991074,
0.005389495752751827,
0.00015941141464281827,
0.032533712685108185,
0.04517390578985214,
0.012103731743991375,
0.013895099982619286,
-0.03622223436832428,
-0.016244035214185715,
-0.020467009395360947,
-0.027784083038568497,
-0.021688533946871758,
0.02470121532678604,
0.01066213846206665,
-0.008155155926942825,
-0.012990794144570827,
0.02293686755001545,
0.0027937234845012426,
-0.021351607516407967,
0.024332504719495773,
0.027628373354673386,
-0.018179986625909805,
-0.009715030901134014,
-0.03943478316068649,
-0.010131222195923328,
0.00966703426092863,
0.01859864592552185,
-0.03582686558365822,
-0.026265274733304977,
-0.0028483467176556587,
0.02859826385974884,
-0.045286111533641815,
-0.019855760037899017,
-0.049151405692100525,
0.038149118423461914,
-0.009151467122137547,
-0.020457196980714798,
0.043378137052059174,
0.011162369512021542,
0.01119887176901102,
-0.041857343167066574,
0.05051761120557785,
0.023481598123908043,
0.06264587491750717,
0.007175719831138849,
0.000848099123686552,
0.01700747199356556,
0.0436706580221653,
0.0659586638212204,
0.003045086283236742,
-0.0658651813864708,
-0.005631882697343826,
0.01345546543598175,
-0.032891616225242615,
-0.031020721420645714,
-0.004769055172801018,
0.02735612727701664,
0.021659348160028458,
-0.03746471926569939,
0.03235768899321556,
-0.007844990119338036,
-0.010124364867806435,
0.035760436207056046,
0.019611939787864685,
-0.01816725730895996,
0.007267576176673174,
-0.034815456718206406,
0.005769285839051008,
-0.028431950137019157,
0.0219778660684824,
0.01786772906780243,
-0.012707462534308434,
0.026450958102941513,
0.03506852313876152,
0.04639396443963051,
0.01792178303003311,
-0.016925787553191185,
0.0673719272017479,
0.012768412940204144,
0.02745484560728073,
0.017388131469488144,
0.005244367755949497,
0.06062272936105728,
0.027943866327404976,
-0.012100858613848686,
-0.023744234815239906,
0.04950232803821564,
0.028805900365114212,
0.04198581725358963,
-0.004666915163397789,
-0.03761406987905502,
0.022850457578897476,
-0.012977737933397293,
0.05678567662835121,
0.07051870226860046,
0.025372883304953575,
-0.04326528683304787,
-0.03770965710282326,
0.018826676532626152,
0.017952682450413704,
0.00030679412884637713,
-0.05212096869945526,
-0.0008711433038115501,
0.006306550465524197,
0.01415181439369917,
-0.005867337342351675,
0.017772279679775238,
0.005720868706703186,
0.001685569528490305,
0.062299780547618866,
0.03658144548535347,
0.03968651592731476,
-0.0091791907325387,
0.029534202069044113,
-0.010166140273213387,
-0.09755922108888626,
-0.003734700381755829,
0.02751237526535988,
-0.00775332935154438,
-0.05931787192821503,
0.01683991029858589,
-0.0058409906923770905,
0.017914170399308205,
0.018896430730819702,
-0.008654549717903137,
0.02242306061089039,
0.0012955208076164126,
-0.08610013872385025,
-0.07898493111133575,
0.011324146762490273,
-0.034234803169965744,
0.00016654141654726118,
-0.04315580427646637,
-0.018043791875243187,
0.019476622343063354,
0.08240214735269547,
-0.028959201648831367,
-0.011183032765984535,
-0.01788560301065445,
0.0322362557053566,
0.0071516637690365314,
-0.011019974946975708,
-0.03605949878692627,
-0.01660129986703396,
-0.039223138242959976,
-0.009260416030883789,
-0.0414014495909214,
0.03547188267111778,
0.043800316751003265,
0.003933120518922806,
-0.020187227055430412,
0.04558483883738518,
-0.04849748685956001,
0.0022977690678089857,
0.012731650844216347,
-0.021373845636844635,
-0.01778510771691799,
0.06894354522228241,
0.005934425629675388,
0.007406029384583235,
0.019903002306818962,
0.05026474595069885,
0.01319280918687582,
-0.005375604145228863,
0.059117503464221954,
0.006119471043348312,
-0.019466882571578026,
-0.014107034541666508,
-0.023630933836102486,
0.035276446491479874,
0.00009262035746360198,
-0.0531693734228611,
-0.024908294901251793,
0.027559122070670128,
0.020903466269373894,
0.004601072985678911,
0.04143605753779411,
-0.02765905298292637,
-0.0015364090213552117,
-0.033393580466508865,
-0.016820315271615982,
0.003636986017227173,
-0.04677256569266319,
0.01985490880906582,
0.0068633365444839,
-0.0026538902893662453,
0.05618414655327797,
0.01633213646709919,
-0.015584197826683521,
-0.02912033721804619,
0.006021900102496147,
0.0006265398696996272,
0.002696842420846224,
-0.0010572557803243399,
-0.016723113134503365,
0.04120737314224243,
0.03914433345198631,
0.051771603524684906,
0.0017070636386051774,
0.03800836578011513,
0.0007755008991807699,
-0.03399742394685745,
0.020311670377850533,
-0.036506589502096176,
0.01167362555861473,
0.004892183002084494,
0.011992205865681171,
-0.017809614539146423,
0.01282561756670475,
0.00807114690542221,
0.023672912269830704,
-0.05800076946616173,
0.033636100590229034,
0.061139028519392014,
0.03292512521147728,
-0.0012535570422187448,
0.06416814774274826,
0.01378443744033575,
0.04710295796394348,
0.010715642012655735,
-0.02359253354370594,
-0.057722803205251694,
-0.0023905839771032333,
0.0399501696228981,
0.034530822187662125,
-0.02725188061594963,
0.015551738440990448,
0.02994939498603344,
0.02698610909283161,
0.034243375062942505,
-0.0380265973508358,
0.01089148037135601,
-0.01616700366139412,
0.044217053800821304,
0.022215012460947037,
-0.016558082774281502,
0.036546263843774796,
0.006327987182885408,
0.011428480967879295,
0.024722248315811157,
-0.027589701116085052,
0.003461916698142886,
0.05012284964323044,
-0.02405620366334915,
0.0037448881193995476,
-0.013716761022806168,
-0.03867688030004501,
0.022344503551721573,
-0.009930329397320747,
0.02670447714626789,
0.04010819271206856,
0.012843506410717964,
0.017286794260144234,
-0.009911946952342987,
-0.00374781945720315,
-0.0031513080466538668,
0.0017735968576744199,
0.015291428193449974,
0.004245213698595762,
0.034542910754680634,
-0.03289566561579704,
0.015690617263317108,
-0.02971602976322174,
-0.0012492942623794079,
-0.0048683020286262035,
-0.018540333956480026,
0.059552211314439774,
-0.0026671509258449078,
-0.00021427964384201914,
-0.02880054898560047,
-0.013141180388629436,
0.01559341698884964,
-0.02216852270066738,
0.014565465971827507,
0.03096410073339939,
-0.05618314817547798,
0.03688199073076248,
-0.028353791683912277,
-0.019474126398563385,
0.04171428829431534,
0.013842477463185787,
0.011280246078968048,
0.05935605987906456,
-0.056803978979587555,
-0.07014507055282593,
-0.012568218633532524,
-0.02716345153748989,
-0.0009285971755161881,
-0.031286899000406265,
0.009845906868577003,
0.049603421241045,
-0.018082786351442337,
-0.045871634036302567,
-0.0075540365651249886,
-0.03340914472937584,
-0.03817306086421013,
-0.031037764623761177,
-0.02169289067387581,
0.02461674064397812,
0.002182900672778487,
0.025065606459975243,
0.06250341236591339,
-0.0708484873175621,
0.005876683164387941,
-0.06957453489303589,
-0.051140207797288895,
-0.012676103040575981,
-0.02647375874221325,
0.039705052971839905,
0.01412759255617857,
-0.02834044024348259,
0.12846525013446808,
0.019337717443704605,
0.02359260804951191,
-0.009331799112260342,
-0.012431743554770947,
-0.016567455604672432,
0.0018129890086129308,
-0.01854684017598629,
0.00041405545198358595,
0.004969332367181778,
0.04832363873720169,
0.011267058551311493,
0.039048001170158386,
0.04097567871212959,
0.0060205403715372086,
-0.0001899908238556236,
0.0023784523364156485,
-0.012586538679897785,
-0.013367065228521824,
0.057570334523916245,
0.010319752618670464,
0.0005656321300193667,
0.03760208562016487,
0.015819689258933067,
0.03312461078166962,
0.028349075466394424,
-0.028619732707738876,
0.04124445840716362,
0.007150911260396242,
0.02492397278547287,
-0.053089439868927,
0.035941533744335175,
0.026846352964639664,
-0.006889672018587589,
-0.004249338526278734,
0.02262127213180065,
0.056641895323991776,
-0.045660968869924545,
0.007387059275060892,
0.013544823974370956,
0.009150662459433079,
-0.02783876657485962,
-0.0363999642431736,
0.0026829952839761972,
-0.017014969140291214,
-0.006683087442070246,
0.0024988579098135233,
0.0007070407154969871,
0.05514926835894585,
0.02806144207715988,
0.05867921561002731,
-0.017499737441539764,
-0.04732172563672066,
-0.010799136012792587,
-0.060733165591955185,
-0.01640871912240982,
-0.035877034068107605,
0.04436633735895157,
-0.01652889885008335,
0.031160620972514153,
0.02744601108133793,
0.027522681280970573,
-0.016201581805944443,
-0.002425265731289983,
-0.0767267644405365,
0.017509546130895615,
-0.0051113152876496315,
-0.024318750947713852,
0.011368319392204285,
-0.0021759599912911654,
-0.012572849169373512,
-0.04976248741149902,
-0.03136727213859558,
0.041510604321956635,
-0.015285593457520008,
-0.04526892304420471,
0.014853797852993011,
-0.04184691980481148,
-0.04186755046248436,
-0.010938613675534725,
0.0035816931631416082,
0.0489104725420475,
-0.03422555699944496,
-0.022723712027072906,
0.05366735905408859,
-0.04992418363690376,
0.03934599831700325,
-0.06159299239516258,
0.0006451574736274779,
0.026476416736841202,
0.026151344180107117,
0.05432157590985298,
0.02791622094810009,
0.0028304706793278456,
-0.029618900269269943,
0.01352536492049694,
0.05698997899889946,
0.012370512820780277,
-0.00956842303276062,
-0.05275000259280205,
-0.03412308916449547,
-0.0467916764318943,
0.013693058863282204,
0.04267871379852295,
0.016841821372509003,
0.04942285269498825,
0.00931759923696518,
0.04601403698325157,
-0.019713161513209343,
0.04228474572300911,
0.04829468950629234,
0.02061430737376213,
-0.021678930148482323,
0.0037641520611941814,
-0.007135247811675072,
-0.009018579497933388,
-0.006983791943639517,
0.008713274262845516,
-0.017558135092258453,
-0.046792272478342056,
-0.0009981397306546569,
0.00341433216817677,
0.014261674135923386,
-0.006130837369710207,
-0.0013781607849523425,
-0.014293605461716652,
0.04817715287208557,
-0.014926532283425331,
-0.01847218908369541,
0.011612562462687492,
0.020336559042334557,
0.04040725156664848,
0.007176527753472328,
-0.009742505848407745,
-0.02846754714846611,
0.009617635048925877,
0.028910327702760696,
0.013470828533172607,
-0.004309869837015867,
-0.017310086637735367,
-0.01482988428324461,
-0.019311560317873955,
0.0160649586468935,
-0.008998353965580463,
0.05595635995268822,
0.0011414717882871628,
-0.0003228670102544129,
0.013089797459542751,
-0.03533440828323364,
-0.010067656636238098,
0.027953023090958595,
0.015272175893187523,
0.03245709836483002,
-0.02558267116546631,
-0.007280298974364996,
-0.03559564799070358,
0.03411243483424187,
-0.0009077803115360439,
0.05138117074966431,
-0.019856277853250504,
-0.04843266308307648,
-0.013466223143041134,
0.011158899404108524,
0.00029372345306910574,
-0.07695167511701584,
0.02435128577053547,
-0.009837262332439423,
0.016554854810237885,
0.018528085201978683,
-0.05073722451925278,
-0.08710169792175293,
0.016639111563563347,
0.02264610305428505,
-0.00770532013848424,
-0.013660467229783535,
-0.042460598051548004,
0.006768791005015373,
0.04151565581560135,
-0.00909204501658678,
0.032973259687423706,
0.020874174311757088,
-0.039044324308633804,
-0.005101384129375219,
-0.047350600361824036,
0.022415831685066223,
-0.047255124896764755,
0.02152145840227604,
-0.04370498284697533,
0.01188176590949297,
-0.01259849313646555,
0.004086557310074568,
0.02628234587609768,
0.024997880682349205,
-0.024565869942307472,
-0.03218306973576546,
-0.012276762165129185,
0.023464540019631386,
0.015901360660791397,
0.04042244330048561,
0.03161387890577316,
0.03562874346971512,
-0.005489780101925135,
0.0001163654014817439,
-0.021805046126246452,
-0.010607218369841576,
-0.00651389267295599,
0.04775410518050194,
0.04356883838772774,
0.04572431370615959,
-0.03208508342504501,
-0.04404041916131973,
0.03721527382731438,
-0.048991188406944275,
0.016963785514235497,
-0.012279353104531765,
0.01375813502818346,
-0.00013697391841560602,
-0.02536424621939659,
-0.01844937540590763,
-0.03010120615363121,
0.004928838927298784,
0.021045789122581482,
-0.041367221623659134,
0.05211935564875603,
0.04536495730280876,
0.010364880785346031,
-0.10224296897649765,
-0.029437756165862083,
0.014969893731176853,
0.01131520513445139,
-0.03618249297142029,
-0.034274447709321976,
-0.0004060216306243092,
-0.006873941048979759,
-0.009633292444050312,
0.022327184677124023,
0.02733834646642208,
-0.00020179203420411795,
-0.03908183425664902,
0.009530498646199703,
0.06523194909095764,
0.042538996785879135,
0.004372978117316961,
-0.025122418999671936,
0.018006112426519394,
-0.020096026360988617,
0.002827676245942712,
0.022377606481313705,
0.05657748505473137,
-0.015232272446155548,
0.0012518397998064756,
0.011124451644718647,
0.0095427380874753,
0.052869535982608795,
0.015113219618797302,
-0.004136741627007723,
0.0325147919356823,
0.0032544853165745735,
-0.02323649637401104,
0.006778308656066656,
0.016428017988801003,
-0.011553773656487465,
0.01678498648107052,
0.0466080941259861,
-0.005715192761272192,
-0.035420939326286316,
-0.0441046766936779,
0.03282015025615692,
-0.032840028405189514,
0.0025005002971738577,
-0.021127520129084587,
0.08989795297384262,
0.01679098792374134,
-0.007958773523569107,
0.000951330759562552,
0.014609530568122864,
0.03322425112128258,
-0.0013279871782287955,
0.0026878484059125185,
-0.02501808851957321,
-0.016833337023854256,
-0.030080223456025124,
-0.02115608938038349,
-0.058163560926914215,
0.046454716473817825,
0.0475873239338398,
-0.003871933789923787,
0.04156726971268654,
-0.0035719345323741436,
-0.008523678407073021,
0.01745842956006527,
-0.03350695222616196,
0.00029824726516380906,
0.0008496126974932849,
0.019732695072889328,
0.011657881550490856,
-0.01908233016729355,
-0.035611461848020554,
0.024045724421739578,
0.060754213482141495,
-0.018037280067801476,
0.004162565805017948,
0.025700891390442848,
0.0018923169700428843,
0.02420113980770111,
-0.04576482996344566,
-0.0308823361992836,
0.054167069494724274,
-0.020946726202964783,
0.02580554224550724,
0.024051740765571594,
-0.014113613404333591,
0.02735191583633423,
0.009549601003527641,
0.003950790967792273,
-0.06727408617734909,
-0.02794920839369297,
-0.030623827129602432,
0.020184064283967018,
0.013735971413552761,
0.013988128863275051,
0.001027532503940165,
-0.0017263427143916488,
0.032532643526792526,
0.041958265006542206,
0.014973661862313747,
-0.0105949267745018,
-0.04941808804869652,
-0.02127102203667164,
-0.03495728597044945,
-0.0547645278275013,
-0.004080808721482754,
-0.03538336232304573,
-0.0266999714076519,
0.04651554673910141,
-0.006910785101354122,
0.02180430293083191,
0.016865674406290054,
0.014949589036405087,
0.01907987706363201,
0.05260004848241806,
0.033231645822525024,
0.05023267865180969,
-0.009068184532225132,
0.003775201737880707,
0.13270226120948792,
0.06520804762840271,
-0.008941508829593658,
-0.018720010295510292,
-0.013287634588778019,
-0.002169942483305931,
0.003010127227753401,
-0.005998419132083654,
0.06982474029064178,
0.012131068855524063,
0.004793952219188213,
-0.025948472321033478,
0.03132878243923187,
-0.03153788298368454,
-0.00513323163613677,
0.023143313825130463,
-0.03738383203744888,
-0.0359121635556221,
-0.018152179196476936,
0.030779698863625526,
-0.008552602492272854,
-0.038661014288663864,
-0.00253185722976923,
0.025063954293727875,
-0.005996279884129763,
-0.0002795043692458421,
-0.010134662501513958,
-0.03803515434265137,
0.039831798523664474,
-0.010307252407073975,
-0.024565881118178368,
0.029282022267580032,
0.020748015493154526,
-0.004238295368850231,
-0.025158021599054337,
0.023982733488082886,
0.058610785752534866,
-0.03655071184039116,
0.039952151477336884,
0.032131049782037735,
-0.008570403791964054,
-0.02058488130569458,
0.06376156955957413,
-0.008405419066548347,
-0.05070038139820099,
-0.03225918859243393,
-0.01787809282541275,
0.04121258482336998,
-0.019983898848295212,
0.008760731667280197,
-0.016719680279493332,
-0.010998273268342018,
0.006825294811278582,
-0.04227307811379433,
-0.014470896683633327,
-0.009202100336551666,
0.02883234992623329,
-0.03098485991358757,
0.006639869883656502,
-0.00818652380257845,
-0.02328244410455227,
0.04245593771338463,
0.02625849097967148,
0.006880396977066994,
-0.02456989884376526,
0.036352165043354034,
-0.021544700488448143,
0.04860492795705795,
-0.019934993237257004,
0.003918196074664593,
-0.009233077056705952,
-0.04530948027968407,
-0.014118017628788948,
-0.03857256472110748,
0.013590926304459572,
0.01404888741672039,
0.048676714301109314,
0.018097203224897385,
0.026047758758068085,
-0.012824969366192818,
-0.07730851322412491,
-0.01314546074718237,
-0.011716595850884914,
-0.013186770491302013,
-0.01311452779918909,
0.01433651801198721,
-0.002241953508928418,
0.06268702447414398,
-0.021381592378020287,
0.011894370429217815,
0.03939779847860336,
0.03484659641981125,
-0.01666947826743126,
-0.03997912257909775,
-0.051845066249370575,
-0.008854232728481293,
-0.05710620433092117,
0.05304284393787384,
0.011136848479509354,
-0.009836015291512012,
0.01684541255235672,
0.04414667561650276,
-0.008625518530607224,
0.08137299865484238,
-0.008416418917477131,
-0.017985660582780838,
-0.006439183373004198,
-0.025277728214859962,
0.015198593959212303,
0.06283672899007797,
0.03575288876891136,
0.005981003399938345,
-0.0695955827832222,
-0.010240384377539158,
0.017088018357753754,
0.004472721833735704,
0.03337725251913071,
-0.03004274144768715,
-0.019803183153271675,
-0.024238774552941322,
0.011966264806687832,
-0.029223576188087463,
-0.01852933131158352,
-0.03576701879501343,
-0.014957059174776077,
0.041785936802625656,
0.010977495461702347,
-0.01947893761098385,
0.024079877883195877,
-0.007710513658821583,
-0.012965269386768341,
0.02290983684360981,
0.0031762414146214724,
0.0027778244111686945,
-0.042344819754362106,
0.003230971982702613,
-0.02413860522210598,
0.033682242035865784,
0.002028957474976778,
-0.025502994656562805,
0.023663077503442764,
-0.021885540336370468,
-0.03328705579042435,
-0.0035034494940191507,
0.005634772125631571,
0.01957598142325878,
0.016170576214790344,
-0.02113719843327999,
-0.031452618539333344,
0.05667367950081825,
-0.023916970938444138,
0.01994774304330349,
-0.01387824211269617,
-0.008475394919514656,
-0.05742485821247101,
-0.00884389691054821,
-0.01991187408566475,
0.0129592539742589,
-0.01755177602171898,
0.02745833992958069,
0.009451154619455338,
-0.006336766295135021,
-0.03813204914331436,
0.012929754331707954,
-0.013434050604701042,
-0.004418684635311365,
0.043720975518226624,
0.04293691739439964,
0.030574962496757507,
0.029286280274391174,
-0.01937135122716427,
0.0061370194889605045,
-0.009337767958641052,
0.01962406374514103,
-0.09000096470117569,
-0.060527265071868896,
0.011162971146404743,
0.004014491103589535,
-0.004547594115138054,
-0.026514166966080666,
-0.010865083895623684,
0.0024240463972091675,
-0.046959493309259415,
0.023364361375570297,
-0.002870135474950075,
0.014774996787309647,
-0.019747141748666763,
-0.0010206870501860976,
-0.03623514249920845,
0.02277282439172268,
0.0476071871817112,
0.009311314672231674,
-0.015177816152572632,
0.004166422877460718,
-0.0054914080537855625,
-0.010937613435089588,
-0.02023261785507202,
0.016152895987033844,
-0.024159209802746773,
-0.02464180998504162,
0.06197482347488403,
-0.03441200777888298,
-0.04997928440570831,
-0.021630004048347473,
-0.06177360936999321,
-0.03964294120669365,
-0.0024120942689478397,
0.02288801781833172,
-0.02241085097193718,
0.06908896565437317,
0.046775177121162415,
-0.0014799308264628053,
-0.009768622927367687,
-0.011283155530691147,
-0.005244237370789051,
0.03762735798954964,
-0.028712525963783264,
0.00009051950473804027,
0.03943450003862381,
-0.043880753219127655,
-0.052373457700014114,
0.02037697844207287,
-0.04407017305493355,
-0.02071509324014187,
0.003888064529746771,
0.004807628225535154,
0.011712823063135147,
-0.05358244851231575,
-0.01073506847023964,
-0.08039819449186325,
-0.032596271485090256,
0.007638261187821627,
0.004403002560138702,
0.03298121318221092,
-0.01365803461521864,
0.01043368224054575,
-0.029345760121941566,
0.03377886489033699,
0.015410063788294792,
-0.03643812611699104,
-0.08803723007440567,
-0.0059354547411203384,
-0.022028841078281403,
-0.006298106163740158,
-0.050912268459796906,
-0.0376889742910862,
-0.04214920476078987,
0.04817059636116028,
0.04013659432530403,
0.019260432571172714,
-0.015361889265477657,
-0.051723770797252655,
-0.034718554466962814,
-0.04686203971505165,
0.01724015362560749,
-0.0027705091051757336,
-0.024706676602363586,
-0.03245781362056732,
-0.03925216943025589,
0.013647684827446938,
-0.0029813607688993216,
0.021460404619574547,
0.0041821724735200405,
-0.03549577668309212,
0.012904602102935314,
0.005298533942550421,
0.041817497462034225,
-0.020877275615930557,
0.024487538263201714,
-0.007017889991402626,
-0.03834238275885582,
0.001025857520289719,
0.009259735234081745,
-0.028884001076221466,
0.017614776268601418,
0.039595916867256165,
-0.040869444608688354,
-0.031961601227521896,
-0.009567986242473125,
-0.012813983485102654,
0.037790898233652115,
0.0038347598165273666,
-0.005436879117041826,
0.08723963797092438,
0.00037651570164598525,
0.05489904060959816,
0.025785690173506737,
-0.01568780653178692,
-0.051525529474020004,
0.028871284797787666,
-0.025300446897745132,
-0.011302148923277855,
-0.027450472116470337,
-0.02547551319003105,
0.0712791383266449,
-0.008556593209505081,
-0.02996123395860195,
0.04049915075302124,
-0.03923461586236954,
-0.006119684781879187,
-0.010189964435994625,
0.020924005657434464,
0.03354545682668686,
0.030444029718637466,
-0.006972145289182663,
0.03403141722083092,
-0.012290728278458118,
0.04083537310361862,
0.09942854195833206,
0.05578973516821861,
0.005085724871605635,
-0.0010470792185515165,
0.023934222757816315,
-0.030937984585762024,
-0.030154526233673096,
-0.015665573999285698,
-0.006716769188642502,
-0.0227374080568552,
-0.012427671812474728,
0.04042366147041321,
-0.008652287535369396,
-0.000600326806306839,
-0.022525940090417862,
-0.022330738604068756,
0.07592107355594635,
0.0040129078552126884,
-0.0038991684559732676,
-0.037480857223272324,
0.020357539877295494,
0.0004922663792967796,
0.0053564379923045635,
0.02123570255935192,
0.022181661799550056,
-0.006495173089206219,
-0.014205039478838444,
-0.04055815190076828,
-0.005736786872148514,
0.012817205861210823,
-0.05844787880778313,
-0.025958102196455002,
0.014298069290816784,
0.01761751063168049,
-0.03506927192211151,
-0.028698788955807686,
-0.006812157109379768,
-0.03275115042924881,
0.03683098405599594,
0.0440014973282814,
0.006982987746596336,
-0.007259831763803959,
-0.032734084874391556,
-0.04230540618300438,
0.06431995332241058,
-0.042543575167655945,
-0.0181327722966671,
-0.009238885715603828,
-0.005135629791766405,
-0.002849564654752612,
-0.019924532622098923
] |
<blockquote>
<p>A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular acceleration of the rod at the instant it is released?</p>
</blockquote>
<p>I just used </p>
<p>$$sin(30) = \frac{9.8}{a_{centripetal}}$$</p>
<p>Then I related</p>
<p>$$a_{rad} = a_{centripetal}$$</p>
<p>Is this right? I am looking at University Physics: </p>
<p>$$a_{rad} = v^2 / r$$</p>
<p>Where 9.8 is gravity. But I got none of the answers in the multiple choice ... so I must be doing wrong. Also I haven't used the radius. Any suggestions would be helpful...</p>
| 10,817 |
[
-0.03031708113849163,
-0.02880716137588024,
-0.02470407634973526,
0.010323750786483288,
0.010821777395904064,
-0.054203249514102936,
-0.05312396585941315,
-0.02649548277258873,
0.005507044494152069,
-0.00005108056575409137,
0.033605869859457016,
0.037473343312740326,
0.05079945549368858,
0.0364355631172657,
0.015098147094249725,
0.014572291634976864,
0.008652821183204651,
-0.01839824952185154,
0.013460827991366386,
0.012287670746445656,
-0.021317286416888237,
-0.032618746161460876,
-0.02227827161550522,
-0.027275176718831062,
-0.020006483420729637,
0.041353754699230194,
0.034197039902210236,
-0.03294296935200691,
0.015585290268063545,
0.07556183636188507,
-0.006068455521017313,
-0.01116290595382452,
0.02262292243540287,
0.021393433213233948,
0.010576044209301472,
0.049228716641664505,
-0.01032769214361906,
0.0053475163877010345,
-0.025880852714180946,
0.05573394149541855,
-0.022491229698061943,
0.020340533927083015,
-0.026760771870613098,
0.05666949227452278,
-0.022567206993699074,
0.03363768756389618,
-0.019349878653883934,
0.0008366640540771186,
0.0699974000453949,
-0.004285680130124092,
0.06350203603506088,
-0.004868233110755682,
0.013344336301088333,
-0.0017446548445150256,
-0.031149528920650482,
-0.002607540925964713,
0.05192616209387779,
0.018017690628767014,
-0.030644947662949562,
-0.03504827618598938,
0.02881118282675743,
-0.005593365058302879,
-0.05554601177573204,
-0.018091421574354172,
-0.031961385160684586,
0.014639758504927158,
-0.0030384408310055733,
-0.012541055679321289,
0.03146154806017876,
0.005364187527447939,
0.014311437495052814,
-0.008808537386357784,
-0.0004431342822499573,
0.009763008914887905,
0.004036847967654467,
-0.05185568332672119,
0.006054817233234644,
0.0055773016065359116,
-0.012349911034107208,
0.06127642095088959,
0.007442067377269268,
0.019667960703372955,
0.06246425583958626,
0.07994753867387772,
0.04073455557227135,
-0.02640327252447605,
0.045573219656944275,
0.02539408765733242,
-0.0036729169078171253,
0.026773428544402122,
0.010759600438177586,
0.0005964658921584487,
0.024050869047641754,
0.028362970799207687,
-0.008702252991497517,
0.03460663557052612,
0.00601567467674613,
0.0603841170668602,
0.045356180518865585,
-0.014687939547002316,
0.03799773380160332,
-0.004244713112711906,
0.011134534142911434,
0.0947418361902237,
-0.02896997705101967,
0.007778318598866463,
0.010532206855714321,
-0.021479273214936256,
-0.048502761870622635,
-0.05486440658569336,
-0.04897632449865341,
0.05078823119401932,
-0.0640902891755104,
-0.019287077710032463,
-0.013028589077293873,
-0.007348790764808655,
0.010965504683554173,
0.03187010437250137,
0.06116462126374245,
0.016537737101316452,
0.04289250075817108,
-0.02331690862774849,
0.017111385241150856,
-0.023488307371735573,
-0.041525110602378845,
0.02713032439351082,
0.032478589564561844,
-0.0008463721023872495,
-0.05938037857413292,
0.03775086626410484,
0.028024977073073387,
0.01551627553999424,
-0.006756890099495649,
-0.025488272309303284,
0.012787522748112679,
0.002774300519376993,
-0.0760657861828804,
-0.07259123027324677,
0.012729164212942123,
0.04091981053352356,
-0.016233054921030998,
-0.07039830833673477,
0.006408832501620054,
0.026197999715805054,
0.05588055029511452,
0.033384524285793304,
0.0054318709298968315,
0.00945725105702877,
0.013181598857045174,
-0.04137881100177765,
-0.043887242674827576,
0.0037225286941975355,
0.012552055530250072,
-0.04159048572182655,
-0.0018393195932731032,
-0.06014250963926315,
0.005502311047166586,
0.009804438799619675,
0.025993861258029938,
-0.016151441261172295,
0.014515076763927937,
-0.02024177275598049,
0.0428912378847599,
0.0332711823284626,
-0.005188584793359041,
-0.04193069040775299,
0.055678706616163254,
0.015823863446712494,
-0.03491576761007309,
0.0613725408911705,
0.03008436970412731,
0.047317225486040115,
-0.005942243617027998,
0.008758150041103363,
0.05991695821285248,
-0.025090985000133514,
-0.0008128889021463692,
-0.0267189834266901,
0.005793729797005653,
0.018679283559322357,
-0.05664674565196037,
-0.044076740741729736,
-0.00952816940844059,
0.007479323539882898,
-0.013061483390629292,
0.07662738114595413,
0.007582776714116335,
-0.007820876315236092,
-0.03699387609958649,
-0.0008902152767404914,
0.028040604665875435,
-0.040052060037851334,
0.04666706174612045,
-0.001611936604604125,
-0.004435153212398291,
-0.00571741908788681,
0.010537969879806042,
0.0049667018465697765,
-0.0256537776440382,
-0.006215004250407219,
-0.025357898324728012,
0.02405397593975067,
0.020502528175711632,
0.028728477656841278,
-0.001947871409356594,
0.014421802014112473,
0.03895072266459465,
-0.01616775617003441,
-0.006757817231118679,
-0.014749259687960148,
0.018234824761748314,
-0.019012507051229477,
0.006067665293812752,
0.025218416005373,
0.013896294869482517,
0.04441939666867256,
0.03703988716006279,
-0.012433870695531368,
0.001907125930301845,
0.04556664451956749,
-0.0085211843252182,
0.0689149796962738,
0.05220770090818405,
0.01563100703060627,
0.03626826032996178,
0.03163054212927818,
-0.010763494297862053,
-0.0012156051816418767,
0.004896832630038261,
-0.02287295274436474,
-0.03654679283499718,
0.002981166122481227,
0.021496737375855446,
0.02735365740954876,
-0.03361807018518448,
0.03506464883685112,
0.06464818865060806,
0.04127192869782448,
-0.011164241470396519,
0.04100309684872627,
-0.04170221462845802,
-0.020717822015285492,
0.04310806095600128,
0.0132410554215312,
-0.04243585094809532,
0.014311599545180798,
0.043699976056814194,
0.05587814003229141,
0.004378985147923231,
0.005391399376094341,
0.007396773435175419,
0.026983048766851425,
-0.027533823624253273,
0.028537385165691376,
0.008741366676986217,
-0.03680514171719551,
0.05650881305336952,
-0.022611040621995926,
0.019282978028059006,
0.03413916751742363,
0.013282246887683868,
-0.016471153125166893,
-0.021396394819021225,
0.049473244696855545,
0.009134332649409771,
0.009739410132169724,
-0.006204897537827492,
-0.036334078758955,
0.03920471668243408,
-0.05912875756621361,
-0.02586987614631653,
-0.004087912384420633,
-0.023900581523776054,
-0.02845131792128086,
0.027113940566778183,
0.037352241575717926,
0.03475848212838173,
0.02646704390645027,
-0.00825883261859417,
-0.004257332533597946,
-0.03367187827825546,
-0.03362858295440674,
-0.011564708314836025,
0.01848076470196247,
-0.034399911761283875,
0.03336459770798683,
-0.02870682068169117,
-0.022306300699710846,
0.05657845735549927,
0.024121761322021484,
-0.034835562109947205,
0.013266989029943943,
0.0065653203055262566,
-0.05063823610544205,
0.009009316563606262,
-0.02382584847509861,
0.019193517044186592,
-0.048969514667987823,
-0.008238730020821095,
0.031091347336769104,
0.018784431740641594,
0.0039295619353652,
0.03363146632909775,
-0.05528532713651657,
-0.025739828124642372,
-0.008608111180365086,
0.04607801139354706,
0.03552321344614029,
-0.017137303948402405,
-0.016057493165135384,
0.03418152406811714,
0.014963053166866302,
0.022842470556497574,
-0.08189520239830017,
-0.06168016418814659,
-0.014310125261545181,
0.012790856882929802,
0.0331512950360775,
0.011224824003875256,
-0.023149393498897552,
0.08858073502779007,
0.0074636186473071575,
-0.04526250436902046,
-0.0167830903083086,
0.018545277416706085,
-0.009186622686684132,
-0.047526419162750244,
0.007055431138724089,
0.007968936115503311,
-0.016101477667689323,
0.005508179310709238,
-0.02346499264240265,
-0.004951403476297855,
0.03701266273856163,
0.03392457216978073,
0.05895869433879852,
-0.01815338432788849,
0.02757934294641018,
-0.019280023872852325,
0.04614078253507614,
0.02426840551197529,
-0.02859022095799446,
-0.028720228001475334,
-0.007242254912853241,
0.04996585100889206,
0.016350744292140007,
-0.04788028076291084,
0.036055341362953186,
-0.03787346929311752,
0.007670570630580187,
-0.010299119167029858,
0.05174238607287407,
0.024102145805954933,
-0.025222549214959145,
0.006968031171709299,
0.0011438195360824466,
0.05791586637496948,
-0.015665989369153976,
-0.0023478581570088863,
0.060641154646873474,
0.03957504779100418,
0.0158853642642498,
-0.04144877940416336,
-0.024902701377868652,
0.004972115159034729,
0.011360379867255688,
-0.06813714653253555,
-0.0030044543091207743,
0.007797556463629007,
0.02922111190855503,
0.06925284117460251,
0.0046965074725449085,
-0.05507224053144455,
0.028505710884928703,
-0.08609282970428467,
-0.0029562299605458975,
-0.038949981331825256,
0.04457478225231171,
0.02472112700343132,
0.04582614451646805,
0.020835822448134422,
0.021701183170080185,
0.011724435724318027,
0.013420499861240387,
-0.0536150299012661,
0.052967265248298645,
-0.0680546760559082,
-0.031120801344513893,
0.02414821647107601,
-0.010314405895769596,
-0.0069429753348231316,
-0.03600738197565079,
0.00489464309066534,
0.008470500819385052,
-0.04400680214166641,
-0.05105983838438988,
-0.009146406315267086,
-0.03114882856607437,
-0.004282980225980282,
0.0027349458541721106,
0.0314914844930172,
0.04938991367816925,
-0.018774833530187607,
0.03260776400566101,
0.07099031656980515,
-0.021087314933538437,
0.002774105640128255,
-0.002381295198574662,
0.024687202647328377,
-0.024335335940122604,
0.01774180680513382,
0.008451046422123909,
0.016956133767962456,
0.04638155177235603,
0.024174615740776062,
0.013031314127147198,
0.05103614181280136,
0.03470577672123909,
-0.028583455830812454,
-0.030661622062325478,
-0.0691259354352951,
0.006216757465153933,
0.005586361978203058,
0.049647342413663864,
-0.014416281133890152,
0.012180372141301632,
0.034196410328149796,
-0.005880766082555056,
-0.014636609703302383,
0.03911186009645462,
0.04476480931043625,
-0.0039014467038214207,
-0.00038553294143639505,
-0.026021301746368408,
0.0007012468413449824,
-0.0030586360953748226,
-0.015705876052379608,
-0.020365117117762566,
-0.042234331369400024,
-0.044686201959848404,
-0.01832360215485096,
0.038082752376794815,
0.02594928815960884,
-0.01211586594581604,
0.047063734382390976,
-0.026214072480797768,
0.045278437435626984,
-0.013571771793067455,
-0.025501646101474762,
-0.006070441100746393,
0.016719918698072433,
0.014962892979383469,
-0.0342276468873024,
-0.03649286553263664,
-0.060665424913167953,
-0.004452891182154417,
0.010172980837523937,
0.057714421302080154,
-0.053138572722673416,
0.001360108028165996,
-0.05071268975734711,
-0.03790970519185066,
0.05859193950891495,
-0.044094257056713104,
0.026660265401005745,
-0.039688482880592346,
0.025989964604377747,
0.007868621498346329,
-0.016654765233397484,
-0.051774319261312485,
-0.049646876752376556,
-0.015163013711571693,
0.020834244787693024,
-0.034350715577602386,
-0.020968085154891014,
0.00942638423293829,
0.018244590610265732,
0.06336215883493423,
0.004105035215616226,
0.022837821394205093,
-0.04840420186519623,
-0.001806772779673338,
0.009820215404033661,
-0.01748678833246231,
-0.06590867042541504,
-0.02612493187189102,
-0.0031517543829977512,
-0.03155531734228134,
-0.00460090022534132,
-0.049387428909540176,
-0.05806790664792061,
0.024213407188653946,
-0.03086148016154766,
0.0145132876932621,
0.011775242164731026,
-0.04251999408006668,
0.0013812098186463118,
0.0440482534468174,
0.01122088823467493,
0.01961686462163925,
0.03193754702806473,
-0.004562492948025465,
0.004615615587681532,
-0.04744606092572212,
0.019308632239699364,
-0.011637711897492409,
-0.00740010803565383,
-0.02959921956062317,
0.03283596411347389,
0.013150735758244991,
0.04776482284069061,
-0.004290084354579449,
0.029645029455423355,
-0.04542475566267967,
-0.036719899624586105,
0.01473908219486475,
0.015028666704893112,
0.018970493227243423,
0.023542864248156548,
0.028475534170866013,
-0.03685788810253143,
-0.004088050220161676,
-0.005957610439509153,
0.016757594421505928,
-0.0029475605115294456,
0.005838946904987097,
0.03127974271774292,
0.00718552153557539,
0.04288695752620697,
-0.010405754670500755,
-0.04954265058040619,
0.0006467322818934917,
-0.08613582700490952,
0.06443329900503159,
-0.010505636222660542,
-0.0031613281462341547,
0.005293790251016617,
-0.02689506486058235,
-0.021441074088215828,
-0.01563921943306923,
0.008947083726525307,
0.05455220490694046,
-0.045507580041885376,
-0.003567429492250085,
0.014036829583346844,
0.015247421339154243,
-0.0023676767013967037,
-0.051515113562345505,
0.040043845772743225,
0.018880730494856834,
-0.023598987609148026,
0.005990020465105772,
0.005339787341654301,
-0.02113357000052929,
-0.03208613395690918,
0.006240824703127146,
0.04581980034708977,
-0.013568353839218616,
0.006185570266097784,
0.025717807933688164,
-0.0014721094630658627,
0.069576695561409,
0.008249393664300442,
-0.03237631171941757,
-0.023132015019655228,
-0.0018954589031636715,
-0.05226624757051468,
0.01142959576100111,
0.0770273357629776,
-0.02126649022102356,
-0.06956097483634949,
-0.012551618739962578,
-0.02088678814470768,
0.02557363733649254,
0.017185870558023453,
0.026515688747167587,
0.02883058413863182,
-0.003562535857781768,
-0.0024166328366845846,
0.0074655041098594666,
0.04840821400284767,
0.0178799107670784,
0.03638119623064995,
-0.002746403217315674,
-0.0077009121887385845,
-0.05315514653921127,
-0.015024416148662567,
0.006432369817048311,
0.01167810708284378,
0.006659851409494877,
-0.008411898277699947,
0.05304548516869545,
-0.014921804890036583,
-0.025234702974557877,
0.021162185817956924,
0.011524568311870098,
0.02586999721825123,
-0.017483461648225784,
-0.02306007780134678,
0.0026489426381886005,
-0.0032230764627456665,
-0.04423198103904724,
-0.02356935851275921,
-0.027410047128796577,
0.007017017342150211,
0.07077082991600037,
-0.02188977785408497,
0.09520852565765381,
0.026309214532375336,
0.008409828878939152,
-0.021665474399924278,
-0.031147776171565056,
-0.019273586571216583,
-0.025784006342291832,
0.018253711983561516,
0.027675721794366837,
-0.009155177511274815,
-0.011503959074616432,
-0.021204767748713493,
0.03209291398525238,
-0.010579976253211498,
0.00615659449249506,
0.02934705838561058,
0.01344757154583931,
-0.007121127564460039,
-0.0029979438986629248,
-0.05057807266712189,
-0.0056757028214633465,
-0.006136201322078705,
0.07481077313423157,
-0.013146317563951015,
-0.029781604185700417,
0.03868122771382332,
0.0032177758403122425,
-0.011094478890299797,
-0.023056760430336,
0.011129291728138924,
0.01038448791950941,
-0.010900715366005898,
-0.021566445007920265,
0.008753815665841103,
-0.06363773345947266,
0.014948188327252865,
0.06346958875656128,
0.015923820436000824,
0.05723991245031357,
-0.02264300361275673,
-0.037923503667116165,
0.004947782959789038,
-0.041445765644311905,
-0.043951671570539474,
0.048616886138916016,
-0.00033596146386116743,
0.006408651825040579,
0.010622944682836533,
-0.035909246653318405,
0.007870962843298912,
0.01143504586070776,
0.058977995067834854,
-0.013903246261179447,
0.09604848176240921,
-0.04131172597408295,
-0.023870326578617096,
-0.022444281727075577,
-0.029547642916440964,
0.10098781436681747,
0.020824596285820007,
-0.006615456193685532,
-0.0472419410943985,
-0.0024591032415628433,
-0.04798338562250137,
0.009123653173446655,
-0.03477175533771515,
-0.0031262885313481092,
-0.046400364488363266,
-0.005922970827668905,
0.05042433366179466,
0.006141460034996271,
-0.04084917902946472,
-0.009570371359586716,
0.009347325190901756,
0.010509205050766468,
-0.02499203383922577,
-0.028264867141842842,
0.0033917624969035387,
0.00592029606923461,
0.0032570965122431517,
-0.04486694931983948,
0.04499748349189758,
-0.022941190749406815,
-0.017617683857679367,
-0.03952307254076004,
-0.03154750540852547,
0.0022928330581635237,
-0.032783761620521545,
-0.06584323942661285,
0.015564394183456898,
-0.0012844277080148458,
-0.03292815759778023,
-0.018313806504011154,
0.008975349366664886,
0.004382833372801542,
-0.003979271277785301,
0.023973871022462845,
0.046281225979328156,
-0.01779855042695999,
0.015795664861798286,
-0.0023889087606221437,
-0.002184505108743906,
-0.06280675530433655,
-0.005451950244605541,
0.0006400606944225729,
0.023098813369870186,
-0.015171115286648273,
-0.018056746572256088,
-0.008014009334146976,
0.025882387533783913,
-0.023226425051689148,
-0.04017123579978943,
0.02025645226240158,
0.007795041427016258,
0.01652088388800621,
-0.04534323513507843,
-0.02162942849099636,
-0.018231157213449478,
0.010259767062962055,
0.023610517382621765,
-0.0026075858622789383,
0.0019688818138092756,
0.006792305503040552,
-0.008990880101919174,
0.009221721440553665,
0.03519057109951973,
-0.0179377980530262,
0.010528250597417355,
0.0059405043721199036,
-0.02082909271121025,
-0.03152605518698692,
-0.008672087453305721,
0.0024237141478806734,
0.011426454409956932,
0.008090916089713573,
0.00200858386233449,
-0.029779942706227303,
-0.0399603396654129,
-0.02220422588288784,
0.01962767168879509,
-0.013892277143895626,
-0.00887264497578144,
-0.033099159598350525,
-0.002636616351082921,
-0.01731961779296398,
0.029654374346137047,
0.014415171928703785,
0.03896446153521538,
-0.026586849242448807,
0.03947149217128754,
0.01189485378563404,
-0.0699092373251915,
-0.015297985635697842,
0.015367109328508377,
-0.012728523463010788,
-0.002799290232360363,
-0.006469145882874727,
0.01003300677984953,
0.030956914648413658,
0.03337324038147926,
0.00851426087319851,
0.0049841259606182575,
0.005270850844681263,
-0.0043648662976920605,
0.008295162580907345,
-0.015299337916076183,
0.012163540348410606,
0.004588144365698099,
0.0017283761408179998,
-0.059917669743299484,
0.009241987951099873,
-0.009709708392620087,
-0.04480032995343208,
-0.019702542573213577,
0.015491385944187641,
0.0014266245998442173,
0.017026597633957863,
-0.07673244178295135,
0.02879904769361019,
-0.06426915526390076,
0.0430489256978035,
-0.011007215827703476,
-0.0020819413475692272,
0.007340462412685156,
0.0022374498657882214,
-0.04344535246491432,
0.026073195040225983,
-0.03344651311635971,
-0.01661498099565506,
0.0467897467315197,
0.007327817380428314,
0.019210783764719963,
-0.0058068400248885155,
0.028590645641088486,
-0.027863560244441032,
0.06541884690523148,
-0.0014459745725616813,
-0.01008679810911417,
0.038887474685907364,
-0.02449956163764,
-0.010790842585265636,
0.03708358481526375,
0.0058493828400969505,
0.05360131710767746,
0.026423238217830658,
-0.03228560462594032,
0.01426919735968113,
0.03751133754849434,
-0.011908454820513725,
-0.03449420630931854,
-0.0004530553997028619,
-0.01141204684972763,
0.013886510394513607,
0.0044992477633059025,
-0.016424549743533134,
-0.014004187658429146,
0.007931165397167206,
0.06352998316287994,
-0.010114626958966255,
-0.040194857865571976,
0.0164046473801136,
0.009816275909543037,
-0.004638271871954203,
-0.04473857209086418,
0.02687200903892517,
-0.001418924075551331,
0.018723005428910255,
0.02625819854438305,
-0.01683163270354271,
0.033093925565481186,
-0.000932812225073576,
-0.003495816607028246,
-0.07968046516180038,
-0.008210770785808563,
-0.01022765226662159,
0.01357345562428236,
0.03156551718711853,
-0.01914713904261589,
-0.01809275895357132,
0.02696959860622883,
-0.06383191049098969,
-0.03663704916834831,
-0.03388606384396553,
-0.045294150710105896,
-0.0030225322116166353,
0.001487066620029509,
0.0391509123146534,
0.04498952999711037,
0.002310399664565921,
0.049232542514801025,
0.03352035582065582,
0.019399993121623993,
-0.014237744733691216,
-0.04416104406118393,
0.019671499729156494,
0.055621132254600525,
-0.020128769800066948,
0.02167692966759205,
0.0492703877389431,
-0.02655925042927265,
0.003512782510370016,
0.035301756113767624,
-0.033473558723926544,
0.06266291439533234,
-0.00654781237244606,
0.0006992343696765602,
-0.011290088295936584,
0.05497872084379196,
-0.002722417237237096,
-0.02104807458817959,
-0.08122123032808304,
0.05374087020754814,
-0.004229195881634951,
0.0365939624607563,
-0.05114232748746872,
-0.011798222549259663,
0.03208377957344055,
-0.02242005430161953,
-0.019854577258229256,
0.025348467752337456,
-0.012318596243858337,
0.004496218636631966,
0.00848397146910429,
0.0045867543667554855,
-0.019182784482836723,
-0.05968513712286949,
-0.019465574994683266,
-0.03483853116631508,
-0.0018681930378079414,
0.03849886357784271,
-0.01602785475552082,
-0.0031451727263629436,
0.024756619706749916,
0.0313994325697422,
0.00419545779004693,
-0.029137523844838142,
-0.03028428740799427,
-0.019149502739310265,
-0.06473484635353088,
-0.02605424076318741,
0.00772049929946661,
-0.030632734298706055,
-0.00917054247111082,
-0.039995282888412476,
-0.01546662487089634,
0.02026553452014923,
0.031428661197423935,
0.0035427259281277657,
0.05321024730801582,
0.00795774720609188,
-0.006740819197148085,
-0.0693865492939949,
0.020558107644319534,
0.039852067828178406,
-0.045050036162137985,
-0.026590319350361824,
-0.034493494778871536,
-0.0034488909877836704,
0.0438946858048439,
0.032625485211610794,
0.0022521279752254486,
-0.02399253286421299,
0.014481833204627037,
-0.01886160299181938,
-0.0226252693682909,
-0.03526116907596588,
0.01770460233092308,
0.0012256059562787414,
-0.02906162291765213,
0.023575451225042343,
0.0027827315498143435,
0.014837817288935184,
-0.020501675084233284,
0.02958974428474903,
-0.02086174674332142,
0.03259960934519768,
-0.03550519794225693,
-0.014853094704449177,
0.04715965688228607,
-0.014840318821370602,
0.0028098642360419035,
0.04051200672984123,
0.029913561418652534,
-0.01799633726477623,
0.03308061882853508,
-0.04549818113446236,
-0.04523223638534546,
0.037034206092357635,
-0.007451737765222788,
-0.039986491203308105,
-0.02838338352739811,
0.0059969136491417885,
-0.006382310297340155,
-0.05031145364046097,
-0.0066314153373241425,
0.021044835448265076,
-0.028130896389484406,
-0.028980422765016556,
0.017293628305196762,
0.006118849851191044,
0.04214131087064743,
-0.03418060392141342,
0.046110671013593674,
0.04038316383957863,
-0.024546155706048012,
0.006039142142981291,
0.0230485200881958,
0.03822694346308708,
-0.009008979424834251,
0.010398374870419502,
0.04676647111773491,
-0.010582798160612583,
0.011952139437198639,
-0.004112072288990021,
0.058892250061035156,
-0.004313975106924772,
-0.020700374618172646,
-0.02979922853410244,
-0.03921036049723625,
-0.014993500895798206,
0.02700367011129856,
-0.02218782715499401,
0.040089938789606094,
-0.0028635282069444656,
-0.010675206780433655,
0.018393905833363533,
0.026401471346616745,
-0.013537476770579815,
0.01950494386255741,
0.023125210776925087,
0.013529621995985508,
-0.006282008718699217,
-0.012201604433357716,
-0.01845904439687729,
-0.01847948133945465,
0.023247871547937393,
0.008168607018887997,
0.010675547644495964,
0.013921945355832577,
-0.007680651731789112,
-0.017818069085478783,
-0.026447128504514694,
-0.02366037108004093,
-0.020722761750221252,
0.03627775236964226,
0.00431747455149889,
0.006765059195458889,
-0.04611354321241379,
0.0026278516743332148,
-0.024551117792725563,
0.05513022094964981,
-0.06059100478887558,
-0.0305331964045763,
-0.03240251541137695,
0.038054440170526505,
0.010667072609066963,
-0.01923360489308834
] |
<p>A BWR reactor core may contain up to 146 tons of uranium. Why does it not form a critical mass when molten? Are there any estimates of the critical mass of the resulting zirconium alloy, steel, concrete and uranium oxide mixture?</p>
| 10,818 |
[
-0.02155098132789135,
-0.032920703291893005,
-0.016396962106227875,
-0.0005844613770022988,
0.03727633133530617,
-0.020097114145755768,
-0.030942397192120552,
-0.06327631324529648,
-0.005675946362316608,
-0.03395960107445717,
0.048375923186540604,
0.02310780994594097,
0.058278925716876984,
-0.017195580527186394,
0.03594454005360603,
0.012036128900945187,
0.021030548959970474,
-0.021681731566786766,
-0.012067224830389023,
-0.024458782747387886,
-0.006663086358457804,
-0.011453733779489994,
0.029260758310556412,
-0.003647930920124054,
0.009618549607694149,
0.029330626130104065,
-0.023426538333296776,
0.018136978149414062,
0.07021194696426392,
0.005303502082824707,
0.034063920378685,
-0.05000738427042961,
0.02262287028133869,
0.02271186001598835,
0.053551752120256424,
-0.00240339245647192,
-0.024038029834628105,
-0.026763135567307472,
-0.035691723227500916,
0.007303357589989901,
-0.00029660589643754065,
-0.008523520082235336,
0.00617562560364604,
0.018971379846334457,
0.006837795488536358,
-0.006113954819738865,
-0.01889532431960106,
-0.031043676659464836,
0.031158016994595528,
-0.023335816338658333,
0.02081121876835823,
0.029382789507508278,
0.029734274372458458,
0.025426333770155907,
-0.0010085831163451076,
-0.02690577693283558,
0.07686057686805725,
0.07504259794950485,
-0.006915954872965813,
-0.03200862929224968,
-0.02774783782660961,
0.0033325874246656895,
-0.042866937816143036,
-0.013695229776203632,
-0.003882121993228793,
0.06848853081464767,
-0.01721460558474064,
0.002777230693027377,
-0.0012630836572498083,
-0.016652081161737442,
0.03860042244195938,
-0.0050923931412398815,
-0.018304696306586266,
0.0006829172489233315,
0.013991408050060272,
-0.027638114988803864,
0.01990484446287155,
0.01631489396095276,
-0.013317897915840149,
0.052929915487766266,
-0.048783835023641586,
0.01379417348653078,
0.019009515643119812,
-0.020150989294052124,
-0.011136394925415516,
-0.007722285110503435,
0.06910407543182373,
0.014677625149488449,
-0.008978264406323433,
0.020825272426009178,
-0.01673285849392414,
0.01024251151829958,
0.03927787393331528,
-0.007814413867890835,
0.020952679216861725,
-0.020766429603099823,
-0.02050023525953293,
0.08047938346862793,
0.004981560166925192,
0.012726787477731705,
0.04116404801607132,
-0.008450627326965332,
0.02168935351073742,
0.0660981684923172,
0.004824697505682707,
-0.017862990498542786,
-0.043173737823963165,
-0.007415661588311195,
-0.0007566218264400959,
-0.023873746395111084,
-0.042667120695114136,
-0.010063445195555687,
0.0025395562406629324,
-0.013331236317753792,
0.024776877835392952,
-0.006322013214230537,
0.02561458759009838,
-0.045470573008060455,
0.03233565762639046,
0.005401667207479477,
0.0374159999191761,
0.0035979575477540493,
0.027857830747961998,
-0.04650852829217911,
-0.0623471699655056,
0.018657103180885315,
0.0075259022414684296,
-0.01612277515232563,
-0.045948270708322525,
0.022679243236780167,
-0.025982938706874847,
-0.023527387529611588,
-0.008186434395611286,
-0.03648251295089722,
0.01690925657749176,
0.031666290014982224,
-0.11114279925823212,
-0.06663940101861954,
0.02950935997068882,
-0.02940867654979229,
-0.06839800626039505,
-0.08907710015773773,
0.026761051267385483,
0.04234619438648224,
0.05279158055782318,
-0.023130562156438828,
0.020810924470424652,
0.008677165023982525,
0.020825939252972603,
-0.017125658690929413,
-0.008180570788681507,
-0.01929517649114132,
0.031216060742735863,
-0.040976330637931824,
0.02041061408817768,
-0.0722624659538269,
-0.003885942744091153,
0.030766069889068604,
0.0060257925651967525,
-0.014558565802872181,
0.027297331020236015,
0.0004811521212104708,
0.006464287638664246,
-0.010267991572618484,
-0.018665272742509842,
-0.02209780365228653,
0.05981577932834625,
-0.007916861213743687,
0.0019094981253147125,
0.05648955702781677,
0.03083854913711548,
0.027840878814458847,
0.03823741897940636,
0.036053381860256195,
0.03866037353873253,
-0.03532066196203232,
-0.0012405668385326862,
-0.039689548313617706,
0.01729208044707775,
0.02395499311387539,
-0.049847111105918884,
0.011475983075797558,
-0.021853022277355194,
0.028317948803305626,
0.02230052277445793,
0.04221893101930618,
0.018360724672675133,
-0.014680025167763233,
0.03508494421839714,
-0.06471511721611023,
-0.008364755660295486,
-0.04844588041305542,
0.02564316615462303,
-0.0024881388526409864,
0.004450784996151924,
-0.0198495052754879,
0.021884584799408913,
0.014176190830767155,
-0.020713504403829575,
-0.005464992485940456,
0.021275287494063377,
0.010253144428133965,
0.02446512132883072,
0.04038336127996445,
0.010072579607367516,
0.01847267895936966,
0.03724182769656181,
-0.008938401937484741,
0.019847217947244644,
-0.01049171295017004,
-0.03511947765946388,
-0.029106298461556435,
-0.009793066419661045,
-0.009537791833281517,
-0.03235713765025139,
-0.058937426656484604,
0.005289393477141857,
-0.03751669079065323,
0.021807581186294556,
0.03738197684288025,
-0.005767516791820526,
0.08693832904100418,
0.031243566423654556,
0.017777280882000923,
-0.0011730589903891087,
0.05453135445713997,
0.0090304771438241,
0.028174424543976784,
-0.007747063413262367,
-0.008608151227235794,
-0.10544823855161667,
-0.03569023683667183,
0.03672581911087036,
0.03289655223488808,
-0.06510260701179504,
0.02871393971145153,
0.0017639320576563478,
0.029772918671369553,
0.005499901250004768,
-0.0005244998610578477,
-0.048916079103946686,
-0.04578172788023949,
0.043407391756772995,
0.01839699037373066,
0.021465549245476723,
-0.001128182397224009,
-0.012783456593751907,
0.045726481825113297,
0.0075813159346580505,
-0.058046720921993256,
-0.011625873856246471,
0.008906928822398186,
-0.00988438818603754,
-0.04140989109873772,
-0.03519199416041374,
-0.062393151223659515,
0.05759941041469574,
-0.029841165989637375,
0.01935034804046154,
0.00904796365648508,
-0.008676132187247276,
0.002747319871559739,
0.012267137877643108,
-0.01805582270026207,
0.009732571430504322,
0.040371011942625046,
-0.02139964886009693,
-0.028800111263990402,
0.03257600963115692,
-0.03579813241958618,
-0.004882023204118013,
-0.043949685990810394,
0.003995679318904877,
-0.026248538866639137,
0.0160820409655571,
0.019073430448770523,
-0.024051867425441742,
0.03954283893108368,
-0.03133847191929817,
-0.04817022755742073,
0.01705314964056015,
-0.021485602483153343,
-0.0031741559505462646,
0.023895353078842163,
-0.045936159789562225,
0.012521980330348015,
0.05065995827317238,
-0.013364966958761215,
0.020877256989479065,
0.04428542032837868,
0.008931336924433708,
0.002334169577807188,
-0.022213559597730637,
-0.04137677699327469,
-0.01106705516576767,
0.024563228711485863,
0.01823229156434536,
-0.004853023216128349,
0.03393132984638214,
0.06204472854733467,
-0.014800678938627243,
-0.018736014142632484,
-0.008576306514441967,
-0.04052691534161568,
0.0012980500468984246,
-0.005937641486525536,
0.029883572831749916,
0.015887148678302765,
-0.035290542989969254,
0.01985354907810688,
0.054301537573337555,
-0.06956882774829865,
0.018377156928181648,
-0.011691008694469929,
-0.047173965722322464,
0.031821466982364655,
-0.06717397272586823,
0.04575905203819275,
0.014387184754014015,
-0.03472248464822769,
0.09097104519605637,
0.0010204559657722712,
-0.031789131462574005,
-0.026094553992152214,
-0.005393349099904299,
0.002498208312317729,
-0.029621487483382225,
0.028779402375221252,
0.04819759726524353,
0.024540316313505173,
-0.015402054414153099,
-0.0023182278964668512,
0.033947188407182693,
0.007319234777241945,
0.03964339569211006,
-0.014654861763119698,
0.016139108687639236,
0.028526030480861664,
0.008853507228195667,
0.02664845995604992,
-0.016024066135287285,
0.006777457892894745,
0.04193870723247528,
-0.01941722258925438,
0.08749409765005112,
0.027733569964766502,
-0.07744818925857544,
0.05078967660665512,
0.03722736984491348,
0.01718313805758953,
-0.04977094754576683,
0.054777514189481735,
-0.01824083738029003,
-0.039987169206142426,
-0.01265706866979599,
0.012701001018285751,
0.0713646337389946,
0.00412206444889307,
-0.0036035017110407352,
0.02460283599793911,
0.05737299844622612,
0.0001943322567967698,
-0.021279236301779747,
-0.016046734526753426,
-0.03619857132434845,
0.038301222026348114,
0.0030751654412597418,
-0.008837747387588024,
0.038639649748802185,
0.019429529085755348,
-0.01818714290857315,
-0.03669948875904083,
0.028567278757691383,
-0.025276226922869682,
-0.0696183443069458,
-0.032658837735652924,
-0.019688747823238373,
0.024050677195191383,
0.00015936850104480982,
0.056859228760004044,
0.010884997434914112,
0.021638598293066025,
-0.019047951325774193,
-0.015226568095386028,
-0.08988603949546814,
0.013329950161278248,
-0.0696982890367508,
0.013298958539962769,
-0.006852820981293917,
-0.018599310889840126,
-0.02427079528570175,
-0.0206534992903471,
-0.05945872142910957,
-0.022220052778720856,
0.013346467167139053,
-0.03758770599961281,
0.026960739865899086,
-0.00003414306775084697,
-0.024676712229847908,
0.008610115386545658,
0.023349503055214882,
0.02450554259121418,
-0.018980616703629494,
0.04473472014069557,
-0.006678091362118721,
-0.009278343990445137,
-0.024438658729195595,
-0.04953405261039734,
0.038690268993377686,
-0.015295300632715225,
0.05374447628855705,
0.003866704646497965,
0.028643570840358734,
-0.04096849635243416,
0.0032547928858548403,
0.0355805829167366,
0.018446214497089386,
-0.02753654308617115,
0.03434180095791817,
-0.04399571940302849,
-0.04630357399582863,
0.017375074326992035,
0.02477571740746498,
0.01822742074728012,
-0.02972463332116604,
0.02437807433307171,
0.009743202477693558,
-0.006457250565290451,
-0.015746669843792915,
0.03836241737008095,
0.0434093102812767,
0.042570650577545166,
0.0035814112052321434,
-0.00043055202695541084,
0.015874411910772324,
-0.018317678943276405,
-0.009907319210469723,
-0.0011124992743134499,
0.029765121638774872,
-0.01988631673157215,
0.0009522024192847311,
0.013520050793886185,
0.010809853672981262,
-0.03752098232507706,
0.01908709667623043,
0.017423929646611214,
0.01953558251261711,
0.008565505035221577,
0.003208420006558299,
0.031614623963832855,
0.0076296282932162285,
0.04823141172528267,
0.008777810260653496,
0.01526125892996788,
-0.05474983528256416,
-0.006545100826770067,
0.049846697598695755,
0.03924647346138954,
-0.015185337513685226,
-0.012813343666493893,
-0.0477924607694149,
-0.029304014518857002,
0.08010850101709366,
0.006498119328171015,
0.04924088343977928,
-0.046560268849134445,
0.022024862468242645,
0.03159051388502121,
-0.010954818688333035,
-0.010435577481985092,
-0.013430614024400711,
-0.018422897905111313,
0.00751854944974184,
-0.02463606745004654,
0.015518123283982277,
0.01613917574286461,
0.014003015123307705,
0.03791067749261856,
0.031398430466651917,
0.02654339373111725,
0.025557924062013626,
-0.0183046143501997,
-0.010177534073591232,
-0.015049672685563564,
-0.07698621600866318,
0.0033731318544596434,
-0.015499092638492584,
-0.018145669251680374,
0.010323351249098778,
-0.038028448820114136,
-0.07923579216003418,
0.046693988144397736,
0.0390208438038826,
-0.0030373185873031616,
-0.022007158026099205,
-0.02801903337240219,
0.043031662702560425,
0.046301212161779404,
-0.0021990337409079075,
0.055129870772361755,
0.01840016432106495,
-0.012936841696500778,
-0.010710402391850948,
-0.04266861453652382,
0.04315178841352463,
-0.02707415260374546,
0.025345491245388985,
0.024726759642362595,
0.04814865067601204,
0.0016552748857066035,
0.015885094180703163,
0.001824200269766152,
0.014906530268490314,
-0.039244163781404495,
-0.028178291395306587,
0.025499891489744186,
-0.02182009443640709,
0.013359617441892624,
-0.040040273219347,
-0.020705215632915497,
0.003391587408259511,
-0.0195547454059124,
-0.047770190984010696,
0.018918385729193687,
-0.021250411868095398,
-0.0014162641018629074,
0.01772916689515114,
-0.019252536818385124,
0.018640831112861633,
-0.021319346502423286,
-0.019716622307896614,
0.0453333780169487,
-0.033702146261930466,
0.049351587891578674,
-0.007241277955472469,
0.027660049498081207,
0.0024054443929344416,
-0.013165352866053581,
0.010123200714588165,
-0.0021232087165117264,
0.033464401960372925,
0.04614313691854477,
-0.026137979701161385,
0.0482642725110054,
0.016612913459539413,
-0.0028073126450181007,
-0.04328744113445282,
-0.056340742856264114,
0.05648457631468773,
0.043969254940748215,
-0.0036103087477385998,
-0.043036796152591705,
0.006021419540047646,
0.004701204132288694,
-0.05309295654296875,
-0.018937069922685623,
0.05633591115474701,
-0.026626477017998695,
-0.006270276382565498,
0.01937885396182537,
0.036752428859472275,
0.06948044151067734,
-0.025686826556921005,
-0.025703303515911102,
0.029992109164595604,
-0.014129456132650375,
0.011365312151610851,
-0.0027145128697156906,
0.052671417593955994,
-0.03957941755652428,
-0.03860839828848839,
0.03573568910360336,
-0.03677278757095337,
0.03905315324664116,
-0.0037146222312003374,
0.021264519542455673,
0.022012051194906235,
0.03408971428871155,
-0.025588419288396835,
-0.001253129099495709,
0.03240968659520149,
0.006171333137899637,
0.031515832990407944,
-0.015053559094667435,
-0.005498645827174187,
-0.033188559114933014,
-0.018782975152134895,
0.04289894178509712,
-0.002349910791963339,
-0.001102543086744845,
0.017344146966934204,
0.04371263459324837,
0.03579450771212578,
-0.03748711943626404,
-0.031169559806585312,
-0.05216458439826965,
0.020653011277318,
0.014648443087935448,
0.02213139832019806,
0.011677649803459644,
-0.005525487009435892,
-0.021372303366661072,
-0.04339100420475006,
0.006034230813384056,
0.014783177524805069,
0.03303651139140129,
-0.04584608972072601,
0.028760267421603203,
-0.0046592578291893005,
-0.0239860899746418,
0.034688904881477356,
-0.003623515833169222,
-0.02124098315834999,
0.03927182778716087,
-0.0022806955967098475,
0.022892851382493973,
0.0059348465874791145,
-0.026658209040760994,
0.0050373561680316925,
0.013897533528506756,
0.015222696587443352,
0.001809028210118413,
0.020069878548383713,
0.013525906950235367,
0.03637877106666565,
0.014617498964071274,
-0.041426099836826324,
-0.0030962093733251095,
0.005051159765571356,
0.008264508098363876,
0.004653443116694689,
-0.018833639100193977,
0.020348967984318733,
-0.040979258716106415,
0.017700273543596268,
-0.028627455234527588,
-0.05209751054644585,
-0.01457206904888153,
0.030717022716999054,
0.0028904082719236612,
0.007398910820484161,
-0.011737684719264507,
0.028644291684031487,
0.0037593876477330923,
-0.001158836530521512,
0.0024552198592573404,
0.003642517141997814,
-0.05686863139271736,
0.020846951752901077,
-0.0042363000102341175,
-0.07072599977254868,
0.020707327872514725,
-0.012200064957141876,
-0.022465014830231667,
0.017373137176036835,
-0.04526824876666069,
0.03792796656489372,
-0.011590090580284595,
0.041563745588064194,
0.004151033703237772,
0.031961604952812195,
0.005271062254905701,
0.024208933115005493,
0.005773474927991629,
0.04563293233513832,
0.11564798653125763,
0.034280773252248764,
-0.008800401352345943,
-0.06624416261911392,
-0.002292801858857274,
-0.020280081778764725,
-0.002692042151466012,
-0.026497649028897285,
-0.001285267760977149,
0.04741179198026657,
-0.0018736496567726135,
0.02809603326022625,
0.03153064474463463,
-0.006915166974067688,
0.007424970157444477,
0.04398644343018532,
-0.025499876588582993,
-0.014053639024496078,
0.001457488746382296,
-0.0010091033764183521,
-0.03367544338107109,
-0.025829531252384186,
-0.05032755434513092,
-0.007129468489438295,
0.014880530536174774,
-0.05959438532590866,
-0.03695425018668175,
-0.007355143316090107,
0.03683418780565262,
-0.006815066561102867,
-0.031364526599645615,
0.017532188445329666,
0.018604541197419167,
-0.02924390137195587,
0.0014140186831355095,
0.009487330913543701,
0.005280588287860155,
-0.014062296599149704,
0.03774009644985199,
-0.005719840992242098,
0.005482228938490152,
0.028442349284887314,
-0.010348683223128319,
0.03507964685559273,
-0.06453971564769745,
0.02563675306737423,
-0.007290361449122429,
0.015605565160512924,
-0.019642014056444168,
-0.02155202440917492,
0.0022284153383225203,
-0.020425446331501007,
-0.0037315483205020428,
0.013434227555990219,
-0.051540959626436234,
0.006845701951533556,
0.017239803448319435,
-0.010468554683029652,
-0.03017851524055004,
-0.0225678700953722,
0.009432999417185783,
-0.030359745025634766,
0.010588264092803001,
0.0337538942694664,
-0.017219552770256996,
-0.01263065543025732,
-0.033813152462244034,
0.02935037575662136,
-0.019276557490229607,
-0.033973824232816696,
-0.0663217082619667,
0.013893837109208107,
-0.03744872286915779,
-0.012839793227612972,
0.008158584125339985,
-0.0013990419683977962,
0.03488875925540924,
0.03244508057832718,
0.013638151809573174,
-0.023137878626585007,
-0.028068093582987785,
0.07765309512615204,
0.006115487776696682,
-0.034954898059368134,
-0.0829852968454361,
0.0005015286151319742,
-0.009292816743254662,
0.03908036649227142,
-0.05163662135601044,
-0.005016714334487915,
-0.027036599814891815,
0.012888477183878422,
0.01735551655292511,
-0.020219601690769196,
-0.014046923257410526,
0.029167499393224716,
-0.024325355887413025,
0.0009307412547059357,
-0.013234332203865051,
-0.0155264213681221,
0.034583598375320435,
-0.0020304624922573566,
0.03752412647008896,
0.028553510084748268,
-0.008028827607631683,
0.009551200084388256,
0.02835509181022644,
-0.01373280119150877,
-0.009622027166187763,
0.006945827975869179,
-0.01090486254543066,
-0.012027306482195854,
-0.058001238852739334,
-0.05268417298793793,
-0.03536531701683998,
0.04229927808046341,
0.05014580488204956,
-0.015172979794442654,
0.020682277157902718,
-0.0025755525566637516,
0.029459521174430847,
0.013728792779147625,
-0.009929673746228218,
-0.031183263286948204,
-0.012523256242275238,
-0.004742257762700319,
0.004088157322257757,
-0.01730242557823658,
0.01591412164270878,
0.01872268319129944,
0.014512701891362667,
-0.0003396526153665036,
-0.004888380412012339,
-0.014485739171504974,
-0.015092923305928707,
-0.0013793508987873793,
0.01644287072122097,
0.0457984060049057,
-0.021507414057850838,
0.002032449236139655,
0.053215160965919495,
-0.017938101664185524,
-0.07282260805368423,
0.03798098489642143,
-0.03559762239456177,
0.02514881268143654,
-0.018849488347768784,
-0.014379081316292286,
-0.001230245572514832,
0.06347667425870895,
-0.019528409466147423,
0.018938397988677025,
-0.017801137641072273,
0.05658574402332306,
0.004077489487826824,
0.016631366685032845,
-0.01102607510983944,
-0.014839920215308666,
-0.026499416679143906,
0.019160011783242226,
0.06362077593803406,
-0.011851680465042591,
0.02025013044476509,
-0.033350709825754166,
0.0014395371545106173,
0.0415581651031971,
0.02008752152323723,
0.049148157238960266,
0.016144780442118645,
0.046689704060554504,
-0.02061382681131363,
0.04618078097701073,
-0.00067690055584535,
-0.02715364471077919,
-0.07545139640569687,
-0.05135362967848778,
-0.029208451509475708,
-0.02918386086821556,
0.013011104427278042,
-0.015883533284068108,
0.024609168991446495,
0.03679114580154419,
-0.05326096713542938,
0.015166735276579857,
-0.05759412795305252,
-0.07247938215732574,
-0.03225168213248253,
-0.04981321841478348,
-0.03245203569531441,
0.042381949722766876,
0.03931416571140289,
0.04224056378006935,
0.03359429910778999,
0.028904341161251068,
-0.03251560032367706,
0.02891407534480095,
0.013229144737124443,
-0.0233303289860487,
-0.027607666328549385,
-0.005045825149863958,
0.06467024236917496,
-0.029835324734449387,
-0.04290514811873436,
0.01647426187992096,
-0.030021073296666145,
-0.005066744051873684,
0.007872733287513256,
0.016494400799274445,
-0.000046442841266980395,
0.06244025006890297,
0.03046497330069542,
-0.02110636793076992,
-0.04830828681588173,
0.02800888381898403,
0.011014636605978012,
0.015055607073009014,
-0.046408046036958694,
0.00753283454105258,
0.008846019394695759,
0.007918364368379116,
0.007619267329573631,
0.05172222852706909,
-0.027309183031320572,
-0.007279123179614544,
-0.01897519826889038,
0.03216765820980072,
0.024047115817666054,
-0.02696891687810421,
0.007859386503696442,
-0.032008230686187744,
-0.021747352555394173,
0.009491641074419022,
0.023115893825888634,
-0.01209246926009655,
0.00646384060382843,
-0.008174688555300236,
0.009548782370984554,
-0.007096822839230299,
-0.0006036402191966772,
-0.04819800704717636,
-0.005301298573613167,
-0.0184582881629467,
0.013905050233006477,
-0.02381044812500477,
0.00855833850800991,
-0.025795212015509605,
-0.04315182939171791,
0.034822601824998856,
0.03081158548593521,
0.02015570178627968,
0.005747383926063776,
-0.021823588758707047,
-0.017388559877872467,
-0.05431833863258362,
0.014257457107305527,
-0.009878634475171566,
-0.007427569013088942,
-0.006357783917337656,
-0.029937347397208214,
-0.0018279460491612554,
-0.004591923672705889,
0.03776787593960762,
0.033941056579351425,
0.004985086154192686,
0.0004065592074766755,
0.004354523960500956,
0.026183057576417923,
-0.02007403038442135,
0.034441057592630386,
0.024925975129008293,
-0.04361112788319588,
-0.010208826512098312,
-0.007222307845950127,
0.01685330457985401,
0.00794210471212864,
0.023796575143933296,
-0.005392297171056271,
-0.03490852564573288,
0.0056702615693211555,
0.0016255092341452837,
0.07825726270675659,
-0.022143948823213577,
0.003487673820927739,
0.08218424767255783,
-0.000393485592212528,
0.033944424241781235,
0.020944248884916306,
0.01571476273238659,
-0.060122281312942505,
0.006239880807697773,
-0.011025691404938698,
0.011849242262542248,
-0.009031726978719234,
-0.0069622984156012535,
0.022998135536909103,
-0.022971056401729584,
0.025228247046470642,
0.033422816544771194,
-0.0216181930154562,
0.002233698032796383,
0.02053503319621086,
0.019061971455812454,
0.04370642453432083,
-0.004870473872870207,
-0.00847130548208952,
-0.0029066484421491623,
-0.021472621709108353,
0.029060179367661476,
0.028840627521276474,
0.039430685341358185,
-0.010717269964516163,
0.005935532506555319,
0.05287223681807518,
-0.045604120939970016,
0.007226809859275818,
0.01794242113828659,
-0.012248831801116467,
-0.03197639808058739,
-0.07926744967699051,
0.0251240786164999,
-0.023755505681037903,
0.02392498031258583,
-0.0005194858531467617,
-0.062436293810606,
0.08788759261369705,
0.025906937196850777,
-0.004241739399731159,
-0.034182868897914886,
-0.005777648184448481,
0.0188235342502594,
0.019263584166765213,
0.00971581693738699,
0.00542964693158865,
-0.02309030294418335,
0.001617736998014152,
0.03007662110030651,
-0.0040312279015779495,
0.010511654429137707,
-0.013531777076423168,
-0.015998028218746185,
-0.04267292469739914,
0.011002111248672009,
-0.0009442272130399942,
-0.042948368936777115,
-0.04795397073030472,
-0.04429113119840622,
0.06444086134433746,
0.08323702961206436,
0.02676927112042904,
0.0027375291101634502,
-0.027886901050806046,
-0.04220805689692497,
0.04063938558101654,
-0.032871972769498825,
-0.03192067891359329,
-0.03301277011632919,
-0.0017297154990956187,
-0.04473355785012245,
-0.02960195764899254
] |
<p>The reply to a question about <a href="http://physics.stackexchange.com/questions/7131/origin-of-elements-heavier-than-iron-fe">nucleosynthesis</a>, that heavier than iron elements are produced in supernovae explosions, raised for me the following question which I could not answer by googling. Partially because the search for planets and stars brings out astrology answers!</p>
<p>Explosions are dispersive, nevertheless we find minerals in clumps, not only uniformly dispersed in the ground. Is there a coherent presentation that explains how minerals end up in veins and bands?</p>
| 10,819 |
[
-0.02580695040524006,
-0.027837499976158142,
-0.023158086463809013,
-0.018036849796772003,
0.06145809218287468,
-0.0065217711962759495,
-0.03587745502591133,
-0.00856810063123703,
0.03044835664331913,
-0.05838313326239586,
0.02685781568288803,
0.01726430468261242,
0.07031142711639404,
0.031036313623189926,
0.022855468094348907,
-0.006481241434812546,
-0.006044700741767883,
-0.022521300241351128,
-0.009792739525437355,
-0.031010925769805908,
-0.004353492055088282,
-0.018195021897554398,
-0.04270307347178459,
-0.005951658356934786,
-0.022781208157539368,
0.032259587198495865,
-0.007586549036204815,
0.0032867477275431156,
0.013953815214335918,
0.015203194692730904,
0.030030587688088417,
0.009502992033958435,
0.02846643701195717,
0.01433313824236393,
0.0277327299118042,
0.023966995999217033,
0.02949191816151142,
-0.030535725876688957,
-0.010573146864771843,
0.03531637042760849,
-0.029844924807548523,
-0.007965654134750366,
0.011956943199038506,
0.018390793353319168,
-0.04321439936757088,
0.012362961657345295,
0.00557068083435297,
-0.003189304145053029,
0.04144605994224548,
-0.04489980638027191,
0.04342141002416611,
-0.008730394765734673,
0.003606904996559024,
0.03992521017789841,
-0.017515527084469795,
-0.0048440685495734215,
0.05935845151543617,
0.07542803883552551,
0.020402008667588234,
-0.03204428404569626,
-0.028896719217300415,
-0.02690301463007927,
-0.029961010441184044,
-0.012957671657204628,
-0.0025237177032977343,
0.03962531313300133,
-0.044269002974033356,
-0.0397212877869606,
-0.0018251164583489299,
0.03782384842634201,
0.04027969762682915,
0.012693041004240513,
0.0002537781256251037,
0.01377607136964798,
-0.026105567812919617,
-0.03415563702583313,
0.08744934946298599,
-0.020538946613669395,
0.024077191948890686,
0.03985967859625816,
-0.00579232070595026,
0.007905039936304092,
-0.003980022855103016,
0.0180197786539793,
-0.006920735351741314,
0.025324443355202675,
0.0820014551281929,
-0.033217016607522964,
0.04037393257021904,
0.029444769024848938,
0.0006238466594368219,
0.03715057671070099,
0.013463455252349377,
0.02133256010711193,
-0.038956254720687866,
0.009567981585860252,
-0.009225323796272278,
0.005247695371508598,
-0.01669897884130478,
-0.015358825214207172,
0.00267172884196043,
-0.002110815839841962,
0.02918871119618416,
0.08643500506877899,
0.039512112736701965,
-0.02638177201151848,
-0.05246364697813988,
-0.0067644002847373486,
-0.06083044037222862,
-0.03210693225264549,
-0.018713422119617462,
0.04151016101241112,
0.01231988612562418,
0.022343404591083527,
0.009082390926778316,
-0.010955408215522766,
0.013014950789511204,
-0.02718799188733101,
0.05370287597179413,
0.05983484163880348,
0.02379177324473858,
-0.013437600806355476,
0.023502210155129433,
-0.018828818574547768,
-0.0667116791009903,
0.0042209383100271225,
0.016266219317913055,
-0.012548154219985008,
-0.017123347148299217,
0.008473433554172516,
-0.006281820125877857,
0.015033181756734848,
-0.014689527451992035,
-0.014414079487323761,
-0.003577808616682887,
0.0048324125818908215,
-0.11275867372751236,
-0.04025930166244507,
0.040949348360300064,
0.009929046966135502,
-0.005185928661376238,
-0.0781526193022728,
-0.009504105895757675,
0.029800765216350555,
0.034702446311712265,
0.00912143848836422,
0.010254688560962677,
-0.0020577108953148127,
0.06457416713237762,
0.0029862963128834963,
-0.027118319645524025,
-0.03218083083629608,
-0.00007094696047715843,
-0.053504008799791336,
0.005111799109727144,
-0.0507231168448925,
0.02534140646457672,
0.016759872436523438,
0.02758331410586834,
-0.01760978437960148,
0.028287531808018684,
-0.045965466648340225,
-0.0018690292490646243,
-0.008584421128034592,
0.030815647915005684,
0.0014106774469837546,
0.05895089730620384,
0.04427150636911392,
0.011095141991972923,
0.031774669885635376,
0.005939154885709286,
0.023270338773727417,
0.019645605236291885,
0.040604427456855774,
0.030745061114430428,
-0.024886589497327805,
-0.019437547773122787,
-0.026888228952884674,
0.022152498364448547,
-0.015561945736408234,
-0.02724977396428585,
-0.023722367361187935,
-0.02538171224296093,
0.022051962092518806,
0.0467836819589138,
0.0283491350710392,
0.03612736240029335,
-0.032765813171863556,
0.029338289052248,
-0.02281535044312477,
0.0028128360863775015,
-0.039666954427957535,
0.016293443739414215,
0.0073260050266981125,
-0.017823344096541405,
0.037217892706394196,
-0.03064734861254692,
-0.0035820244811475277,
0.036199308931827545,
-0.015067200176417828,
0.02703590877354145,
0.02335476689040661,
0.01740775629878044,
-0.0024789210874587297,
-0.024002235382795334,
0.0650729387998581,
-0.015320926904678345,
-0.00856691598892212,
0.011915656737983227,
-0.009783806279301643,
-0.02203712798655033,
-0.024622570723295212,
0.03685721382498741,
0.008715405128896236,
-0.013480092398822308,
-0.03242040053009987,
0.005063986871391535,
0.03572843223810196,
0.023021524772047997,
0.028094107285141945,
-0.030360322445631027,
0.08238988369703293,
0.05748159438371658,
0.010627941228449345,
0.003672060091048479,
0.018428849056363106,
0.0040773553773760796,
0.02926315926015377,
0.0060710604302585125,
-0.04505438730120659,
-0.058927152305841446,
-0.026354625821113586,
0.05177359655499458,
0.014066915027797222,
-0.007369727827608585,
0.003116670763120055,
0.02699761465191841,
0.025915686041116714,
-0.0064696394838392735,
0.017478035762906075,
-0.04522380605340004,
-0.01184111088514328,
-0.0007309033535420895,
-0.0007205614820122719,
0.028626976534724236,
-0.005203763488680124,
-0.02637416310608387,
0.030571909621357918,
0.009567216970026493,
-0.045477189123630524,
-0.006425935309380293,
-0.004538822919130325,
0.008190696127712727,
0.008789526298642159,
0.0204586461186409,
-0.02789480797946453,
0.03536887839436531,
-0.01707567647099495,
0.028752963989973068,
0.050483714789152145,
0.025447770953178406,
0.004348103888332844,
-0.027865104377269745,
-0.003357834182679653,
0.03841306269168854,
0.004681163001805544,
-0.01661895215511322,
-0.014831025153398514,
0.010746823623776436,
-0.045867037028074265,
0.010502610355615616,
-0.01109537947922945,
-0.02869039960205555,
-0.019199617207050323,
0.025298867374658585,
0.03365291282534599,
0.05309755727648735,
-0.02921270579099655,
-0.03097584843635559,
-0.03429953008890152,
-0.025205234065651894,
-0.00010366774949943647,
-0.007231967523694038,
0.05699137970805168,
-0.03581135347485542,
0.041891615837812424,
-0.025289636105298996,
-0.020507697016000748,
-0.006379534024745226,
0.005548090673983097,
0.0009836319368332624,
0.00023584156588185579,
-0.01129184290766716,
-0.048452045768499374,
0.01196917612105608,
0.005007124971598387,
-0.019392164424061775,
-0.001238813973031938,
0.0008832694147713482,
0.062436480075120926,
-0.03855372220277786,
-0.03948492556810379,
-0.004978937562555075,
-0.060109518468379974,
-0.06622695177793503,
-0.03146534040570259,
0.004954262636601925,
0.0007911411230452359,
0.00668291375041008,
0.026154285296797752,
0.046083010733127594,
-0.01679292321205139,
-0.009547561407089233,
-0.031395141035318375,
-0.03244407847523689,
-0.01160492841154337,
-0.037390369921922684,
0.01852576807141304,
-0.026615414768457413,
-0.003379274858161807,
0.04871485009789467,
0.029107671231031418,
-0.03354893624782562,
-0.014319433830678463,
-0.003271179972216487,
0.023116648197174072,
0.00046172316069714725,
0.04928519204258919,
0.01646728254854679,
0.03914697468280792,
0.03851817548274994,
-0.010585402138531208,
0.049339137971401215,
0.047437094151973724,
0.025103051215410233,
-0.01741885393857956,
0.01794997788965702,
0.005999134387820959,
0.01055076252669096,
0.0013789375079795718,
0.022354284301400185,
0.004125344101339579,
0.027748946100473404,
-0.005478874314576387,
0.054545462131500244,
0.06187533959746361,
-0.06715273857116699,
0.02972962148487568,
0.0004010962729807943,
-0.007403203751891851,
-0.064804807305336,
0.036003414541482925,
0.015706367790699005,
-0.009228157810866833,
0.0021475013345479965,
0.01288590021431446,
0.07850281894207001,
-0.02153008058667183,
0.007858569733798504,
-0.0029503677505999804,
0.020755935460329056,
-0.0281923096626997,
-0.035127364099025726,
0.02500913478434086,
-0.007433186750859022,
-0.016787981614470482,
-0.005003608763217926,
0.04187866300344467,
0.0245512742549181,
0.02577478438615799,
-0.028621278703212738,
-0.052303247153759,
-0.07511119544506073,
0.00019085065287072212,
-0.05405450612306595,
0.0028501388151198626,
-0.015137183479964733,
0.01092588435858488,
0.0057091303169727325,
0.05544567108154297,
-0.012545021250844002,
-0.028079481795430183,
-0.0194232277572155,
-0.01661410927772522,
-0.08061693608760834,
0.007370826788246632,
-0.01428936142474413,
0.006204535253345966,
-0.026175038889050484,
-0.007068506442010403,
-0.03224111720919609,
-0.015821808949112892,
-0.003799507860094309,
-0.03857826441526413,
-0.03256679326295853,
-0.0629306361079216,
0.02639835700392723,
-0.04609250649809837,
-0.06192278861999512,
-0.006693190895020962,
0.033688366413116455,
0.06306346505880356,
-0.008731240406632423,
0.0588514618575573,
-0.004377827513962984,
-0.029870571568608284,
-0.003183334833011031,
-0.01859579235315323,
-0.02267523482441902,
-0.004061460494995117,
-0.018607880920171738,
0.0012578475289046764,
-0.0028548045083880424,
-0.002682772930711508,
0.0031724076252430677,
0.04028743878006935,
0.02197037823498249,
-0.003907207865267992,
-0.03301394730806351,
-0.005895392969250679,
-0.013353784568607807,
-0.0007580253877677023,
0.008389543741941452,
0.02812700904905796,
-0.015225222334265709,
0.030168455094099045,
0.04832060635089874,
0.0050438521429896355,
-0.002156378934159875,
0.06929843872785568,
0.03967238590121269,
0.0024777210783213377,
-0.006393777672201395,
-0.01320610474795103,
-0.01256526354700327,
-0.010816897265613079,
-0.02587929740548134,
0.04505467042326927,
0.0353897362947464,
0.009838835336267948,
-0.02447991631925106,
0.019878949970006943,
0.0192056093364954,
-0.014211445115506649,
0.011473510414361954,
-0.030502332374453545,
0.0033040207345038652,
-0.04157675802707672,
-0.015061360783874989,
-0.005404159426689148,
0.018093978986144066,
0.03695058822631836,
-0.010396760888397694,
-0.02955768071115017,
-0.08274569362401962,
-0.0383724607527256,
0.02196519263088703,
0.06504330784082413,
-0.05524437502026558,
0.012199237942695618,
-0.05524665489792824,
-0.0216775331646204,
0.0098359864205122,
-0.05404100567102432,
0.024398012086749077,
-0.027022460475564003,
0.006097740959376097,
0.031117388978600502,
-0.009784291498363018,
-0.008079913444817066,
0.04431784898042679,
0.0019384132465347648,
0.0036440829280763865,
0.003101983107626438,
0.01313585601747036,
-0.03050769492983818,
0.005650673061609268,
0.02526543289422989,
0.019768740981817245,
0.0004554994229692966,
-0.007578147109597921,
-0.036368127912282944,
0.0014921455876901746,
-0.0027345989365130663,
-0.06210875138640404,
-0.006910990457981825,
-0.008359085768461227,
-0.040762584656476974,
0.029215702787041664,
-0.03768082335591316,
-0.0984860435128212,
0.040974464267492294,
0.04655103012919426,
-0.010486106388270855,
-0.015023618005216122,
-0.04321474954485893,
0.0878218486905098,
0.040121711790561676,
0.025166096165776253,
0.032710809260606766,
0.040627703070640564,
-0.010958883911371231,
0.017520001158118248,
-0.004643762484192848,
0.021020323038101196,
-0.03048595041036606,
0.01803780160844326,
-0.0030852952040731907,
0.03234180063009262,
0.001420734217390418,
0.04971671476960182,
0.01689014956355095,
-0.005399477668106556,
0.014381004497408867,
-0.05268515273928642,
0.007645509205758572,
0.0007983189425431192,
0.011258670128881931,
-0.011689002625644207,
-0.02576095052063465,
0.029273591935634613,
0.030338048934936523,
0.00966764334589243,
0.036275822669267654,
-0.03010864369571209,
0.003959287889301777,
0.00541351456195116,
-0.03398286923766136,
0.011601748876273632,
-0.07039930671453476,
-0.002970958361402154,
0.004589964170008898,
-0.05146224796772003,
0.0410563088953495,
0.015866324305534363,
0.027437454089522362,
0.027998875826597214,
-0.02407878078520298,
0.002571234479546547,
-0.02203190140426159,
-0.0395364984869957,
0.018743125721812248,
-0.06476731598377228,
0.023651907220482826,
0.017005518078804016,
0.016667185351252556,
-0.0875924676656723,
-0.034774571657180786,
0.022390874102711678,
-0.006596003193408251,
-0.06033138558268547,
-0.0325622521340847,
0.012382536195218563,
0.01836608722805977,
-0.02481517381966114,
0.02166057750582695,
0.03021574579179287,
-0.03108932636678219,
-0.0316709466278553,
-0.003982681781053543,
0.03860500082373619,
0.11177042126655579,
-0.030489061027765274,
-0.02923005446791649,
0.044967010617256165,
0.004926321096718311,
0.03549826890230179,
-0.02719016559422016,
0.0027363148983567953,
-0.005546603351831436,
-0.04818536713719368,
-0.006877745036035776,
0.021176600828766823,
0.01645701192319393,
-0.018031755462288857,
-0.016776345670223236,
0.018268335610628128,
0.023249175399541855,
0.015066971071064472,
-0.016802381724119186,
0.02600361779332161,
0.007678319234400988,
0.008394752629101276,
-0.05621560662984848,
-0.006892363075166941,
0.021762173622846603,
0.0011087203165516257,
0.01445816084742546,
-0.022677456960082054,
0.03127189353108406,
0.0191042460501194,
0.029432648792862892,
0.0055707585997879505,
0.00826522521674633,
0.05501154810190201,
-0.0008578943670727313,
0.02318068966269493,
-0.011938917450606823,
0.026948243379592896,
0.03588227927684784,
-0.0008619019063189626,
-0.013100932352244854,
-0.03276125341653824,
-0.032834235578775406,
0.024180853739380836,
0.07204966992139816,
-0.03541511669754982,
0.01874753087759018,
-0.028260363265872,
0.026545947417616844,
0.004984305705875158,
-0.07237720489501953,
0.005096725653856993,
-0.016847945749759674,
-0.030171798542141914,
0.05769272521138191,
-0.024150649085640907,
0.0022268081083893776,
0.0670563131570816,
0.063136026263237,
-0.033356018364429474,
0.023443257436156273,
0.025816956534981728,
0.01011059433221817,
0.03584759682416916,
0.015453210100531578,
-0.042340558022260666,
0.030609676614403725,
-0.030819153413176537,
0.02344334125518799,
0.05532196909189224,
-0.037587642669677734,
0.04095015302300453,
-0.01169799454510212,
-0.02027282677590847,
-0.04114558547735214,
-0.0274078156799078,
-0.017812572419643402,
0.01040829997509718,
0.013251006603240967,
0.03821536526083946,
-0.018356356769800186,
0.003986691124737263,
-0.007862764410674572,
-0.0005461261607706547,
-0.024767842143774033,
0.006114890333265066,
-0.06306131184101105,
-0.029381228610873222,
-0.029985764995217323,
-0.047666627913713455,
0.037898581475019455,
-0.011307137086987495,
-0.03830616548657417,
0.01099830400198698,
-0.05056259408593178,
0.021118901669979095,
-0.013197815977036953,
0.004811475519090891,
0.011056916788220406,
0.08505308628082275,
-0.038550812751054764,
0.02011946588754654,
0.007247189525514841,
0.020791536197066307,
0.10612166672945023,
0.024063754826784134,
0.01383412815630436,
-0.009488210082054138,
0.0035288811195641756,
0.02706454135477543,
-0.01843446120619774,
0.01724235527217388,
-0.006247842218726873,
-0.007599067874252796,
0.006783684249967337,
-0.004456211347132921,
0.05066053941845894,
-0.00031685124849900603,
0.01665549911558628,
0.04722564294934273,
-0.027414223179221153,
0.006593417841941118,
-0.02738754078745842,
-0.009336026385426521,
-0.002115910407155752,
0.027645926922559738,
-0.09142257273197174,
0.03463456779718399,
0.006059528794139624,
-0.011274055577814579,
-0.01893354207277298,
-0.034283436834812164,
0.000821700319647789,
0.03209486976265907,
-0.05350169911980629,
-0.018802696838974953,
0.04216166213154793,
-0.041428130120038986,
-0.014211858622729778,
-0.024801086634397507,
0.005497632082551718,
-0.020810632035136223,
0.012420960702002048,
0.0033339045476168394,
0.04287921264767647,
0.02269021049141884,
0.017354266718029976,
0.04115927964448929,
-0.055142540484666824,
-0.015628281980752945,
-0.031099094077944756,
0.016102384775877,
-0.01898506097495556,
-0.02255845256149769,
-0.04919755086302757,
-0.01570206694304943,
0.016386160627007484,
-0.015085882507264614,
-0.014478344470262527,
0.010938486084342003,
0.04165416210889816,
-0.004957002121955156,
-0.03211447596549988,
0.0018274334724992514,
0.002271733246743679,
0.013475563377141953,
0.036770228296518326,
0.022025445476174355,
0.0141434445977211,
0.020408768206834793,
-0.010753643698990345,
0.011843141168355942,
0.018914004787802696,
0.004416250623762608,
-0.07789220660924911,
0.007680349983274937,
-0.04870372638106346,
0.0012588785029947758,
0.030520115047693253,
0.054186899214982986,
0.03869754076004028,
0.045037008821964264,
-0.02372048981487751,
-0.000221442969632335,
0.016651563346385956,
0.03274146467447281,
-0.014584827236831188,
-0.03675157576799393,
-0.021795660257339478,
0.005908209830522537,
-0.017563963308930397,
0.024350404739379883,
-0.022733651101589203,
0.03523688390851021,
-0.007617957424372435,
0.03806750848889351,
0.024759646505117416,
-0.04276785999536514,
-0.01994924806058407,
-0.01766349747776985,
-0.01686232164502144,
-0.0010989656439051032,
0.0012735499767586589,
0.004538173787295818,
0.043488893657922745,
0.014843082055449486,
0.05578659847378731,
0.04284089803695679,
-0.02089294232428074,
0.027365107089281082,
0.007963504642248154,
-0.012449612841010094,
-0.0047499933280050755,
0.012675900012254715,
-0.008558753877878189,
-0.00834900513291359,
-0.021181464195251465,
-0.004212819039821625,
-0.020590541884303093,
0.012889455072581768,
0.01929631270468235,
-0.032362814992666245,
0.03191303461790085,
-0.06819379329681396,
0.020855722948908806,
-0.01761890947818756,
0.01661250740289688,
-0.019080210477113724,
0.02884461171925068,
0.011913678608834743,
-0.02598046138882637,
-0.04352335259318352,
0.03221122920513153,
-0.02809780463576317,
0.005908306688070297,
0.015559622086584568,
-0.0066455756314098835,
0.03690194711089134,
0.00664239376783371,
-0.00017879102961160243,
-0.027263149619102478,
0.04267359524965286,
-0.039961010217666626,
-0.007390822283923626,
0.007647720631211996,
0.013712946325540543,
-0.08247077465057373,
0.03772218897938728,
-0.012961202301084995,
0.011400281451642513,
0.021351436153054237,
0.002709608990699053,
-0.03456044942140579,
0.07439253479242325,
-0.034092433750629425,
-0.013107131235301495,
0.03118310123682022,
0.02899099513888359,
0.007508180569857359,
-0.025700891390442848,
-0.01750006340444088,
0.01981227844953537,
-0.020266138017177582,
0.034670405089855194,
0.006428612396121025,
0.013382461853325367,
-0.013941335491836071,
-0.0022412757389247417,
-0.043796319514513016,
-0.0037570816930383444,
0.0051251561380922794,
0.005008460953831673,
0.03448386490345001,
0.0442463681101799,
-0.029127711430191994,
0.08203329890966415,
0.025044862180948257,
-0.02118806168437004,
-0.0653737485408783,
-0.009564475156366825,
-0.00648112827911973,
0.005764726549386978,
0.014974878169596195,
-0.04551508277654648,
0.01764632761478424,
0.021898992359638214,
-0.10445314645767212,
-0.01673540659248829,
-0.06474701315164566,
-0.05489585921168327,
-0.025152793154120445,
-0.007287889719009399,
-0.03511321172118187,
0.019071653485298157,
0.017404459416866302,
0.068287193775177,
0.035783566534519196,
0.021493859589099884,
-0.024376513436436653,
0.041546531021595,
-0.013596936129033566,
0.008143254555761814,
-0.009661408141255379,
0.015524501912295818,
0.09942326694726944,
0.013345446437597275,
-0.01566718891263008,
0.030087774619460106,
0.007100352086126804,
0.002659119665622711,
0.042164940387010574,
-0.0012014841195195913,
-0.03608838841319084,
0.004946185741573572,
-0.0040237512439489365,
0.006654685363173485,
0.0003072672407142818,
0.04143639653921127,
0.010681633837521076,
0.038276173174381256,
-0.00761473597958684,
-0.0011589174391701818,
0.01875530183315277,
-0.015779851004481316,
0.019759656861424446,
0.020637456327676773,
-0.022450238466262817,
0.011121245101094246,
0.01567990519106388,
0.035518959164619446,
0.02747276984155178,
0.01036972925066948,
-0.0007271079812198877,
-0.02984224632382393,
-0.015290047973394394,
-0.00002096880598401185,
0.0012460729340091348,
0.005534193944185972,
0.02341822162270546,
-0.037003740668296814,
-0.040951501578092575,
-0.06494414061307907,
-0.0008450057939626276,
-0.03671546280384064,
-0.013945883139967918,
0.00378644117154181,
0.018354540690779686,
-0.019470740109682083,
-0.019673388451337814,
-0.0247271079570055,
-0.015800587832927704,
0.07663749903440475,
0.02886953391134739,
0.05545209348201752,
-0.016656938940286636,
-0.060108523815870285,
0.0198301263153553,
-0.033683277666568756,
0.029365109279751778,
-0.04947252571582794,
-0.0064787836745381355,
-0.034308284521102905,
-0.04061398282647133,
0.026259692385792732,
0.02830706164240837,
0.048240117728710175,
-0.030361022800207138,
-0.0024671214632689953,
0.015553883276879787,
-0.04639629274606705,
0.05150037631392479,
-0.04339909553527832,
0.01936475932598114,
0.02056511677801609,
0.008054913952946663,
0.008109345100820065,
-0.03612745925784111,
-0.038383517414331436,
0.030079593881964684,
0.014620223082602024,
0.012686179019510746,
0.006729353219270706,
0.02427647076547146,
-0.018223173916339874,
0.034142591059207916,
-0.003684860887005925,
-0.03258683159947395,
0.09201861172914505,
-0.0018795462092384696,
-0.029482632875442505,
0.02559361420571804,
0.004591462202370167,
-0.05073881894350052,
0.04918745160102844,
-0.009766485542058945,
-0.014498217962682247,
0.002019317587837577,
0.0011068828171119094,
0.051242779940366745,
-0.06125481426715851,
0.004978430923074484,
0.024355990812182426,
0.007766352035105228,
-0.04449055716395378,
0.012941566295921803,
-0.0012172908755019307,
0.03715228661894798,
0.04729698598384857,
-0.003038739552721381,
0.007097834721207619,
-0.016537614166736603,
-0.041448790580034256,
0.019596576690673828,
0.01805381290614605,
0.027186313644051552,
0.006911902222782373,
0.0009570023976266384,
0.0019564987160265446,
0.03820500150322914,
0.01856883056461811,
0.002312441123649478,
-0.01882496289908886,
0.007738637272268534,
0.007795019540935755,
0.01731388084590435,
-0.0008777015609666705,
0.022489169612526894,
-0.012396538630127907,
0.06775518506765366,
-0.01764293573796749,
0.006996857933700085,
-0.0356534980237484,
-0.016441157087683678,
-0.012917198240756989,
0.022311579436063766,
-0.03362084925174713,
-0.025862742215394974,
-0.01895943097770214,
-0.03802668675780296,
-0.01592736691236496,
0.029018936678767204,
0.04901476949453354,
-0.0246419757604599,
-0.0010547167621552944,
-0.04445575177669525,
-0.032011497765779495,
-0.006214193534106016,
-0.01386736799031496,
-0.054037559777498245,
-0.0264741163700819,
0.017865650355815887,
0.030247123911976814,
-0.018638353794813156,
-0.016690731048583984,
-0.01717555522918701,
-0.063607357442379,
0.03160814195871353,
-0.06058148294687271,
0.0178539901971817,
-0.04386206343770027,
0.021433457732200623,
-0.0371696874499321,
-0.05851180478930473
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/6400/are-tidal-power-plants-slowing-down-earths-rotation">Are tidal power plants slowing down Earth's rotation?</a> </p>
</blockquote>
<p>Since we have various energy acquiring facilities that harvest energy from earth rotation. (e.g. wind, tidal power planet)</p>
<p>Will our earth rotation be slower down? Is there any form of force to accelerate earth rotation speed? </p>
| 349 |
[
-0.049236174672842026,
-0.029415274038910866,
-0.03778327628970146,
0.011380686424672604,
0.05737263709306717,
-0.013412343338131905,
-0.048360470682382584,
-0.045278824865818024,
0.011218666099011898,
-0.057080961763858795,
0.028529329225420952,
0.05350697413086891,
0.04607773199677467,
0.027662713080644608,
0.009415111504495144,
0.02232012152671814,
-0.04269485920667648,
0.031036019325256348,
0.014002509415149689,
-0.002722063334658742,
-0.03956678509712219,
-0.007099931128323078,
0.008677390404045582,
0.033033426851034164,
-0.014664411544799805,
-0.001965062227100134,
0.055136729031801224,
0.01622863858938217,
-0.0342637374997139,
0.07201959192752838,
0.03658473864197731,
0.00856130849570036,
0.02249784581363201,
0.04634929075837135,
0.002586922375485301,
0.02024383842945099,
-0.040509745478630066,
-0.006185407750308514,
0.01763986237347126,
0.029336029663681984,
-0.04441728815436363,
-0.01176456082612276,
-0.0269397534430027,
0.03386056050658226,
-0.023947114124894142,
0.0347619503736496,
-0.0036546713672578335,
-0.007785345893353224,
0.031588297337293625,
-0.03590237349271774,
0.07706227153539658,
-0.032387521117925644,
0.024412447586655617,
0.029269441962242126,
-0.0013257681857794523,
-0.011842305772006512,
0.048248689621686935,
0.061952855437994,
-0.05451025813817978,
-0.030817287042737007,
0.010613571852445602,
-0.008356107398867607,
-0.0030392101034522057,
0.0032115394715219736,
-0.017132315784692764,
0.04172089695930481,
-0.016631226986646652,
0.023548277094960213,
0.03918604552745819,
0.0012876500841230154,
0.01325186062604189,
-0.006242311093956232,
-0.03092030994594097,
-0.022641487419605255,
-0.03240818530321121,
-0.03530513867735863,
-0.017015747725963593,
0.023770269006490707,
0.04203794524073601,
0.054006852209568024,
-0.02178264409303665,
0.01817643828690052,
0.05048616603016853,
0.01908261515200138,
0.06142725795507431,
0.008996413089334965,
0.04357963427901268,
-0.015720348805189133,
0.046123310923576355,
0.025003276765346527,
0.009258469566702843,
0.0032197050750255585,
-0.030969087034463882,
-0.03546031564474106,
-0.03002224490046501,
0.04556307941675186,
-0.020135805010795593,
0.05378111079335213,
0.04174957796931267,
-0.0187516026198864,
-0.00959470123052597,
-0.0011506148148328066,
0.03896789997816086,
0.03347097337245941,
0.016656162217259407,
-0.01652008481323719,
-0.07168020308017731,
-0.00500538619235158,
-0.04478076845407486,
-0.013537276536226273,
-0.044412076473236084,
0.00782513152807951,
-0.015202591195702553,
-0.028842801228165627,
0.00490445364266634,
-0.00665280083194375,
-0.005627130623906851,
0.0029639715794473886,
0.03831097111105919,
0.06472952663898468,
0.04186663031578064,
-0.021382290869951248,
0.03287347033619881,
-0.012154693715274334,
-0.04669263958930969,
0.005697614513337612,
0.045024532824754715,
-0.03769472613930702,
-0.023375384509563446,
0.012086725793778896,
0.02515999786555767,
-0.005649661645293236,
-0.012463131919503212,
-0.00031143176602199674,
0.07077790051698685,
0.0007431493140757084,
-0.09471695125102997,
-0.07464122772216797,
0.06536487489938736,
0.022745558992028236,
0.018289323896169662,
-0.06492017209529877,
0.0016883308999240398,
-0.05069155991077423,
0.0728701502084732,
0.015501365065574646,
0.004052824340760708,
-0.005021923687309027,
0.03901353105902672,
-0.01972912810742855,
-0.01156106311827898,
0.03431341424584389,
0.03743784502148628,
-0.0476205088198185,
-0.004467974416911602,
-0.0954870656132698,
0.03291891887784004,
0.02404257096350193,
0.011626810766756535,
0.003110561752691865,
0.03478231281042099,
0.005041292868554592,
0.01560269482433796,
-0.011702314019203186,
-0.005538614932447672,
-0.053957194089889526,
0.07323367893695831,
-0.003826919011771679,
-0.004007750656455755,
0.009446609765291214,
-0.007368007209151983,
0.03384541720151901,
-0.02534666657447815,
-0.0075790779665112495,
0.039055243134498596,
-0.04254425689578056,
-0.004124030936509371,
-0.031375348567962646,
0.015890829265117645,
-0.01878857985138893,
-0.02934127114713192,
-0.013569919392466545,
-0.02264029160141945,
-0.029291043058037758,
0.02666405588388443,
0.08601667732000351,
-0.0037743004504591227,
-0.015782082453370094,
-0.01029130443930626,
-0.044668249785900116,
0.030539661645889282,
-0.05395044758915901,
0.02825980819761753,
-0.026765208691358566,
0.0008485513972118497,
0.014171147719025612,
0.00919985119253397,
0.033732328563928604,
-0.010913511738181114,
0.011629805900156498,
0.009016555733978748,
0.06409388035535812,
0.00683887442573905,
0.013542425818741322,
0.01017716247588396,
0.05140145868062973,
0.03492208197712898,
-0.018899165093898773,
-0.007302770856767893,
0.010390463285148144,
-0.03503400459885597,
-0.004037031438201666,
-0.04389176145195961,
0.013029241934418678,
-0.005871466360986233,
0.016796277835965157,
0.023360930383205414,
0.06634527444839478,
-0.02570115029811859,
0.009770006872713566,
-0.03822715952992439,
0.05380161851644516,
0.030599793419241905,
-0.024625902995467186,
0.04466358572244644,
0.04736599326133728,
0.023687919601798058,
0.012926043011248112,
-0.01182524859905243,
-0.016624681651592255,
-0.05040162429213524,
0.020317422226071358,
0.038588810712099075,
0.03075007162988186,
-0.05122413486242294,
0.04064593464136124,
0.020956620573997498,
0.04406873881816864,
0.037583090364933014,
-0.00894774030894041,
0.007643337361514568,
-0.027256272733211517,
0.028288904577493668,
0.012414793483912945,
-0.02378861978650093,
0.02226630598306656,
0.04269680380821228,
0.017409373074769974,
0.009389214217662811,
0.003288612002506852,
-0.009300950914621353,
0.04318942129611969,
0.005555229261517525,
0.001891628373414278,
0.005703098606318235,
-0.004835209809243679,
0.046859800815582275,
-0.03522390127182007,
-0.01897924579679966,
0.01332886889576912,
-0.007803976070135832,
0.043325040489435196,
-0.026871735230088234,
0.004980094265192747,
-0.0076726279221475124,
0.0040125008672475815,
-0.021345850080251694,
-0.012847629375755787,
0.04289041459560394,
-0.042728446424007416,
0.016361545771360397,
-0.024449938908219337,
-0.003045000834390521,
-0.001435935264453292,
0.007222134154289961,
0.029405297711491585,
-0.01973326876759529,
0.061690255999565125,
-0.02446528524160385,
0.0134406303986907,
0.019527889788150787,
-0.0423428975045681,
-0.027698611840605736,
-0.004929217044264078,
-0.03212491050362587,
0.016183706000447273,
0.0009906468912959099,
-0.041410934180021286,
0.051070209592580795,
-0.011735321953892708,
0.0074105034582316875,
0.023821847513318062,
0.003941718488931656,
-0.051751669496297836,
0.02182883955538273,
-0.04833988472819328,
0.03201562166213989,
-0.005787292495369911,
-0.012249384075403214,
0.0427950881421566,
0.024908440187573433,
-0.023680759593844414,
0.010274428874254227,
-0.05096425488591194,
-0.02595149539411068,
0.0041231196373701096,
0.002187419217079878,
0.02260148897767067,
-0.04352051764726639,
-0.010581730864942074,
0.010892082937061787,
-0.09178540110588074,
0.0033536129631102085,
-0.04338148608803749,
-0.05324069410562515,
-0.005162615794688463,
-0.02323051728308201,
0.06689045578241348,
-0.011832894757390022,
-0.029483623802661896,
0.056707367300987244,
0.04509159177541733,
-0.02781751938164234,
-0.021960431709885597,
-0.04775193706154823,
0.0036585794296115637,
-0.010053349658846855,
-0.0043355622328817844,
0.035602129995822906,
-0.0163193941116333,
-0.015388456173241138,
-0.0007978667854331434,
0.022689564153552055,
0.0003440765431150794,
0.015337774530053139,
-0.020868796855211258,
0.006389022804796696,
0.009341603145003319,
0.01462620124220848,
0.04732189700007439,
0.014007006771862507,
-0.032133735716342926,
0.0034306379966437817,
-0.016298912465572357,
0.047308407723903656,
-0.0012555550783872604,
-0.03727879375219345,
0.051902707666158676,
0.010772430337965488,
-0.002131320768967271,
-0.027885103598237038,
0.03771120309829712,
0.02613404579460621,
0.004963510669767857,
0.012375684455037117,
0.0009255079203285277,
0.06266399472951889,
0.03497335687279701,
-0.012433759868144989,
0.008466135710477829,
0.06710784137248993,
-0.00986037589609623,
0.0012529201339930296,
-0.05398118868470192,
-0.0019462978234514594,
-0.002328455913811922,
-0.02288319543004036,
-0.03052707202732563,
0.049486592411994934,
0.023327600210905075,
0.03898606449365616,
-0.0009305148851126432,
-0.02680519036948681,
0.006567242089658976,
-0.06344339996576309,
0.01275723334401846,
-0.04112497344613075,
0.027431923896074295,
0.002279093023389578,
0.01487383246421814,
0.010371553711593151,
0.006545310840010643,
0.007022087462246418,
0.02382105216383934,
-0.06112492457032204,
0.030655037611722946,
-0.05339307710528374,
-0.014617696404457092,
0.020020736381411552,
0.03456741198897362,
-0.022492285817861557,
-0.0029867319390177727,
0.0034229601733386517,
-0.0497431680560112,
-0.02146359719336033,
-0.060042206197977066,
0.0023537175729870796,
0.018978916108608246,
-0.018702154979109764,
-0.004279129207134247,
0.040998611599206924,
0.04636824131011963,
-0.06115559861063957,
0.06260059028863907,
0.030650686472654343,
-0.058996714651584625,
0.01957803964614868,
0.011992198415100574,
-0.013906127773225307,
-0.01195644773542881,
-0.0026308840606361628,
0.03108994849026203,
0.017517441883683205,
0.002977140247821808,
0.0019805736374109983,
0.01146257296204567,
0.006342299282550812,
0.019101817160844803,
-0.01765936240553856,
-0.028272902593016624,
-0.01467621885240078,
-0.016169512644410133,
0.019828468561172485,
0.039392776787281036,
0.010959755629301071,
-0.009833450429141521,
0.0108066750690341,
-0.014805486425757408,
0.009090323001146317,
0.027035577222704887,
0.030700841918587685,
0.0006126287044025958,
-0.021988309919834137,
-0.05610235780477524,
-0.021274564787745476,
0.009375292807817459,
0.005300930701196194,
0.005737214349210262,
0.004232104867696762,
-0.016478685662150383,
0.00980993639677763,
0.025601668283343315,
0.023512009531259537,
-0.020990347489714622,
0.04723724350333214,
-0.003908627200871706,
0.03220238909125328,
0.014960781671106815,
-0.0055576809681952,
0.008697805926203728,
0.016461333259940147,
0.03430401161313057,
0.002993299625813961,
-0.0015781887341290712,
-0.10350370407104492,
-0.0030368780717253685,
0.020676953718066216,
0.04865238443017006,
-0.04991629347205162,
-0.03649041801691055,
-0.05310877785086632,
-0.01854865439236164,
0.03559646010398865,
-0.03862852603197098,
0.031229957938194275,
-0.03533171862363815,
-0.006888081785291433,
-0.01146915927529335,
-0.02632780745625496,
0.008960180915892124,
-0.017002394422888756,
-0.011739098466932774,
0.035257890820503235,
-0.03135453164577484,
0.00889523420482874,
0.018865806981921196,
0.009071117267012596,
0.027653662487864494,
0.04080252721905708,
0.02660788781940937,
-0.02037341333925724,
-0.02267490141093731,
0.005837547592818737,
-0.024078717455267906,
-0.06578625738620758,
0.016098175197839737,
0.013022588565945625,
-0.035320673137903214,
0.03633128106594086,
-0.06261460483074188,
-0.05314859375357628,
0.02453005500137806,
0.00427595991641283,
-0.02740008756518364,
-0.026318730786442757,
-0.06608397513628006,
-0.0029950132593512535,
0.04979665204882622,
0.03144964948296547,
0.02761472761631012,
0.0949404314160347,
-0.05865587294101715,
0.014120731502771378,
0.0033991101663559675,
0.016951780766248703,
-0.051940564066171646,
-0.004751658532768488,
0.028756117448210716,
-0.017545411363244057,
-0.035901911556720734,
0.027202792465686798,
-0.000046882119931979105,
0.0037449931260198355,
-0.005582863464951515,
0.0009733392507769167,
-0.0025990649592131376,
0.01575726829469204,
0.03650492802262306,
-0.013127768412232399,
-0.038900356739759445,
0.046682532876729965,
-0.02706841751933098,
-0.0010072434088215232,
0.018027011305093765,
0.004555795341730118,
-0.00813949853181839,
0.028278807178139687,
0.0176389142870903,
-0.02985239587724209,
-0.02929503470659256,
0.002403037855401635,
0.013131566345691681,
-0.031906139105558395,
0.05712949484586716,
-0.012780275195837021,
-0.01151462085545063,
0.03236265107989311,
-0.07187341898679733,
-0.041932396590709686,
0.016880180686712265,
-0.0036685627419501543,
-0.005488750524818897,
0.0031350913923233747,
0.037818606942892075,
0.041042231023311615,
0.0028246918227523565,
-0.02849770151078701,
-0.02943367324769497,
0.019575543701648712,
0.029689427465200424,
0.026413021609187126,
-0.04220835492014885,
-0.011972985230386257,
-0.06377684324979782,
-0.01637980341911316,
-0.046269189566373825,
0.0448576845228672,
-0.03810077905654907,
0.011622791178524494,
0.025966642424464226,
-0.029189612716436386,
0.07174654304981232,
-0.008869444951415062,
-0.01783495955169201,
0.010528444312512875,
-0.029830345883965492,
-0.023771140724420547,
-0.0665779635310173,
0.060324233025312424,
-0.047088928520679474,
-0.026406923308968544,
-0.010087979957461357,
-0.037502504885196686,
-0.012679439969360828,
-0.000027139043595525436,
-0.008138592354953289,
0.06439734250307083,
0.02346223220229149,
-0.018382815644145012,
-0.028949687257409096,
0.04487394541501999,
-0.015554556623101234,
0.05544467642903328,
-0.017215868458151817,
-0.007315313443541527,
-0.02976609207689762,
-0.0590977780520916,
-0.009202358312904835,
-0.004685424268245697,
-0.0386190265417099,
-0.0032978097442537546,
0.0558590367436409,
-0.027334880083799362,
-0.0015723810065537691,
0.019095204770565033,
0.025624286383390427,
0.042977217584848404,
0.003866651328280568,
0.008337737992405891,
-0.01587686315178871,
-0.0446234755218029,
-0.010182013735175133,
-0.045269694179296494,
-0.019847247749567032,
-0.018361076712608337,
0.06682898104190826,
-0.010310168378055096,
0.06102626398205757,
0.0031154919415712357,
-0.013089138083159924,
-0.017173148691654205,
-0.05062291398644447,
0.028544796630740166,
0.0171684417873621,
0.02868121676146984,
-0.001414159662090242,
-0.04668014496564865,
0.03010373003780842,
0.050654273480176926,
0.00608270475640893,
0.023332538083195686,
0.026345977559685707,
0.00660087401047349,
0.019481899216771126,
0.04382013902068138,
-0.018682407215237617,
-0.01343988161534071,
-0.001063753617927432,
-0.044775478541851044,
0.03508130460977554,
0.020460205152630806,
-0.03528718650341034,
0.05261087790131569,
0.04432928189635277,
0.0011852943571284413,
-0.034261103719472885,
0.0028898469172418118,
-0.05413829907774925,
0.0036936639808118343,
-0.015309500508010387,
0.013258797116577625,
-0.010766022838652134,
0.008585291914641857,
0.019612489268183708,
0.023073751479387283,
0.02138582244515419,
-0.042572397738695145,
-0.06496115773916245,
-0.0023071137256920338,
-0.018670344725251198,
-0.06159241497516632,
0.051923513412475586,
0.04581206664443016,
-0.04496483504772186,
0.023276619613170624,
-0.02966221608221531,
0.0074176667258143425,
0.0006372173666022718,
0.03526201844215393,
-0.04869888722896576,
0.09496262669563293,
-0.03573243319988251,
0.011686663143336773,
-0.01594344712793827,
-0.019049130380153656,
0.07747547328472137,
0.01984328217804432,
-0.003954686224460602,
-0.05199575424194336,
0.014331066980957985,
0.01924903690814972,
-0.016952995210886,
-0.035412706434726715,
-0.04687611758708954,
0.03851138800382614,
-0.026400865986943245,
-0.0063448441214859486,
0.04825843498110771,
0.013135071843862534,
-0.011321299709379673,
0.04897124320268631,
0.0007737198611721396,
-0.013790096156299114,
0.019922753795981407,
0.020950304344296455,
0.01329734269529581,
0.037706952542066574,
-0.034072425216436386,
0.018230276182293892,
-0.03300612047314644,
0.0061463406309485435,
-0.027704717591404915,
-0.04611983150243759,
0.011978075839579105,
0.014690611511468887,
-0.05332978814840317,
0.004619032144546509,
0.007790073286741972,
-0.028001416474580765,
-0.044388677924871445,
0.04597825929522514,
0.011821385473012924,
0.003230664413422346,
0.015883684158325195,
0.029443996027112007,
-0.02324773743748665,
0.021928295493125916,
0.03182147070765495,
0.03631601855158806,
-0.05863293260335922,
0.0361165851354599,
-0.03971997648477554,
0.005342287011444569,
0.03659763187170029,
0.005594242364168167,
-0.0035048811696469784,
0.006523496937006712,
0.02396881952881813,
-0.03724449500441551,
0.020882006734609604,
-0.016969116404652596,
0.011083382181823254,
-0.01946641318500042,
-0.05342298001050949,
-0.04045740142464638,
0.014724744483828545,
-0.013254838064312935,
0.03587043285369873,
-0.02844228222966194,
-0.024234123528003693,
0.020328007638454437,
0.012720591388642788,
0.03630799800157547,
-0.013390655629336834,
-0.019910309463739395,
-0.030512657016515732,
0.0007922122604213655,
-0.009695159271359444,
0.023256126791238785,
0.037652939558029175,
0.0013296115212142467,
0.04237772524356842,
0.015571581199765205,
0.005588488187640905,
-0.008275466039776802,
-0.051878202706575394,
0.0443982370197773,
-0.0015674663009122014,
-0.023287126794457436,
-0.003988021519035101,
0.005364480894058943,
0.03463497757911682,
0.020829658955335617,
0.022348036989569664,
-0.0010937961051240563,
-0.02032490074634552,
0.026831187307834625,
0.03625551238656044,
-0.0352059006690979,
-0.03507724404335022,
0.0075440132059156895,
-0.020301230251789093,
-0.05067929998040199,
-0.007036203518509865,
0.025297412648797035,
0.02087859995663166,
0.012865066528320312,
0.00041728594806045294,
0.005733609199523926,
-0.0273516234010458,
-0.03224923461675644,
0.034215305000543594,
-0.005322676617652178,
-0.030504833906888962,
0.023015348240733147,
-0.02114945277571678,
-0.026213202625513077,
0.007430422585457563,
-0.005844933446496725,
-0.006332306191325188,
0.03219696879386902,
0.01925726607441902,
-0.045615147799253464,
0.008963088504970074,
-0.03389947861433029,
0.02000228874385357,
-0.05693037435412407,
-0.006988468114286661,
-0.0553559884428978,
-0.027288751676678658,
0.0056914822198450565,
-0.01934381015598774,
0.017218146473169327,
0.0387144573032856,
-0.014396431855857372,
-0.0002786899858620018,
0.01745585724711418,
0.0058625005185604095,
-0.02890455722808838,
0.015271563082933426,
0.04835289716720581,
-0.024353547021746635,
0.02559041418135166,
-0.020763546228408813,
-0.037135012447834015,
0.07168566435575485,
-0.01211410854011774,
-0.005674234591424465,
0.02219940535724163,
-0.05248425528407097,
0.03658411651849747,
0.0195454154163599,
-0.029055949300527573,
0.02516794204711914,
0.06449107825756073,
-0.036209799349308014,
0.009029592387378216,
-0.00663447380065918,
0.002691673580557108,
-0.019832823425531387,
0.027950631454586983,
0.023199934512376785,
-0.049727510660886765,
-0.014427723363041878,
0.05030273273587227,
0.04829256236553192,
-0.026889121159911156,
0.00019530343706719577,
-0.025523008778691292,
0.00045481257257051766,
0.007450187113136053,
-0.007378134876489639,
-0.0076096137054264545,
0.009115678258240223,
0.02160865068435669,
-0.015566238202154636,
0.02821088768541813,
-0.010891915298998356,
0.010094482451677322,
-0.0665949359536171,
0.02095227688550949,
0.02535383030772209,
-0.0034562209621071815,
0.01761246658861637,
-0.013415093533694744,
-0.00858956016600132,
0.011520210653543472,
-0.0936664268374443,
-0.008093676529824734,
-0.00453652860596776,
-0.019817648455500603,
-0.05406074598431587,
0.04519950971007347,
0.021238556131720543,
-0.006698601879179478,
0.006994673050940037,
0.047676973044872284,
-0.019293438643217087,
0.03197371959686279,
0.0032151699997484684,
-0.034333404153585434,
0.004782234784215689,
0.013702097348868847,
0.012777110561728477,
0.009507084265351295,
0.059143152087926865,
-0.04530094936490059,
-0.03868109732866287,
0.01039145141839981,
0.014685789123177528,
0.030380113050341606,
-0.024783795699477196,
0.0036951242946088314,
0.011777011677622795,
0.01096087135374546,
0.05499424412846565,
-0.04679359495639801,
-0.02088664099574089,
0.028139103204011917,
-0.00783816259354353,
0.02201163023710251,
0.013910019770264626,
0.0056995488703250885,
0.02361246570944786,
-0.023170793429017067,
0.017208216711878777,
0.01112052146345377,
-0.01795532926917076,
0.0006105232750996947,
-0.013732084073126316,
-0.005932880099862814,
0.009926790371537209,
0.009097744710743427,
-0.016958804801106453,
-0.04279531538486481,
-0.026797065511345863,
0.017323629930615425,
-0.07435289025306702,
0.02242088131606579,
0.020067190751433372,
-0.007379502058029175,
-0.007202396634966135,
0.0030478646513074636,
-0.05929163843393326,
-0.016674775630235672,
-0.040920913219451904,
0.00676344009116292,
0.015575975179672241,
-0.026613524183630943,
-0.04660683125257492,
-0.011065189726650715,
-0.00548853725194931,
0.05631999298930168,
0.020106272771954536,
0.016313031315803528,
0.022471116855740547,
-0.0341264009475708,
-0.01542588695883751,
-0.033859673887491226,
-0.0008954238146543503,
0.010481255128979683,
0.015256068669259548,
-0.053987614810466766,
-0.04184369742870331,
-0.016594624146819115,
0.03100694715976715,
0.024135872721672058,
-0.004804602824151516,
0.007979094982147217,
0.06413961201906204,
-0.04404303804039955,
0.020068500190973282,
-0.06536240130662918,
-0.00010071736323880032,
0.006628550123423338,
-0.03625800460577011,
0.03425852209329605,
-0.04109455645084381,
-0.0055436803959310055,
-0.008390492759644985,
0.04769514501094818,
0.00951074343174696,
0.004997702315449715,
0.020527729764580727,
0.009831172414124012,
0.050172120332717896,
0.01688328944146633,
0.036003027111291885,
0.07438630610704422,
-0.007443500217050314,
0.016424208879470825,
0.011597647331655025,
-0.009713750332593918,
-0.03530479967594147,
0.034779660403728485,
-0.038968075066804886,
0.015637263655662537,
0.0065444414503872395,
-0.03531447425484657,
0.030233724042773247,
-0.028279360383749008,
-0.01374734751880169,
0.056672535836696625,
-0.04528379440307617,
0.02026880532503128,
0.035652048885822296,
0.01175706833600998,
0.015188517048954964,
-0.03436417505145073,
0.01787448301911354,
-0.013134746812283993,
0.014059090986847878,
-0.004109069239348173,
0.03974180668592453,
0.03752985969185829,
0.020787792280316353,
-0.012620490975677967,
0.016022775322198868,
0.022450849413871765,
0.027248959988355637,
0.035628676414489746,
0.034230172634124756,
-0.04058380797505379,
-0.06745463609695435,
0.006701154634356499,
0.016080746427178383,
-0.012637678533792496,
0.05960820987820625,
0.017237592488527298,
0.054070327430963516,
0.0025428137741982937,
0.013943038880825043,
-0.012871804647147655,
-0.02450510486960411,
-0.02854120545089245,
-0.0015680966898798943,
0.022693468257784843,
-0.00916342344135046,
0.014091125689446926,
-0.01691543683409691,
-0.013161848299205303,
-0.006447060499340296,
0.010070008225739002,
-0.04250430315732956,
0.02022465504705906,
-0.020603567361831665,
0.008071007207036018,
0.027213023975491524,
-0.0046356478706002235,
-0.03726699575781822,
-0.05343717336654663,
0.03445003926753998,
-0.0018394571961835027,
0.03127646818757057,
-0.020260270684957504,
-0.01711920090019703,
-0.013395010493695736,
0.054204292595386505,
-0.06341797858476639,
-0.03705741465091705,
0.022593045607209206,
-0.0008817283087410033,
-0.015362081117928028,
-0.0226085614413023
] |
<p>I don't really know anything about physics even though I pretended studying it for years.</p>
<p>How is this explained?: <a href="http://andrewsullivan.theatlantic.com/the_daily_dish/2011/01/if-you-think-youre-cold-.html" rel="nofollow">http://andrewsullivan.theatlantic.com/the_daily_dish/2011/01/if-you-think-youre-cold-.html</a></p>
<p><img src="http://i.stack.imgur.com/wAlNJ.png" alt="enter image description here"></p>
<p>What is there to be said about it?</p>
<p>My apologies if you find the question too vague or silly.</p>
| 10,820 |
[
-0.022317415103316307,
-0.03333921730518341,
-0.0022039893083274364,
-0.057650234550237656,
0.024378707632422447,
0.01867472566664219,
-0.018717186525464058,
-0.025955762714147568,
-0.03132922947406769,
-0.00521507952362299,
0.03805384784936905,
0.059827715158462524,
-0.001859296578913927,
-0.000043973701394861564,
0.014753740280866623,
0.022964835166931152,
0.0159543976187706,
0.008094699122011662,
0.0065614813938736916,
-0.01034012995660305,
-0.040454424917697906,
0.021526066586375237,
-0.0248588714748621,
0.014294926077127457,
-0.05326296016573906,
0.004739150404930115,
0.04131631180644035,
-0.007969960570335388,
0.023968733847141266,
0.037532586604356766,
-0.011289449408650398,
-0.0014265991048887372,
0.016232280060648918,
-0.002302115550264716,
0.03649606928229332,
-0.013161998242139816,
-0.013412426225841045,
-0.010088963434100151,
0.008952769450843334,
0.03082210011780262,
-0.02455039694905281,
-0.02962609753012657,
-0.020015889778733253,
0.007804071065038443,
-0.03724629804491997,
0.015534433536231518,
-0.008049344643950462,
-0.006167868617922068,
0.056387051939964294,
-0.07050121575593948,
0.045245200395584106,
-0.013534353114664555,
0.04053468629717827,
0.04663901403546333,
0.012075459584593773,
-0.005254239775240421,
0.06066897138953209,
0.04246998950839043,
-0.04300190135836601,
-0.05633930861949921,
-0.0007337314309552312,
-0.0029732706025242805,
-0.048709798604249954,
-0.03171156719326973,
0.007360310293734074,
0.022498970851302147,
-0.011924375779926777,
-0.03792111203074455,
0.014545094221830368,
0.015039271675050259,
0.016602249816060066,
0.013196660205721855,
0.03601762652397156,
-0.018991390243172646,
0.028516145423054695,
-0.021685181185603142,
0.023131031543016434,
0.03590451925992966,
0.05539865419268608,
0.03953872621059418,
-0.018929852172732353,
0.0009984009666368365,
0.03969774767756462,
0.019320819526910782,
0.012235171161592007,
-0.03040885180234909,
0.08884473890066147,
-0.033122193068265915,
0.016078202053904533,
0.06199390068650246,
-0.028481556102633476,
0.022502446547150612,
-0.01920081302523613,
0.011844383552670479,
-0.010076278820633888,
0.0206034854054451,
0.006842194125056267,
0.041835278272628784,
0.005519794765859842,
-0.030628621578216553,
-0.008998065255582333,
-0.0008184367325156927,
0.008046970702707767,
0.0597822405397892,
-0.03635190427303314,
-0.042006734758615494,
-0.031675197184085846,
0.010220307856798172,
-0.004114838317036629,
-0.02051793783903122,
-0.03902642801403999,
0.01390205416828394,
-0.03297256678342819,
-0.0005682558985427022,
0.025780370458960533,
-0.025958627462387085,
-0.0007168459706008434,
0.005680637899786234,
0.011630656197667122,
0.043754033744335175,
0.027336910367012024,
-0.008289552293717861,
0.011763091199100018,
-0.01127326674759388,
-0.047544099390506744,
0.013952640816569328,
0.01320317666977644,
-0.010591987520456314,
-0.012531236745417118,
0.006373954936861992,
-0.019652599468827248,
-0.028280531987547874,
0.010927054099738598,
0.034096818417310715,
0.01666203886270523,
0.011013220995664597,
-0.09732281416654587,
-0.04028495028614998,
0.08270709216594696,
-0.01216923724859953,
-0.021970221772789955,
-0.08224283158779144,
0.023652072995901108,
0.012363423593342304,
0.06087498739361763,
-0.014224128797650337,
0.015588207170367241,
-0.03797515854239464,
0.022483527660369873,
0.014729144982993603,
-0.012569013051688671,
-0.02294745482504368,
-0.01139814592897892,
-0.02470969408750534,
0.000505726900883019,
-0.06769098341464996,
0.04246710240840912,
0.046400368213653564,
-0.01025476586073637,
-0.020640728995203972,
0.037980660796165466,
-0.021286001428961754,
-0.013794398866593838,
0.02496083825826645,
-0.03480565920472145,
-0.04645495489239693,
0.10121193528175354,
0.006755491252988577,
-0.004826746415346861,
0.03890069201588631,
-0.011740396730601788,
0.03375799581408501,
-0.026555905118584633,
0.01501279417425394,
0.04779890924692154,
-0.022867875173687935,
0.0034436597488820553,
-0.019983217120170593,
-0.019329478964209557,
0.035455942153930664,
-0.09313352406024933,
-0.01798872835934162,
-0.002566421404480934,
-0.007528523448854685,
-0.008856508880853653,
0.07270213961601257,
-0.010880980640649796,
-0.01027722842991352,
0.009680402465164661,
-0.059738337993621826,
-0.04597657546401024,
-0.10417874902486801,
0.005403517745435238,
-0.034819722175598145,
-0.0030794336926192045,
0.0034971002023667097,
0.039616066962480545,
0.029735930263996124,
-0.028301754966378212,
-0.023077476769685745,
-0.004654018674045801,
0.038643091917037964,
-0.007376784924417734,
-0.008650282397866249,
-0.004885524045675993,
0.05547162890434265,
0.02964808978140354,
0.003936027176678181,
0.025339331477880478,
-0.048377376049757004,
-0.03239985927939415,
0.0205876212567091,
-0.023869939148426056,
0.030157849192619324,
0.0027100087609142065,
0.010555580258369446,
0.042785272002220154,
0.02058563008904457,
-0.003705690149217844,
0.020068136975169182,
-0.019518963992595673,
0.06552310287952423,
-0.008047920651733875,
-0.0061709084548056126,
0.00978594459593296,
0.05477231740951538,
0.00823146291077137,
0.019368499517440796,
-0.002314896322786808,
-0.0036000290419906378,
-0.05837329477071762,
-0.022800076752901077,
0.03695860877633095,
-0.0038865022361278534,
-0.025413626804947853,
0.00833663810044527,
-0.010060237720608711,
0.06773541867733002,
0.004239758942276239,
0.0013751426013186574,
-0.005517703481018543,
0.00005912399501539767,
-0.019806301221251488,
0.008289509452879429,
0.020409608259797096,
0.014505326747894287,
0.015280121006071568,
0.04173313453793526,
0.032378312200307846,
-0.0025018423330038786,
-0.05270543321967125,
0.07092398405075073,
0.007190022151917219,
0.03575705364346504,
-0.007646547164767981,
-0.009964740835130215,
0.03315667808055878,
-0.016116121783852577,
0.048508595675230026,
0.035046596080064774,
0.00285097723826766,
0.016827546060085297,
-0.03134290874004364,
-0.009596055373549461,
-0.010387546382844448,
0.07261034101247787,
-0.002063639694824815,
-0.016597608104348183,
0.021503116935491562,
-0.0312633290886879,
0.007307789754122496,
-0.01657908223569393,
-0.00262639787979424,
-0.0024586778599768877,
-0.0040616365149617195,
0.010272536426782608,
0.03106723539531231,
0.008263793773949146,
-0.055906545370817184,
-0.05575741082429886,
0.0019096113974228501,
-0.04268714413046837,
0.015862349420785904,
0.007102282717823982,
-0.04667031019926071,
0.01777421124279499,
-0.020611479878425598,
-0.05561983585357666,
0.037276286631822586,
-0.002423503901809454,
-0.01407008059322834,
0.004255643580108881,
-0.014057292602956295,
-0.030441777780652046,
-0.02832840196788311,
-0.028271783143281937,
0.020062517374753952,
-0.04331083968281746,
0.01806030049920082,
0.06568026542663574,
-0.03852430358529091,
-0.044532086700201035,
0.015100925229489803,
-0.06929223984479904,
-0.06021394953131676,
0.004822401329874992,
-0.005781690590083599,
0.010765060782432556,
-0.01024047750979662,
-0.00472161965444684,
0.012666660360991955,
-0.05429805442690849,
0.006241596303880215,
-0.04204869642853737,
-0.0287416260689497,
0.038449645042419434,
0.020439397543668747,
-0.0043636527843773365,
0.0064077540300786495,
-0.03084496594965458,
0.06671272218227386,
0.010179835371673107,
-0.030978266149759293,
0.005751890130341053,
0.0006019535358063877,
-0.04679710045456886,
-0.04439609497785568,
0.0032786387018859386,
0.06285765022039413,
-0.01966514252126217,
0.008964648470282555,
0.04306647554039955,
0.05198022350668907,
0.010653890669345856,
0.015820670872926712,
-0.039262693375349045,
-0.028611907735466957,
0.0005322559154592454,
-0.01482747495174408,
0.040684979408979416,
-0.024114947766065598,
-0.03321303427219391,
-0.014201465994119644,
-0.017953118309378624,
0.049180012196302414,
0.04849812015891075,
-0.042961880564689636,
0.08609505742788315,
-0.0028449520468711853,
-0.008644732646644115,
-0.0514870248734951,
0.04627620056271553,
-0.01181317400187254,
-0.024628929793834686,
0.00542102986946702,
0.04573586583137512,
0.050239384174346924,
0.018242284655570984,
-0.0017475676722824574,
0.04155909642577171,
0.04659620299935341,
-0.025927655398845673,
-0.01879122480750084,
0.0005127358017489314,
0.0034907155204564333,
0.000249260279815644,
-0.007273131050169468,
-0.02116379328072071,
0.05533137172460556,
0.060572292655706406,
0.05630524829030037,
0.011643442325294018,
-0.039887286722660065,
0.00015643960796296597,
-0.048418305814266205,
-0.012254120782017708,
0.017999237403273582,
0.037469517439603806,
-0.015518675558269024,
0.07570020109415054,
0.04371440410614014,
0.048397865146398544,
0.04608692601323128,
-0.019269857555627823,
-0.08634908497333527,
0.03799299895763397,
-0.015723373740911484,
-0.023633774369955063,
-0.027245383709669113,
-0.002630518516525626,
-0.01265663094818592,
-0.03950873762369156,
0.0005161044537089765,
0.01554842945188284,
0.011911990121006966,
-0.01944238506257534,
-0.006288626696914434,
0.01825169287621975,
-0.03466981649398804,
-0.015342098660767078,
0.011186384595930576,
0.034424036741256714,
-0.04261009767651558,
-0.009041216224431992,
0.04513195902109146,
-0.005678430665284395,
-0.01857439987361431,
-0.013767242431640625,
0.0189627967774868,
0.021617764607071877,
0.0031811860390007496,
-0.018893081694841385,
-0.004612525925040245,
-0.011428731493651867,
0.01144870463758707,
0.026797451078891754,
0.017006991431117058,
-0.014129411429166794,
-0.02064030058681965,
-0.025053823366761208,
-0.0377596877515316,
-0.0077512445859611034,
-0.023999452590942383,
0.025788510218262672,
-0.006947341840714216,
0.04335344582796097,
-0.003480810672044754,
0.007311319001019001,
-0.04009092599153519,
0.028558282181620598,
0.04477246105670929,
-0.009663592092692852,
-0.022716503590345383,
-0.0651688501238823,
0.0020033319015055895,
-0.04625086113810539,
0.045004282146692276,
0.03521054610610008,
0.011897866614162922,
-0.030405858531594276,
0.04421074688434601,
0.00022436707513406873,
-0.0103602334856987,
-0.0012329742312431335,
-0.004289674572646618,
-0.020708225667476654,
0.026650043204426765,
0.015091496519744396,
0.009325495921075344,
0.0008247497607953846,
0.03746464475989342,
0.0009402607101947069,
-0.030671950429677963,
-0.01940055750310421,
-0.0900140181183815,
0.002553724916651845,
0.03339133784174919,
0.025868378579616547,
-0.022037837654352188,
-0.009476939216256142,
-0.06835753470659256,
0.0031615598127245903,
0.05385148525238037,
-0.04982737451791763,
0.04423648118972778,
-0.0261219535022974,
0.00012580418842844665,
-0.010405778884887695,
-0.027721405029296875,
-0.015241111628711224,
0.01187036745250225,
-0.015370103530585766,
-0.005274481605738401,
-0.012941235676407814,
-0.0377889983355999,
0.009675547480583191,
0.011797500774264336,
0.0010451567359268665,
0.03599678725004196,
-0.03056926280260086,
0.027124464511871338,
-0.025611290708184242,
-0.002356576267629862,
-0.0653114914894104,
-0.09196581691503525,
-0.0498165637254715,
0.025501873344182968,
0.0026317036245018244,
0.04154494032263756,
-0.04880039021372795,
-0.0650116577744484,
0.025104641914367676,
-0.004073258955031633,
0.013525537215173244,
0.001707282499410212,
-0.041519466787576675,
0.05753514915704727,
0.045424796640872955,
0.023113533854484558,
0.023930994793772697,
0.026898378506302834,
-0.031713586300611496,
-0.0011047817533835769,
0.0012317874934524298,
0.022759001702070236,
-0.02408776991069317,
-0.0180699173361063,
-0.04398243874311447,
0.017274273559451103,
-0.04622037336230278,
0.04716278612613678,
-0.0358046293258667,
0.011311630718410015,
0.017991309985518456,
-0.044500309973955154,
-0.022578580304980278,
-0.0146527960896492,
0.03567114472389221,
-0.004184888210147619,
0.019540967419743538,
0.025611909106373787,
0.035982951521873474,
-0.030536571517586708,
0.038408804684877396,
-0.01501833088696003,
0.015048379078507423,
0.046421535313129425,
-0.021852979436516762,
0.02151893451809883,
-0.001965637318789959,
-0.02590283565223217,
0.018435927107930183,
-0.04990047588944435,
0.01224618498235941,
-0.059978436678647995,
-0.021681027486920357,
0.005082234740257263,
-0.04272088780999184,
-0.03406621515750885,
0.006857644766569138,
-0.00011745788651751354,
0.051748812198638916,
-0.003176589496433735,
0.036169104278087616,
0.029925338923931122,
0.023317089304327965,
-0.0530502051115036,
-0.04765113443136215,
0.03911491483449936,
0.017025381326675415,
-0.040358029305934906,
-0.06552425771951675,
-0.017429234459996223,
-0.019094130024313927,
-0.061718735843896866,
0.017831504344940186,
0.01034790463745594,
-0.012811415828764439,
-0.008083133026957512,
0.021376797929406166,
-0.020012209191918373,
0.0329379066824913,
0.042415257543325424,
-0.019671868532896042,
0.018562911078333855,
-0.0540790818631649,
-0.04222087189555168,
0.01266537792980671,
0.0502120740711689,
-0.025264909490942955,
-0.01653735153377056,
0.026422731578350067,
0.005571142304688692,
0.05512804165482521,
0.009956038556993008,
0.013058256357908249,
0.022581182420253754,
0.0177474282681942,
-0.01912684366106987,
-0.04906865954399109,
0.03193127363920212,
0.013418823480606079,
0.03371996060013771,
0.0024967885110527277,
-0.012978380545973778,
-0.04320288822054863,
-0.032751020044088364,
0.031775835901498795,
0.01678435131907463,
-0.02172262780368328,
-0.010485649108886719,
0.057483479380607605,
-0.04303934797644615,
-0.018319685012102127,
-0.000041914630855899304,
0.008157719857990742,
-0.0087326904758811,
0.053378332406282425,
-0.024880001321434975,
0.021547645330429077,
-0.024836918339133263,
-0.005551404785364866,
-0.02916736528277397,
-0.03383186087012291,
0.02478628233075142,
0.052428312599658966,
-0.011411872692406178,
0.02878534607589245,
0.012537811882793903,
-0.033797264099121094,
0.02180447243154049,
0.006496085785329342,
-0.004052892327308655,
0.007375843357294798,
-0.013090969994664192,
-0.011745958589017391,
-0.012464642524719238,
0.008453699760138988,
0.05365394428372383,
0.04058798775076866,
-0.013329090550541878,
-0.01148197427392006,
0.06164391338825226,
0.027491392567753792,
0.00951654464006424,
-0.00121556525118649,
-0.012187138199806213,
0.058610789477825165,
-0.054196007549762726,
0.021241972222924232,
-0.0062739672139286995,
-0.024448342621326447,
0.007697493303567171,
0.00933520682156086,
0.00796178076416254,
-0.06442983448505402,
-0.005421790294349194,
-0.006796260364353657,
0.000016402073015342467,
0.024066748097538948,
-0.006247358396649361,
0.03795749694108963,
0.0009664421668276191,
0.028314078226685524,
0.008290305733680725,
0.00397682748734951,
0.0065873758867383,
-0.07542657852172852,
0.005428831093013287,
0.00044086630805395544,
-0.031904060393571854,
0.0012181783095002174,
-0.0031328853219747543,
-0.032356493175029755,
0.00978071242570877,
-0.03975619003176689,
0.02145177125930786,
0.03781669959425926,
0.06266792863607407,
-0.01026669330894947,
0.07012627273797989,
-0.015377786010503769,
0.021459760144352913,
-0.009565155021846294,
0.0002319479244761169,
0.10499735921621323,
0.022588718682527542,
0.017100216820836067,
-0.07074546068906784,
-0.010420874692499638,
-0.01702849194407463,
0.011272932402789593,
-0.010936178267002106,
0.0016254154033958912,
-0.0260513536632061,
0.043609049171209335,
0.02517344243824482,
0.06628244370222092,
0.01659616455435753,
-0.0035875318571925163,
0.03572797775268555,
-0.0515371710062027,
-0.0042441594414412975,
0.016757125034928322,
0.01614682748913765,
0.002676822943612933,
0.007976646535098553,
-0.041114442050457,
0.02026425115764141,
0.003016391769051552,
0.026893777772784233,
-0.023930976167321205,
-0.027806377038359642,
0.026012301445007324,
0.008865430019795895,
-0.05653354898095131,
0.03467326611280441,
-0.01305087748914957,
-0.016124358400702477,
-0.019300587475299835,
0.025328995659947395,
0.05096794664859772,
-0.005749706644564867,
0.03477414324879646,
0.018977193161845207,
-0.00015453470405191183,
0.010436064563691616,
0.011429255828261375,
0.01978352665901184,
0.0007782597094774246,
-0.013658113777637482,
-0.018658483400940895,
0.03398199751973152,
-0.004681583493947983,
-0.013719345442950726,
0.017617860808968544,
0.0093086501583457,
-0.002339979400858283,
-0.0524977445602417,
0.000556027633138001,
0.00002691529516596347,
0.024634838104248047,
-0.0196328517049551,
-0.03933745250105858,
-0.05023781955242157,
0.016300112009048462,
0.021949710324406624,
0.016283966600894928,
0.014264417812228203,
-0.0036186070647090673,
-0.019840268418192863,
0.02880779653787613,
0.019068043678998947,
0.004919092170894146,
0.006412538234144449,
-0.024784795939922333,
-0.026562411338090897,
-0.02937576174736023,
-0.030776789411902428,
0.023424915969371796,
0.01941634714603424,
0.03706379607319832,
0.012488162145018578,
-0.00043129216646775603,
-0.02108500339090824,
-0.053438130766153336,
0.011310308240354061,
-0.010166797786951065,
-0.012456961907446384,
-0.00997823104262352,
-0.009873433038592339,
-0.003686970565468073,
0.05314004793763161,
-0.015907760709524155,
-0.005139160435646772,
0.02313672937452793,
0.048548635095357895,
-0.02306811511516571,
-0.011188402771949768,
-0.06668564677238464,
0.009757776744663715,
-0.0349002480506897,
0.020876634865999222,
0.008775202557444572,
0.04961908608675003,
0.00933602824807167,
-0.004197335802018642,
-0.0032149290200322866,
0.01409563422203064,
-0.06442654132843018,
-0.012316305190324783,
0.047969285398721695,
-0.03137807548046112,
-0.03883900120854378,
0.019647255539894104,
-0.05131809040904045,
-0.04015374928712845,
-0.002368202665820718,
0.0208943672478199,
-0.01919407956302166,
0.01027605775743723,
0.03782614693045616,
-0.009868312627077103,
0.0062223696149885654,
0.02379843406379223,
0.015745650976896286,
-0.037651848047971725,
-0.010091692209243774,
-0.05808420479297638,
-0.002808848861604929,
0.0001786229113349691,
-0.04634272679686546,
-0.026325739920139313,
0.024496791884303093,
-0.005198979284614325,
0.004336518235504627,
0.02206573449075222,
0.012036921456456184,
-0.012589499354362488,
-0.02159319631755352,
0.024382179602980614,
0.0012794426875188947,
0.026154816150665283,
0.002220774069428444,
-0.053410306572914124,
0.05474596470594406,
-0.04948987439274788,
-0.029307032003998756,
0.04264207184314728,
0.00038836366729810834,
0.039886247366666794,
0.04359668493270874,
-0.021773001179099083,
0.031214725226163864,
0.07937591522932053,
-0.018404772505164146,
-0.01352858729660511,
-0.020507747307419777,
-0.008406129665672779,
0.03576008230447769,
0.00568383140489459,
-0.007837639190256596,
-0.026249011978507042,
-0.006761251948773861,
0.06412045657634735,
0.01118075754493475,
-0.015876205638051033,
-0.007562779355794191,
0.011318163014948368,
0.01920177973806858,
-0.004362898413091898,
0.020236879587173462,
0.03826350346207619,
-0.006154695991426706,
0.02861003391444683,
-0.018132632598280907,
0.03144962713122368,
-0.028721436858177185,
0.014036358334124088,
-0.11568774282932281,
0.004846787545830011,
0.01655922643840313,
-0.018246663734316826,
0.0506625659763813,
-0.05239250883460045,
0.03448191285133362,
0.03507804870605469,
-0.05329635366797447,
0.020961817353963852,
0.023815741762518883,
-0.011648724786937237,
-0.03654218092560768,
0.030458183959126472,
-0.016997911036014557,
0.06516632437705994,
0.008511352352797985,
0.03443484380841255,
-0.005459816660732031,
0.0028346299659460783,
-0.0033730510622262955,
-0.0427531935274601,
0.024041784927248955,
0.07633619755506516,
0.0028568825218826532,
0.004482902120798826,
0.04886482283473015,
-0.010661425068974495,
-0.02940460853278637,
0.0385783426463604,
-0.01720684953033924,
0.0326000340282917,
0.029745806008577347,
0.024342006072402,
-0.01647374778985977,
0.03683171421289444,
-0.005749560426920652,
0.007860257290303707,
0.016827665269374847,
0.06475216150283813,
0.03441512584686279,
0.0306132510304451,
0.013861716724932194,
-0.013887465000152588,
-0.013620402663946152,
-0.051633093506097794,
-0.03691009059548378,
0.04568640515208244,
-0.012570355087518692,
0.04553024843335152,
0.029492102563381195,
-0.019445903599262238,
0.023528603836894035,
-0.04979366436600685,
-0.020742978900671005,
-0.05266134813427925,
0.024328799918293953,
0.024291403591632843,
0.0063835796900093555,
-0.0034809247590601444,
0.005111155100166798,
-0.029353586956858635,
-0.0071241362020373344,
0.0014368294505402446,
-0.013337183743715286,
-0.04135458916425705,
-0.016118120402097702,
-0.01547847781330347,
0.005346680525690317,
0.03574329987168312,
-0.009641601704061031,
-0.012875711545348167,
-0.04435079172253609,
0.04724341630935669,
0.05132582411170006,
0.023322351276874542,
-0.013731067068874836,
-0.061554547399282455,
-0.0519091822206974,
-0.06253119558095932,
0.029660796746611595,
-0.0032476510386914015,
0.006395100615918636,
-0.062108997255563736,
-0.019688012078404427,
-0.03675641864538193,
0.016315165907144547,
0.05357511341571808,
0.020944634452462196,
0.00005986444011796266,
0.01066440436989069,
-0.011924329213798046,
-0.0023824945092201233,
-0.04483999311923981,
-0.0017756572924554348,
-0.0176154226064682,
-0.0006574692670255899,
-0.0014836688060313463,
0.005535890348255634,
-0.034226614981889725,
-0.0315544568002224,
0.04271545633673668,
-0.0034867844078689814,
0.04725881665945053,
-0.013097267597913742,
-0.013716564513742924,
0.007879717275500298,
0.04032871127128601,
-0.014432450756430626,
0.045870762318372726,
-0.02296592853963375,
0.01144340168684721,
0.03083915449678898,
-0.005591078195720911,
-0.019745444878935814,
0.035483721643686295,
0.00026279501616954803,
0.018425187095999718,
-0.031142937019467354,
-0.028424812480807304,
0.033991340547800064,
-0.030246121808886528,
-0.011862615123391151,
0.014048345386981964,
-0.03456176817417145,
-0.047424327582120895,
0.031078966334462166,
0.030103392899036407,
0.025846166536211967,
-0.024093110114336014,
0.028425760567188263,
0.0008586128242313862,
-0.022187957540154457,
0.0034599234350025654,
0.04817558079957962,
0.008064782246947289,
0.0035779024474322796,
0.016926564276218414,
0.04420051351189613,
0.0204653050750494,
0.04331114515662193,
0.011136106215417385,
0.016556689515709877,
-0.011005437932908535,
-0.025606511160731316,
-0.002175974426791072,
-0.03844979777932167,
0.02253006398677826,
0.023669302463531494,
0.004873837344348431,
0.08016490936279297,
-0.010295992717146873,
0.010350126773118973,
0.0012098647421225905,
0.018845923244953156,
-0.0068962471559643745,
0.0060792351141572,
0.03372209146618843,
-0.00002724890327954199,
-0.015280620194971561,
0.0050362893380224705,
-0.015772225335240364,
-0.0027163722552359104,
0.01864095777273178,
-0.028026072308421135,
0.020937057211995125,
-0.005252016242593527,
0.016097018495202065,
0.008659400045871735,
-0.018775388598442078,
-0.03013230301439762,
-0.01160584855824709,
0.03489317372441292,
0.042447686195373535,
0.02998368628323078,
-0.00781345460563898,
0.019036956131458282,
-0.032811008393764496,
0.03606598079204559,
-0.06307240575551987,
-0.008662443608045578,
-0.03396543860435486,
0.053068917244672775,
-0.01517986785620451,
-0.04188798740506172
] |
<p>I was reading an article in this months issue of Physics World magazine on the three main theories of extra dimensions and stumbled across something I didn't quite understand when the author began talking about detecting particles in extra dimensions at a particle lab, such as the LHC in Geneva, Switzerland.</p>
<p>The energy of a particle in 3-dimensional space consists of its rest energy, $E=mc^2$, and the kinetic energy of its motion.
If extra dimensions do exist, then the particle will have extra space to move in, so will obtain an additional, independent contribution to its kinetic energy. Since we don't observe the motion of the particle in the extra dimension, this kinetic energy will be interpreted as rest energy, or in other words, the mass of the particle. </p>
<p>This is all understood perfectly fine, but it is this quote that comes next that confuses me:</p>
<blockquote>
<p>To us, the particle would not look like one particle, but a set of particles - all with different masses.</p>
</blockquote>
<p>Why would the particle look like a set of particles rather than just the one that is being observed?</p>
<p>Furthermore, why would they all have different masses?</p>
<p>How many particles would there be in this set?</p>
<p>Please keep your answers as simple as possible, as I am just a Layman.</p>
| 10,821 |
[
0.009174036793410778,
-0.015286233276128769,
0.01035203319042921,
-0.04173525422811508,
0.048730336129665375,
0.025137918069958687,
-0.015120054595172405,
-0.04123542457818985,
-0.022546304389834404,
-0.026299918070435524,
0.03587701544165611,
-0.0000062267699831863865,
0.03537764400243759,
0.03224997967481613,
0.009409971535205841,
0.03645293787121773,
-0.012442728504538536,
0.0030274398159235716,
-0.01353020966053009,
-0.045819368213415146,
0.004448191728442907,
0.03083440288901329,
0.0250028595328331,
0.007180313114076853,
-0.035594116896390915,
0.02653125673532486,
0.03813191130757332,
0.03347098082304001,
0.06298394501209259,
0.04839630424976349,
-0.02038836106657982,
-0.03892805427312851,
0.0302618145942688,
0.004002959933131933,
-0.0015867049805819988,
-0.00861575361341238,
-0.008480170741677284,
-0.01493760198354721,
0.03882954269647598,
0.03525029867887497,
-0.03369351476430893,
-0.027743494138121605,
0.018672142177820206,
0.05331786349415779,
-0.052677202969789505,
0.007403556723147631,
0.01815246045589447,
-0.03367731720209122,
0.06112915277481079,
-0.061430446803569794,
0.09655477106571198,
0.011960795149207115,
0.02707747556269169,
-0.0005308910622261465,
0.0022862665355205536,
-0.014716748148202896,
0.035367436707019806,
0.05401585251092911,
-0.004485484212636948,
-0.049070898443460464,
-0.02677157148718834,
-0.008265875279903412,
0.02329157292842865,
-0.004041342064738274,
0.017208687961101532,
0.03520238399505615,
-0.007762415800243616,
0.0318082831799984,
0.0025202499236911535,
0.0079225217923522,
0.04531697928905487,
0.024795299395918846,
0.04677557945251465,
-0.0009200063650496304,
-0.0066052209585905075,
0.005079475697129965,
0.011159301735460758,
0.028374066576361656,
0.05601818859577179,
0.018610404804348946,
-0.024789171293377876,
-0.0016414065612480044,
0.0577101968228817,
0.03761092945933342,
0.023129642009735107,
-0.017195796594023705,
0.047420307993888855,
-0.03702060133218765,
0.0018688951386138797,
0.041032176464796066,
-0.037754449993371964,
0.03896433860063553,
0.050117552280426025,
0.0103211160749197,
-0.02541591040790081,
0.04393019527196884,
0.00620617251843214,
0.02843782678246498,
-0.022257229313254356,
-0.005073952488601208,
0.002672374015673995,
0.005456019192934036,
0.017303666099905968,
0.03761298581957817,
0.0050013428553938866,
-0.002271388191729784,
-0.04300447180867195,
0.0257139652967453,
-0.0336625799536705,
0.0007283945451490581,
-0.012180247344076633,
0.0026905143167823553,
0.0049125635996460915,
0.0392645001411438,
0.01685139536857605,
0.0022486604284495115,
0.03293268010020256,
-0.017150651663541794,
0.04078683629631996,
0.034527551382780075,
0.014389026910066605,
-0.05489591136574745,
0.017962664365768433,
-0.013888536021113396,
-0.09784630686044693,
0.020893992856144905,
0.01901545748114586,
0.013544751331210136,
-0.03247136250138283,
0.018907660618424416,
-0.006471042986959219,
0.005048602819442749,
0.015576559118926525,
0.01909954473376274,
0.053793519735336304,
-0.009843437001109123,
-0.09887296706438065,
-0.04628840088844299,
0.04363106191158295,
0.0037764180451631546,
-0.04329006001353264,
-0.07338300347328186,
-0.05030154809355736,
0.04830097779631615,
0.09084181487560272,
-0.044558946043252945,
-0.011075076647102833,
-0.008242967538535595,
0.028848325833678246,
0.0011111184721812606,
-0.008262249641120434,
-0.01442553848028183,
-0.022422486916184425,
-0.047969620674848557,
0.009224188514053822,
-0.04915029555559158,
0.0334504097700119,
0.04202296957373619,
0.008145979605615139,
-0.004240718670189381,
0.037198957055807114,
-0.0021347065921872854,
-0.00337368156760931,
0.03360484167933464,
0.0015645901439711452,
-0.003973755054175854,
0.052702438086271286,
-0.001815839554183185,
-0.00996007863432169,
0.03804772347211838,
0.0011584649328142405,
0.009487082250416279,
0.0019001837354153395,
0.04408910125494003,
0.035364747047424316,
-0.005684393458068371,
-0.0482037290930748,
-0.029189910739660263,
-0.0007176104700192809,
-0.0049140541814267635,
-0.06008337438106537,
-0.05515020713210106,
0.036867011338472366,
-0.011643552221357822,
0.021857336163520813,
0.007337231654673815,
-0.008283034898340702,
-0.033850036561489105,
0.011906436644494534,
-0.03010883554816246,
-0.04487258568406105,
-0.07012960314750671,
-0.004380537196993828,
0.005269888788461685,
-0.004941939376294613,
0.015571724623441696,
0.028173724189400673,
0.013800752349197865,
-0.023201806470751762,
-0.012223688885569572,
-0.014794480986893177,
0.027327565476298332,
0.011039406061172485,
-0.00041229691123589873,
0.00012678172788582742,
0.06722991168498993,
0.052819494158029556,
0.015350647270679474,
-0.035537753254175186,
0.060015395283699036,
-0.03476695343852043,
-0.01329745166003704,
-0.019528131932020187,
-0.0031266885343939066,
0.0013212180929258466,
0.00909790862351656,
-0.007134145125746727,
0.01739451289176941,
-0.05118396878242493,
0.03923754394054413,
-0.008441027253866196,
0.04143710806965828,
0.013235973194241524,
-0.028780043125152588,
-0.017036616802215576,
0.01167490053921938,
0.009157201275229454,
0.03622158616781235,
-0.010534007102251053,
-0.030198095366358757,
-0.04973432794213295,
-0.044416606426239014,
-0.009670983068645,
0.025614747777581215,
-0.05634571239352226,
0.024393389001488686,
0.05229920893907547,
0.05488435551524162,
0.003657321445643902,
0.02666916884481907,
0.009850739501416683,
-0.05302365869283676,
0.020127195864915848,
-0.0035385473165661097,
-0.0037324591539800167,
0.004097772762179375,
0.03809206187725067,
0.012036697939038277,
-0.03137064352631569,
-0.023418104276061058,
-0.001977595966309309,
-0.004716287832707167,
-0.02923709526658058,
0.023686369881033897,
-0.019825687631964684,
-0.033132195472717285,
0.014162678271532059,
-0.018913978710770607,
0.0661626085639,
0.019457263872027397,
0.004528885241597891,
-0.0344977080821991,
-0.05764898657798767,
-0.024087321013212204,
-0.025972286239266396,
0.04478490352630615,
-0.04394938796758652,
-0.02548874542117119,
0.026643432676792145,
-0.055950842797756195,
0.032354772090911865,
-0.024735262617468834,
-0.044822387397289276,
-0.02175702527165413,
0.00616847537457943,
0.0172272976487875,
0.006207177881151438,
0.04938701167702675,
-0.04675109311938286,
-0.04894578456878662,
0.006708407774567604,
-0.0435098372399807,
-0.01177371758967638,
0.022457778453826904,
-0.05394386872649193,
0.022709351032972336,
-0.06923817843198776,
-0.032790690660476685,
0.018728358671069145,
-0.016260750591754913,
0.020574470981955528,
0.030593134462833405,
-0.021137267351150513,
-0.026323067024350166,
0.003512114519253373,
-0.00024657449102960527,
0.0377720445394516,
-0.01945250853896141,
-0.018325095996260643,
0.0409516766667366,
-0.008148383349180222,
-0.03329547494649887,
0.027676820755004883,
-0.05643922835588455,
-0.023932235315442085,
-0.021903708577156067,
0.009456719271838665,
0.03118804469704628,
-0.04651670530438423,
0.029611391946673393,
0.045080412179231644,
-0.010747333988547325,
0.011902340687811375,
-0.05140239745378494,
-0.06133813038468361,
-0.0073931170627474785,
0.00863878894597292,
0.039262618869543076,
-0.020839350298047066,
-0.042445629835128784,
0.07836379110813141,
0.022390995174646378,
-0.037703175097703934,
-0.004665246233344078,
0.0009280612575821579,
0.014511405490338802,
-0.06067541986703873,
0.04309897497296333,
-0.005751427263021469,
-0.003937865607440472,
0.010857399553060532,
0.028776265680789948,
0.04992295056581497,
0.034980203956365585,
-0.008063800632953644,
-0.025402389466762543,
-0.024020306766033173,
0.014097373001277447,
0.013487789779901505,
0.04346119984984398,
-0.007169126532971859,
-0.022595573216676712,
0.01529724057763815,
0.012002945877611637,
0.0553571954369545,
0.00840455386787653,
-0.047796428203582764,
0.0839001014828682,
0.03214770928025246,
0.024891171604394913,
-0.013584161177277565,
0.01823495700955391,
-0.003336928552016616,
-0.035502590239048004,
0.015059339813888073,
0.006027267314493656,
0.04018944874405861,
-0.013299933634698391,
0.009416923858225346,
0.02835167944431305,
0.024612419307231903,
-0.048273976892232895,
-0.029487596824765205,
-0.0015261780936270952,
-0.010833065956830978,
-0.0007107145502232015,
-0.01741000823676586,
-0.026307787746191025,
0.0278746597468853,
0.012900819070637226,
0.06162573769688606,
-0.014069278724491596,
-0.02476557344198227,
-0.028722424060106277,
-0.04186311364173889,
-0.00895589031279087,
0.029987148940563202,
0.026713808998465538,
-0.010597062297165394,
0.08111758530139923,
-0.009385453537106514,
-0.0069651370868086815,
0.03880138695240021,
-0.01680014282464981,
-0.0964774414896965,
-0.009803930297493935,
-0.035327013581991196,
0.007822122424840927,
-0.017078517004847527,
-0.050513364374637604,
0.007931790314614773,
-0.013043394312262535,
-0.0165580902248621,
0.028918832540512085,
-0.019429059699177742,
-0.03839391469955444,
0.01880333572626114,
-0.058084771037101746,
-0.006507229525595903,
-0.007905866950750351,
0.07030723243951797,
0.0370585173368454,
-0.0022104610688984394,
-0.015077595598995686,
0.0477382130920887,
-0.04840630292892456,
-0.01113065518438816,
0.014534715563058853,
0.009568816050887108,
0.029798857867717743,
0.030999504029750824,
0.01274750754237175,
0.02655717544257641,
-0.02031843177974224,
0.02156851254403591,
0.004684904124587774,
0.02785605750977993,
-0.03157396242022514,
-0.020486164838075638,
-0.0247944425791502,
-0.007894860580563545,
0.004019386600703001,
0.011097945272922516,
0.056582655757665634,
0.01642463356256485,
0.020653599873185158,
0.023155082017183304,
0.030976446345448494,
-0.0011697993613779545,
0.03963519260287285,
0.054506316781044006,
-0.005869080778211355,
-0.05815545842051506,
-0.03757167235016823,
0.03403965383768082,
-0.0198379959911108,
-0.019406044855713844,
0.0015143458731472492,
-0.008266637101769447,
-0.031404390931129456,
0.033851515501737595,
0.0012484376784414053,
-0.01918652094900608,
-0.05503934621810913,
-0.007201021071523428,
-0.03543223440647125,
-0.005924385040998459,
-0.033007945865392685,
-0.021606726571917534,
-0.00080575403990224,
0.04020790755748749,
0.023936308920383453,
-0.005394157487899065,
0.003656541695818305,
-0.08405733853578568,
-0.02384396642446518,
0.04071490466594696,
0.06506451219320297,
-0.014871246181428432,
-0.015422584488987923,
-0.03188229352235794,
0.013039530254900455,
0.01594514586031437,
-0.04044382646679878,
-0.016163893043994904,
-0.020529301837086678,
0.011678854934871197,
-0.01891971006989479,
-0.02039400115609169,
-0.012402023188769817,
0.008067660965025425,
-0.0032527276780456305,
0.013273714110255241,
-0.02039715088903904,
0.011015079915523529,
0.014698181301355362,
0.030772292986512184,
0.0286451056599617,
0.03241901099681854,
0.019632963463664055,
0.030955495312809944,
0.011223319917917252,
0.01968635618686676,
-0.009558332152664661,
-0.08495880663394928,
0.002945471787825227,
0.03274239972233772,
0.014387896284461021,
0.035533979535102844,
-0.06627846509218216,
-0.08671901375055313,
-0.017800182104110718,
0.020343370735645294,
0.01674746163189411,
-0.02177048847079277,
-0.08573441952466965,
0.02007211185991764,
0.05294206365942955,
-0.001952450373210013,
0.04786660894751549,
-0.001548954052850604,
-0.019324742257595062,
-0.008411373011767864,
-0.022486096248030663,
0.03547581285238266,
-0.0320020392537117,
0.009151281788945198,
-0.03689536079764366,
0.005984377581626177,
-0.05806942656636238,
0.018116619437932968,
-0.026285817846655846,
0.007672178093343973,
-0.012044047936797142,
-0.04497820883989334,
-0.03725998476147652,
0.02921404130756855,
0.023448342457413673,
0.014192458242177963,
-0.04461336508393288,
0.019872505217790604,
-0.035330880433321,
-0.002808819292113185,
0.018867872655391693,
0.016580499708652496,
-0.015402676537632942,
0.04141649231314659,
0.026792073622345924,
0.02195196971297264,
-0.031992893666028976,
-0.008352520875632763,
0.05470650643110275,
-0.044297777116298676,
0.020617321133613586,
0.009164979681372643,
0.018954791128635406,
0.011000280268490314,
-0.06785774976015091,
-0.051462434232234955,
-0.023667672649025917,
-0.037159647792577744,
0.01594480872154236,
-0.028292639181017876,
0.020626520738005638,
-0.014271010644733906,
0.047144483774900436,
-0.08916424214839935,
-0.02991153486073017,
-0.012496521696448326,
0.0021927054040133953,
0.012303510680794716,
-0.025253793224692345,
-0.008044448681175709,
-0.0628681629896164,
0.0008453804184682667,
-0.030611161142587662,
0.03621925041079521,
-0.00475373025983572,
-0.012552889063954353,
0.025156628340482712,
0.03218585252761841,
0.02803274244070053,
0.012508093379437923,
-0.012942060828208923,
0.03222189098596573,
0.013423064723610878,
-0.00839216448366642,
-0.006017592735588551,
0.03866032510995865,
-0.005537885241210461,
-0.025714347139000893,
0.01766783744096756,
0.011451050639152527,
0.025819135829806328,
-0.055552851408720016,
0.0026470073498785496,
0.039372194558382034,
0.013228698633611202,
0.008238205686211586,
-0.017005691304802895,
0.022807082161307335,
-0.015498816967010498,
0.034816280007362366,
-0.002211346523836255,
-0.001913786749355495,
-0.03184705600142479,
-0.028626451268792152,
0.058328233659267426,
-0.036272335797548294,
0.016256971284747124,
0.0004652949864976108,
0.017063552513718605,
0.0034909513778984547,
-0.0033535342663526535,
-0.012934381142258644,
-0.01493003685027361,
0.04080041125416756,
-0.024931399151682854,
0.0010005887597799301,
-0.0018293578177690506,
0.007250173948705196,
-0.019612886011600494,
-0.018509579822421074,
-0.028910458087921143,
0.012666481547057629,
0.024005135521292686,
-0.03691498935222626,
0.05801074206829071,
-0.006331459619104862,
-0.044320929795503616,
0.024949487298727036,
-0.024964943528175354,
0.02013145387172699,
0.015993578359484673,
0.03549797087907791,
0.026153557002544403,
-0.0202335175126791,
-0.004864606540650129,
0.030797841027379036,
0.060359351336956024,
-0.029539039358496666,
0.03093571960926056,
0.01494833454489708,
0.00333426333963871,
-0.0019943062216043472,
-0.010105067864060402,
-0.02359014004468918,
0.034870445728302,
0.004866780247539282,
0.0010029403492808342,
0.012704059481620789,
-0.005949471611529589,
0.049660760909318924,
0.023346593603491783,
0.016359979286789894,
-0.021755453199148178,
0.016677888110280037,
-0.06475652754306793,
0.04467545449733734,
0.0342959463596344,
0.039880260825157166,
-0.003657273482531309,
-0.004469520412385464,
0.006262642331421375,
0.012119702994823456,
-0.00006776009104214609,
0.024501679465174675,
-0.07815562933683395,
-0.02168155089020729,
-0.03474688529968262,
-0.024110455065965652,
0.0015779805835336447,
-0.03174293413758278,
-0.02039860375225544,
-0.013705129735171795,
-0.0418013259768486,
0.019885487854480743,
0.022726839408278465,
0.04295359551906586,
-0.04810463264584541,
0.05915844067931175,
-0.00838381052017212,
0.029234543442726135,
-0.05611025542020798,
0.03954370319843292,
0.11205915361642838,
0.05992131307721138,
0.016636021435260773,
-0.06995301693677902,
0.007043702993541956,
-0.019598878920078278,
-0.01655666157603264,
-0.011869867332279682,
0.0072609977796673775,
-0.006511558312922716,
0.03495756909251213,
-0.03524038940668106,
0.052617136389017105,
-0.032845836132764816,
-0.02250084839761257,
0.02454311214387417,
-0.02985507622361183,
-0.05232143774628639,
-0.004718290641903877,
0.0278802327811718,
0.010851811617612839,
-0.00041148209129460156,
-0.06151687726378441,
0.034857943654060364,
0.007591460831463337,
0.01466324832290411,
-0.010867079719901085,
-0.045974571257829666,
0.0027827920857816935,
0.028119275346398354,
-0.0560445562005043,
-0.0140245845541358,
0.004352909978479147,
-0.031171247363090515,
-0.06122901290655136,
0.02212582156062126,
0.008797346614301205,
-0.035418543964624405,
0.03395678102970123,
0.031031688675284386,
-0.005376436281949282,
0.00578232342377305,
0.004961464088410139,
0.015020078979432583,
-0.04130110517144203,
-0.03679816052317619,
-0.019199615344405174,
0.04441652074456215,
0.0084530059248209,
-0.028414322063326836,
-0.004711017478257418,
0.023043114691972733,
-0.01660905033349991,
-0.04693423956632614,
-0.0019076329190284014,
-0.027186015620827675,
0.007404832169413567,
0.019505904987454414,
0.006087742280215025,
-0.013399525545537472,
0.02105308696627617,
-0.011011450551450253,
0.030200816690921783,
0.0028932371642440557,
0.011766452342271805,
0.03145001456141472,
-0.025172194465994835,
0.03262568637728691,
-0.0016439385944977403,
0.019120635464787483,
-0.01891554519534111,
-0.03130742162466049,
-0.04615992680191994,
-0.001496124197728932,
0.014248600229620934,
0.015529879368841648,
0.022974880412220955,
0.003776813391596079,
-0.003015421098098159,
-0.014810658060014248,
-0.015137397684156895,
0.0456254817545414,
-0.01126660406589508,
0.0020101817790418863,
0.008675873279571533,
0.01965065859258175,
-0.00033620113390497863,
0.044795919209718704,
-0.01125380489975214,
0.003201904008165002,
-0.012386317364871502,
0.003094963962212205,
-0.011536872945725918,
-0.024268362671136856,
-0.0005731513956561685,
-0.007483079098165035,
-0.05433600768446922,
0.015947867184877396,
-0.017797183245420456,
-0.0065500978380441666,
0.005556078627705574,
0.011591009795665741,
0.012035772204399109,
0.06245364248752594,
-0.027436019852757454,
-0.027859799563884735,
-0.005770199466496706,
-0.011291787028312683,
0.01415820699185133,
0.045206326991319656,
0.006407170556485653,
-0.03443952649831772,
-0.01566758193075657,
0.004264081362634897,
0.008971932344138622,
0.0008304525399580598,
0.03852894902229309,
-0.024958785623311996,
0.02011248469352722,
-0.013218909502029419,
0.0035380972549319267,
0.007666063494980335,
0.00605959864333272,
-0.04573606699705124,
0.048470258712768555,
-0.008584586903452873,
-0.03264615312218666,
-0.03646010532975197,
-0.008860361762344837,
-0.015967492014169693,
-0.010689590126276016,
0.003598790382966399,
0.01737494021654129,
-0.03656253591179848,
-0.004817395471036434,
0.04119422286748886,
0.006087814923375845,
0.046091314405202866,
0.002707968233153224,
-0.007508400361984968,
0.03174877166748047,
-0.032156430184841156,
-0.05025626718997955,
0.014403353445231915,
-0.019327210262417793,
0.03107324056327343,
0.01907692663371563,
-0.0018034809036180377,
-0.0647001788020134,
0.051132507622241974,
-0.03114311397075653,
-0.018570048734545708,
0.007744998205453157,
-0.018848637118935585,
-0.028643006458878517,
-0.030374301597476006,
0.019519874826073647,
0.019391603767871857,
0.0007583986734971404,
0.05651823803782463,
0.020245032384991646,
-0.01138954609632492,
-0.027116961777210236,
-0.011892512440681458,
0.0042833443731069565,
0.020289847627282143,
0.025006145238876343,
0.02214050479233265,
-0.011970141902565956,
0.054539378732442856,
-0.06587262451648712,
0.04126664996147156,
0.023855499923229218,
0.010820867493748665,
-0.10116247087717056,
-0.006672606337815523,
0.001908565522171557,
0.010051222518086433,
0.014445947483181953,
-0.04216330498456955,
0.023613398894667625,
0.04775034636259079,
-0.06911394000053406,
0.03503911569714546,
-0.026032468304038048,
0.0008636082638986409,
-0.027770277112722397,
-0.0032034453470259905,
-0.002050841460004449,
0.04771009460091591,
0.051350247114896774,
0.04677366092801094,
0.010930539108812809,
-0.0024911239743232727,
-0.04376618191599846,
-0.06253089755773544,
-0.001607196987606585,
0.07202921062707901,
-0.008992684073746204,
0.004903789144009352,
0.10246270895004272,
0.0034822106827050447,
-0.015737952664494514,
0.04004785791039467,
0.004068311303853989,
-0.013969212770462036,
-0.02516912668943405,
-0.0034403158351778984,
0.02041454240679741,
-0.0034748222678899765,
0.036037325859069824,
-0.0012072225799784064,
0.015036681666970253,
0.001054692082107067,
0.037732843309640884,
0.0019418755546212196,
0.029926825314760208,
-0.008283034898340702,
-0.004053902812302113,
-0.01358878891915083,
0.00615793326869607,
0.041723161935806274,
-0.007964191026985645,
-0.017550768330693245,
-0.004292330704629421,
0.011095196008682251,
0.009085397236049175,
-0.02329857274889946,
-0.005276202689856291,
-0.04851589351892471,
0.0014724652282893658,
0.013797552324831486,
0.014711055904626846,
0.01995128020644188,
0.005372160114347935,
-0.004263416863977909,
-0.011309539899230003,
-0.001786355976946652,
0.016688719391822815,
-0.013354159891605377,
-0.04673982784152031,
-0.0018751525785773993,
0.03659184277057648,
0.014669904485344887,
-0.00027606613002717495,
-0.05536132678389549,
-0.04684494435787201,
0.00941513106226921,
0.037658967077732086,
0.0379180870950222,
-0.019947202876210213,
-0.043508049100637436,
-0.030974717810750008,
-0.07664384692907333,
0.04214910417795181,
0.035650357604026794,
-0.01591397635638714,
-0.058463774621486664,
-0.018347611650824547,
-0.007801877334713936,
0.039861101657152176,
0.0541883185505867,
0.025880232453346252,
-0.01290457509458065,
0.0017038348596543074,
0.02614792250096798,
0.010546454228460789,
-0.03023860789835453,
-0.018142255023121834,
0.018416741862893105,
-0.042648203670978546,
-0.014553804881870747,
-0.010081837885081768,
-0.0011620339937508106,
0.016179611906409264,
0.07905252277851105,
-0.032044053077697754,
0.011423147283494473,
-0.013720669783651829,
-0.016940411180257797,
0.05990025773644447,
0.013927274383604527,
-0.024950550869107246,
0.0312655046582222,
-0.005231888964772224,
0.032030802220106125,
0.019788967445492744,
-0.014192294329404831,
-0.0174295324832201,
-0.007493979297578335,
-0.0414685495197773,
0.016635017469525337,
-0.003981885500252247,
0.013344061560928822,
0.023683328181505203,
-0.026208342984318733,
-0.004760404117405415,
0.0673782229423523,
-0.025492848828434944,
-0.03148948401212692,
0.07834497094154358,
0.0439077764749527,
0.03998316451907158,
0.029069431126117706,
0.024498460814356804,
0.013136623427271843,
-0.014586210250854492,
0.03665066510438919,
0.06115584820508957,
0.029093949124217033,
0.011432277038693428,
-0.01506827399134636,
0.03134540468454361,
0.011299963109195232,
-0.003964403178542852,
-0.0023732108529657125,
0.021468088030815125,
-0.03782954066991806,
-0.009849820286035538,
-0.0024459941778331995,
-0.026874760165810585,
0.028196265920996666,
0.0077273049391806126,
-0.02367667481303215,
0.10009191930294037,
-0.023136677220463753,
-0.005139951594173908,
0.0024688804987818003,
-0.006440915632992983,
0.03463985398411751,
-0.0029236599802970886,
-0.00232687802053988,
0.014123588800430298,
-0.0018132496625185013,
-0.014038151130080223,
-0.028846899047493935,
0.009948787279427052,
0.01759345643222332,
-0.04788913577795029,
-0.025342866778373718,
0.0011128064943477511,
0.013137088157236576,
0.0008274067658931017,
-0.01963568478822708,
-0.0023425875697284937,
-0.017457669600844383,
0.042158905416727066,
0.042082834988832474,
0.025251105427742004,
-0.013022339902818203,
-0.016593260690569878,
-0.04045189544558525,
0.039536554366350174,
-0.04115123674273491,
-0.053006868809461594,
-0.04213409498333931,
0.027560530230402946,
-0.012461098842322826,
0.015573225915431976
] |
<p>While studying quantum mechanics from standard textbooks I always felt some conceptual gap that was never mentioned or explained. In what follow I tried to formulate my question, please be patient with me.</p>
<p>For a quantum particle in an infinite potential well the stationary states are labelled by the quantum number $n$ which labels the eigenenergies. An eigenenergy, that corresponds to a stationary state, does not change with time, hence is a conserved quantity.</p>
<p>For a spinless electron in Coulomb potential, to model the hydrogen atom, again we have the same story, the stationary states are labeled by the quantum numbers $n$, $l$, $m$ which corresponds to conserved quantities.</p>
<p>My question is rather general since I am trying to understand conceptually why only conserved quantities are used to label the quantum states.</p>
<p>I mean how would someone think in advance that he has to look for conserved quantities, and then use such conserved quantities to label the states ? </p>
| 10,822 |
[
-0.028480473905801773,
0.009596914984285831,
-0.03392753377556801,
-0.035920098423957825,
0.029950181022286415,
-0.035256631672382355,
-0.06463226675987244,
-0.005446956492960453,
0.01510829571634531,
-0.03250500559806824,
0.016080284491181374,
-0.018482215702533722,
0.03978080675005913,
-0.024416480213403702,
0.04239002615213394,
0.044130709022283554,
-0.004258399363607168,
-0.034406378865242004,
-0.034541841596364975,
0.005307566374540329,
0.006093069911003113,
0.014050660654902458,
0.01838863082230091,
-0.015570255927741528,
-0.03056669421494007,
0.03731779754161835,
-0.013540548272430897,
0.01119935605674982,
0.0326751247048378,
0.06303782761096954,
-0.004340878687798977,
-0.01929405704140663,
0.024288559332489967,
0.04749487340450287,
-0.016170982271432877,
-0.01893768459558487,
-0.010990223847329617,
-0.06038209795951843,
-0.014396009966731071,
0.013785111717879772,
-0.02792138047516346,
-0.03970920667052269,
0.006420018617063761,
0.07139288634061813,
-0.012395569123327732,
0.028594426810741425,
-0.0231345035135746,
-0.01572694256901741,
0.020333945751190186,
-0.04457889124751091,
0.04659229516983032,
0.029910240322351456,
0.06222037971019745,
-0.009918351657688618,
-0.016766628250479698,
-0.0075570084154605865,
0.06280583143234253,
0.06335554271936417,
0.02617649734020233,
-0.06664062291383743,
-0.02859419770538807,
-0.01422883290797472,
0.003292950801551342,
-0.005620182491838932,
-0.011960303410887718,
0.0038104173727333546,
0.011367235332727432,
0.0047313799150288105,
0.056350912898778915,
-0.011288920417428017,
-0.01589425839483738,
0.004327632486820221,
0.030087152495980263,
-0.045597098767757416,
0.02429523505270481,
-0.022417137399315834,
0.012966231442987919,
-0.009623113088309765,
0.023555520921945572,
0.006033326033502817,
-0.00511033833026886,
0.009544895961880684,
0.014503699727356434,
0.038796089589595795,
0.0027121452149003744,
-0.011424311436712742,
0.05443073809146881,
0.01241302490234375,
0.024017566815018654,
0.06312254071235657,
-0.019147252663969994,
0.03883747756481171,
0.0004094027972314507,
-0.02623748779296875,
-0.002403674880042672,
0.0216436218470335,
0.007671104744076729,
0.016353972256183624,
0.02140982262790203,
-0.01631394773721695,
0.016378754749894142,
-0.04381059855222702,
0.018131203949451447,
0.05917489156126976,
-0.026328815147280693,
-0.023689836263656616,
-0.027755338698625565,
0.0064130728133022785,
-0.0034533506259322166,
-0.013232691213488579,
-0.04541036859154701,
0.020900817587971687,
0.013592434115707874,
0.019508974626660347,
0.014345256611704826,
-0.0711435079574585,
0.002870085882022977,
-0.020867865532636642,
0.0586223378777504,
0.06891211122274399,
0.014030370861291885,
-0.041369978338479996,
0.031688667833805084,
-0.0026540877297520638,
-0.05898553133010864,
-0.012339827604591846,
0.03578133508563042,
0.04851287230849266,
-0.013371181674301624,
0.018776897341012955,
0.03030024655163288,
-0.022371651604771614,
0.022146448493003845,
-0.014719361439347267,
0.059962205588817596,
-0.011940427124500275,
-0.1146249994635582,
-0.025810524821281433,
0.04046773537993431,
-0.051743924617767334,
-0.0006760723772458732,
-0.0689825490117073,
-0.018420396372675896,
-0.0040433709509670734,
0.03720308095216751,
-0.015581448562443256,
0.0027495133690536022,
0.020716115832328796,
0.01932511292397976,
0.01771603338420391,
-0.00705987773835659,
-0.03957526758313179,
0.016042454168200493,
-0.022421540692448616,
-0.005518220830708742,
-0.027813658118247986,
0.01454710029065609,
0.020103899762034416,
0.020128898322582245,
-0.00850929319858551,
0.05187757685780525,
-0.03745780512690544,
0.009868369437754154,
0.006340689025819302,
-0.003230238566175103,
-0.026703493669629097,
0.06951254606246948,
0.020216835662722588,
0.021991729736328125,
0.05864648148417473,
0.005722923204302788,
0.010610423982143402,
-0.02048172987997532,
0.02465290017426014,
0.011647683568298817,
-0.050055187195539474,
-0.01187354326248169,
-0.037778548896312714,
-0.0012005912140011787,
0.016687477007508278,
-0.053847942501306534,
-0.03423060104250908,
0.007910069078207016,
0.019500484690070152,
0.008817973546683788,
0.031672053039073944,
0.007440007291734219,
0.02488713525235653,
-0.03006879799067974,
-0.06153560057282448,
0.008463206700980663,
-0.08559080958366394,
0.050640154629945755,
0.01566692627966404,
-0.001505569671280682,
0.06028411164879799,
-0.004238583613187075,
0.020698612555861473,
-0.01095195859670639,
-0.021236946806311607,
-0.02597176842391491,
0.061281681060791016,
-0.02804252877831459,
-0.03768951818346977,
0.027050752192735672,
0.021129434928297997,
0.03762182220816612,
0.036331791430711746,
0.04497457295656204,
-0.034641243517398834,
-0.02076788805425167,
0.01789044961333275,
-0.032207053154706955,
0.013020278885960579,
0.03687060996890068,
-0.028118906542658806,
-0.014507012441754341,
-0.05918086692690849,
0.00039012599154375494,
0.04346197471022606,
-0.010324851609766483,
0.045253507792949677,
0.0263535063713789,
-0.03597959876060486,
-0.0019648491870611906,
0.03527772054076195,
-0.013473994098603725,
0.014748325571417809,
0.007871195673942566,
-0.025867214426398277,
-0.02727506123483181,
-0.00025723734870553017,
0.04795119911432266,
0.06338585168123245,
-0.05498916283249855,
-0.018796224147081375,
-0.00460234098136425,
0.029631232842803,
0.05137115716934204,
-0.00017421823577024043,
-0.06910210102796555,
-0.048108071088790894,
0.03605089336633682,
0.022379089146852493,
-0.020789192989468575,
0.018873751163482666,
0.03182072937488556,
0.013611087575554848,
0.046280961483716965,
0.0023412848822772503,
-0.01186920702457428,
0.05957697331905365,
-0.049191590398550034,
0.011052587069571018,
0.008621563203632832,
-0.019994935020804405,
0.0015250107971951365,
-0.019633932039141655,
0.02229684218764305,
0.020841244608163834,
-0.016749992966651917,
0.004196986556053162,
-0.015286531299352646,
-0.03376996889710426,
0.025377264246344566,
-0.003465887624770403,
-0.012345339171588421,
-0.01165997888892889,
0.006877939682453871,
-0.016057902947068214,
0.035821396857500076,
-0.02690190076828003,
-0.020665578544139862,
-0.00562667939811945,
-0.007042598910629749,
0.04535483568906784,
0.00009877904085442424,
0.011895005591213703,
-0.03349601849913597,
-0.01599727012217045,
0.019615652039647102,
-0.04319462180137634,
0.010747706517577171,
0.022184429690241814,
-0.0347590409219265,
-0.0012084789341315627,
-0.05439872294664383,
-0.03682376816868782,
0.043923042714595795,
-0.024326549842953682,
0.020944565534591675,
-0.018746471032500267,
-0.03377979248762131,
-0.07264617830514908,
-0.008304090239107609,
-0.044501807540655136,
0.02749023027718067,
-0.004229856189340353,
-0.003923838958144188,
0.0884220227599144,
-0.019130315631628036,
-0.015577222220599651,
0.0037629627622663975,
-0.035529717803001404,
-0.042114824056625366,
-0.013473107479512691,
-0.03069455735385418,
0.00973336212337017,
-0.0466158501803875,
0.039279304444789886,
0.019002432003617287,
-0.03716708719730377,
-0.02748124673962593,
-0.03699960559606552,
-0.02397148869931698,
0.00980154238641262,
0.006244489457458258,
0.030632048845291138,
-0.014367050491273403,
-0.008979744277894497,
0.07794024795293808,
0.01760539971292019,
-0.04061805084347725,
-0.009691202081739902,
0.0010985262924805284,
-0.013974439352750778,
-0.03878232091665268,
-0.0012161419726908207,
0.025775471702218056,
-0.01619642972946167,
0.031759727746248245,
0.008814944885671139,
0.04573926329612732,
0.007550166919827461,
-0.0015515522100031376,
-0.011632466688752174,
0.007855727337300777,
-0.002804362215101719,
0.05571993067860603,
0.06934407353401184,
-0.012346026487648487,
-0.051280677318573,
-0.022473150864243507,
0.006033515091985464,
0.014683817513287067,
0.010238430462777615,
-0.05487601459026337,
0.09436241537332535,
-0.01597771979868412,
0.03484541177749634,
-0.030054699629545212,
0.029506580904126167,
-0.010498704388737679,
-0.0008350679418072104,
-0.01553661935031414,
-0.003251271555200219,
0.029034094884991646,
-0.02152750827372074,
0.009298840537667274,
0.05665428563952446,
0.008793171495199203,
-0.02359422855079174,
0.0017449717270210385,
0.015536727383732796,
-0.005253697745501995,
0.03511480242013931,
-0.022741541266441345,
-0.044740911573171616,
0.023226626217365265,
0.02087235264480114,
-0.000744021323043853,
-0.016129452735185623,
-0.0616728775203228,
-0.02589329518377781,
-0.04241450875997543,
-0.007631191983819008,
0.019889123737812042,
0.05126606673002243,
-0.02389698475599289,
0.06313791871070862,
0.04433699697256088,
-0.009664298966526985,
0.009200438857078552,
-0.0074777184054255486,
-0.05113137885928154,
0.035244837403297424,
-0.033928386867046356,
0.0183083638548851,
-0.006820871494710445,
0.0010839286260306835,
-0.009823833592236042,
-0.028662748634815216,
-0.005407888907939196,
0.0009381645359098911,
-0.004722010809928179,
-0.05572886019945145,
-0.025767765939235687,
-0.05676926299929619,
-0.03278578445315361,
-0.06400597095489502,
0.04478022828698158,
0.03239770233631134,
-0.02967621199786663,
0.01992262713611126,
0.05497923493385315,
-0.038680549710989,
-0.008008996956050396,
-0.015367913991212845,
-0.006448651198297739,
0.051944807171821594,
0.004205893259495497,
0.03782320395112038,
0.04416049271821976,
0.019905490800738335,
-0.025902798399329185,
0.026167016476392746,
0.03641168400645256,
-0.010880131274461746,
0.01382630504667759,
0.023155121132731438,
-0.03848098963499069,
0.005972979590296745,
0.013409828767180443,
0.08311324566602707,
0.02045847289264202,
0.011420574970543385,
0.02574032172560692,
0.008671242743730545,
-0.0007716683903709054,
0.012710980139672756,
0.039408713579177856,
0.01733376272022724,
-0.0360565185546875,
-0.04309280589222908,
0.0467681810259819,
-0.04892181232571602,
0.0022780566941946745,
-0.012065140530467033,
-0.024182122200727463,
-0.00731689715757966,
-0.0015349900349974632,
0.023175133392214775,
-0.011201402172446251,
0.014492662623524666,
-0.009707971476018429,
0.003308005863800645,
0.03823946416378021,
0.01261190790683031,
0.0047030458226799965,
0.04213104769587517,
0.02419334463775158,
0.024966228753328323,
0.017112353816628456,
0.04208236560225487,
-0.050049830228090286,
-0.013559061102569103,
0.009804298169910908,
0.010792919434607029,
0.0003431187360547483,
-0.020561765879392624,
-0.07651122659444809,
-0.024942010641098022,
0.03502796217799187,
-0.028595706447958946,
0.03308451175689697,
-0.025801464915275574,
-0.017743777483701706,
0.0022779435385018587,
0.0007538766949437559,
-0.008389158174395561,
0.024878667667508125,
0.006600195076316595,
0.031655680388212204,
-0.035082943737506866,
0.03748627379536629,
-0.022874346002936363,
-0.0009331668261438608,
-0.039725251495838165,
0.032295651733875275,
-0.00029576299129985273,
0.013424842618405819,
0.01982393115758896,
0.023379214107990265,
0.026842795312404633,
-0.07757142186164856,
0.010553302243351936,
0.030072534456849098,
0.001730244024656713,
0.029322536662220955,
-0.05159997567534447,
-0.07350430637598038,
-0.01043054461479187,
0.007019283715635538,
-0.013103481382131577,
0.009219082072377205,
-0.03602394834160805,
0.053314097225666046,
0.023153433576226234,
-0.029865087941288948,
0.031017854809761047,
0.0040565854869782925,
0.023103266954421997,
-0.022663768380880356,
-0.0069678123109042645,
0.022985639050602913,
-0.04371105507016182,
-0.010115023702383041,
-0.06313817203044891,
0.012605839408934116,
-0.04483799263834953,
0.06308430433273315,
-0.017274167388677597,
0.009648031555116177,
-0.01793254353106022,
-0.014444376341998577,
-0.021913940086960793,
0.029857812449336052,
-0.008057037368416786,
-0.014517247676849365,
-0.02313831076025963,
0.0043643382377922535,
-0.009749018587172031,
-0.025034863501787186,
-0.010606491938233376,
0.008966578170657158,
-0.017053654417395592,
0.05628565326333046,
0.005173886194825172,
0.016890428960323334,
-0.015469884499907494,
-0.03281904757022858,
0.04832559451460838,
-0.02726680412888527,
0.003240506164729595,
0.012549255974590778,
0.022295629605650902,
0.004023145418614149,
-0.08543703705072403,
-0.059025220572948456,
0.01749400980770588,
-0.02233920246362686,
-0.0018196558812633157,
-0.027646342292428017,
0.005575847811996937,
0.025682292878627777,
0.010232960805296898,
-0.058351173996925354,
-0.01135462336242199,
0.009607990272343159,
-0.003930324222892523,
-0.025722289457917213,
-0.006621095817536116,
0.03465188294649124,
0.010876109823584557,
-0.039832986891269684,
0.000272639881586656,
0.02903279848396778,
-0.03870849311351776,
-0.0023171475622802973,
0.021334338933229446,
0.04178953543305397,
0.048632387071847916,
-0.02125287614762783,
0.0020963919814676046,
-0.015515648759901524,
0.005724770482629538,
-0.019095800817012787,
-0.007660283241420984,
0.04521704092621803,
-0.007377785164862871,
-0.04016340523958206,
-0.028970489278435707,
-0.002098947763442993,
0.05673394352197647,
-0.02301124297082424,
-0.014178541488945484,
0.008558602072298527,
-0.003394352039322257,
-0.01593969203531742,
-0.013343251310288906,
-0.011269296519458294,
-0.006661995314061642,
0.055323850363492966,
-0.00691381748765707,
-0.005402745679020882,
-0.003918176982551813,
-0.031451113522052765,
0.027173705399036407,
0.009560062550008297,
0.024472439661622047,
0.023409217596054077,
0.03038080222904682,
-0.007886262610554695,
-0.014180097728967667,
0.04158100113272667,
-0.02456582337617874,
0.013500314205884933,
0.0032780154142528772,
0.017312094569206238,
-0.021754775196313858,
-0.003990387078374624,
-0.021407246589660645,
-0.052983954548835754,
-0.027846984565258026,
0.03522035852074623,
0.03840736672282219,
0.007972251623868942,
0.05869443342089653,
0.01456577517092228,
0.03170998394489288,
-0.0145485270768404,
-0.038509637117385864,
-0.036693159490823746,
-0.010369924828410149,
0.007262331899255514,
0.02274470217525959,
-0.023274334147572517,
-0.009752226993441582,
0.042267072945833206,
0.05258341133594513,
0.00554687948897481,
0.014261986128985882,
0.04233737662434578,
-0.011139241978526115,
0.00500133540481329,
-0.018329322338104248,
-0.0316149927675724,
0.06574726104736328,
-0.015174292959272861,
0.04507225751876831,
-0.00013082503573969007,
-0.041802212595939636,
0.03877347335219383,
0.013157240115106106,
0.004811294376850128,
-0.03382474556565285,
-0.0263687651604414,
-0.051145877689123154,
0.04330610856413841,
0.018917346373200417,
-0.01740943267941475,
-0.02135016955435276,
0.03247276693582535,
-0.0035695936530828476,
0.00828766729682684,
0.023293528705835342,
-0.009466937743127346,
-0.03142961114645004,
-0.02684776857495308,
-0.037686288356781006,
-0.03106667473912239,
0.04110444337129593,
0.008938794024288654,
-0.027169812470674515,
0.004584094975143671,
-0.00806623138487339,
0.019985372200608253,
0.004617356229573488,
0.004202303942292929,
-0.04981456324458122,
0.09128660708665848,
0.015869110822677612,
0.024002259597182274,
0.0119725177064538,
0.02010037936270237,
0.11634843051433563,
0.051809996366500854,
-0.007785399444401264,
-0.05849906802177429,
0.0036148589570075274,
0.013701790943741798,
0.015438571572303772,
-0.006592568475753069,
0.040079765021800995,
0.025974011048674583,
0.030669743195176125,
-0.028731174767017365,
0.021247997879981995,
-0.014447084628045559,
0.048268601298332214,
0.06735923886299133,
-0.02923787385225296,
-0.03053727000951767,
-0.014847742393612862,
0.027507195249199867,
0.015393149107694626,
0.024695809930562973,
-0.055334459990262985,
0.03658061474561691,
-0.0025556122418493032,
0.00518573634326458,
-0.003260132623836398,
-0.03147294744849205,
-0.0018869981868192554,
-0.020273219794034958,
-0.002270859433338046,
0.011603795923292637,
-0.011428688652813435,
-0.00503501994535327,
-0.01956976018846035,
0.019239626824855804,
0.025336598977446556,
0.014806306920945644,
0.06053948774933815,
0.010756085626780987,
0.0053328052163124084,
-0.0043304371647536755,
0.004793345462530851,
0.0035142600536346436,
-0.013424115255475044,
-0.026095816865563393,
-0.032021813094615936,
0.057017434388399124,
-0.007455089595168829,
-0.02819550409913063,
-0.0016661318950355053,
-0.022210540249943733,
-0.006047109607607126,
-0.03616144880652428,
-0.02533581852912903,
0.0033179011661559343,
0.02321617305278778,
-0.0027560251764953136,
0.003306897124275565,
-0.03837975114583969,
-0.020487932488322258,
0.0006544445059262216,
0.013746518641710281,
-0.029415801167488098,
-0.0021385098807513714,
0.017039097845554352,
-0.023602871224284172,
-0.00567519711330533,
-0.014215823262929916,
0.023690925911068916,
-0.00802482757717371,
-0.025649147108197212,
-0.04709574580192566,
-0.048864446580410004,
0.026153042912483215,
0.020229453220963478,
0.03465260937809944,
0.0012591524282470345,
0.014713715761899948,
-0.01172358077019453,
-0.11260358989238739,
0.03226717561483383,
0.018605241551995277,
-0.029056809842586517,
-0.003316130954772234,
0.0012679784558713436,
-0.0009177435422316194,
0.06624487042427063,
-0.02835548296570778,
0.025231758132576942,
0.00230451300740242,
-0.0033233491703867912,
0.022811684757471085,
-0.033568091690540314,
-0.02468619868159294,
0.03099120780825615,
-0.0468866191804409,
-0.006950736045837402,
-0.02696998417377472,
-0.0344109870493412,
0.015243412926793098,
0.008741093799471855,
-0.01655920036137104,
0.06747853010892868,
-0.012382765300571918,
0.019230352714657784,
0.002453792840242386,
-0.032002173364162445,
0.030853988602757454,
0.012047778815031052,
0.02828071638941765,
-0.05215328186750412,
-0.054214879870414734,
-0.01206495612859726,
0.02137785777449608,
0.016826411709189415,
0.012907063588500023,
-0.03433368355035782,
0.009006603620946407,
-0.02681843191385269,
0.03799542412161827,
-0.030946683138608932,
-0.031119180843234062,
-0.0635700672864914,
0.028226790949702263,
0.02111649513244629,
-0.028370462357997894,
-0.021604033187031746,
0.018249262124300003,
0.002296667080372572,
-0.02535712718963623,
0.024892887100577354,
0.026261605322360992,
-0.022409172728657722,
-0.022775301709771156,
0.015851754695177078,
-0.022921588271856308,
0.03464540094137192,
-0.03108765184879303,
0.007302745711058378,
0.01296911295503378,
-0.04335174709558487,
-0.049498721957206726,
0.025830574333667755,
-0.0019372556125745177,
0.01896454580128193,
0.06922407448291779,
0.0011894186027348042,
-0.0037160497158765793,
0.020586617290973663,
-0.047117024660110474,
0.030288735404610634,
0.008411448448896408,
-0.03177887946367264,
-0.0034744071308523417,
-0.03213057667016983,
0.03430505096912384,
0.003630446968600154,
0.010240226052701473,
0.029920393601059914,
0.0333523154258728,
-0.005977162625640631,
-0.0060864463448524475,
0.006274933461099863,
0.026897111907601357,
0.059370577335357666,
0.06082155555486679,
0.0003467001661192626,
-0.01639918051660061,
0.0663532093167305,
-0.056422729045152664,
0.023890435695648193,
0.03478609770536423,
0.008676990866661072,
-0.08044973015785217,
-0.00919743999838829,
-0.018545130267739296,
0.006472254171967506,
0.039306458085775375,
-0.03470969200134277,
-0.007230187766253948,
0.03836020827293396,
-0.09454160928726196,
0.056055303663015366,
-0.037223462015390396,
0.010178673081099987,
-0.007581824436783791,
-0.016831044107675552,
-0.03475883603096008,
0.06684724241495132,
0.03130534291267395,
0.053048886358737946,
0.03036566637456417,
0.012086324393749237,
0.014679775573313236,
-0.019993647933006287,
-0.021476196125149727,
0.041336484253406525,
-0.00428763497620821,
0.013811837881803513,
0.0654759481549263,
-0.01965855434536934,
-0.033825214952230453,
0.024200841784477234,
-0.0311892069876194,
-0.003690594807267189,
0.005682372488081455,
0.01617492362856865,
-0.00981161743402481,
0.011936469934880733,
0.034658342599868774,
-0.004261217080056667,
-0.01300065964460373,
0.01697012223303318,
0.04634644091129303,
-0.014901385642588139,
0.02260727807879448,
-0.017411816865205765,
0.018189363181591034,
-0.07807083427906036,
-0.06635410338640213,
0.03632936626672745,
-0.0006234449101611972,
-0.0001332940737484023,
0.012941964901983738,
0.019040491431951523,
0.020636020228266716,
-0.032738763839006424,
-0.011238807812333107,
-0.01710136979818344,
-0.038047898560762405,
0.018490195274353027,
0.032538462430238724,
0.011819449253380299,
0.005281948484480381,
-0.01610141433775425,
-0.043384481221437454,
0.06529761850833893,
0.018748704344034195,
-0.031963709741830826,
-0.07037205994129181,
-0.012368259020149708,
0.02893640473484993,
-0.026208071038126945,
-0.03148576617240906,
-0.017515933141112328,
-0.06765566766262054,
0.028508801013231277,
-0.011463206261396408,
0.019214436411857605,
-0.03886771947145462,
-0.06402850151062012,
-0.014230597764253616,
-0.0606742687523365,
0.02531803958117962,
0.015814270824193954,
-0.007314166985452175,
-0.007141684181988239,
-0.011519652791321278,
-0.010380060411989689,
0.024027520790696144,
0.07099030911922455,
-0.005388955119997263,
-0.012024441733956337,
0.03850341588258743,
-0.01925305277109146,
0.014475621283054352,
-0.011419772170484066,
-0.0034695896320044994,
-0.01055062934756279,
0.012097298167645931,
-0.010604565031826496,
0.005445640534162521,
-0.0022377828136086464,
0.028530269861221313,
0.028203602880239487,
-0.010508149862289429,
-0.010245714336633682,
0.00014752158313058317,
-0.06154700368642807,
0.06413019448518753,
0.014887901954352856,
-0.021350974217057228,
0.04431721568107605,
-0.00023590002092532814,
0.007200326304882765,
0.030774317681789398,
-0.01447082869708538,
-0.05360660329461098,
0.02793443202972412,
-0.022878028452396393,
-0.006355234421789646,
0.009208474308252335,
-0.00869698915630579,
0.04192625358700752,
-0.039296191185712814,
-0.020355917513370514,
0.06485378742218018,
-0.018249383196234703,
-0.030987199395895004,
0.02970825508236885,
0.016817143186926842,
0.039987847208976746,
0.0090297507122159,
0.030167588964104652,
0.00726294657215476,
0.04631822928786278,
0.041610922664403915,
0.058751482516527176,
0.016485419124364853,
-0.0033403588458895683,
0.03211340680718422,
0.020333344116806984,
-0.014254821464419365,
0.03191402554512024,
0.040398623794317245,
0.018511218950152397,
-0.03463774174451828,
-0.00417446019127965,
0.027624957263469696,
-0.00529432250186801,
-0.021100303158164024,
-0.007585529703646898,
-0.0022629147861152887,
0.07432954758405685,
-0.02765820175409317,
-0.0013104528188705444,
-0.007052016444504261,
0.03231377527117729,
-0.02455448918044567,
-0.020414330065250397,
-0.0067307716235518456,
0.026010436937212944,
-0.016481010243296623,
-0.005207750480622053,
-0.030310090631246567,
0.02417699806392193,
0.007203360088169575,
-0.0451180674135685,
0.03571997210383415,
-0.0013786782510578632,
-0.025201020762324333,
-0.023787958547472954,
-0.01750153675675392,
-0.026495829224586487,
-0.012796725146472454,
0.007347229868173599,
0.050411663949489594,
0.06310021132230759,
0.001777247409336269,
-0.005472601857036352,
-0.042736031115055084,
0.05266605317592621,
-0.05274413898587227,
-0.04384568706154823,
0.011973045766353607,
-0.00068955885944888,
-0.002626764588057995,
-0.000353175331838429
] |
<p>Why different objects have different colour? When a white light (composed of all colour) falls on a red book, is it true that only red colour is reflected back? If no, then why it appears red. If yes, then why does the book doesn't get warmer even if it absorbed rest other wavelengths. How is hot red iron rod different than red book?</p>
<p>Kindly help in clearing this confusion. </p>
| 10,823 |
[
-0.05931166186928749,
-0.056824009865522385,
0.003383217379450798,
-0.02427774854004383,
0.023581234738230705,
0.017693448811769485,
-0.029131198301911354,
-0.006055840756744146,
-0.009983401745557785,
-0.0008393963216803968,
0.014864793978631496,
0.03223168104887009,
0.05404627323150635,
0.010518064722418785,
0.026519086211919785,
0.004097326658666134,
0.014200836420059204,
0.004531064070761204,
-0.017591435462236404,
0.02187441475689411,
0.019757097586989403,
0.027896810322999954,
0.023742130026221275,
-0.012195293791592121,
-0.0483282208442688,
0.011485811322927475,
-0.0013600143138319254,
0.02106349729001522,
0.044192783534526825,
0.022545328363776207,
0.0031060976907610893,
0.0217711441218853,
-0.03419515863060951,
0.026998650282621384,
0.011284718289971352,
-0.00037171810981817544,
-0.009974924847483635,
0.00023266572679858655,
-0.03562818467617035,
-0.01610136590898037,
0.021166708320379257,
-0.026089537888765335,
-0.015577901154756546,
0.06493353098630905,
-0.0031722153071314096,
-0.008870599791407585,
-0.014299105852842331,
-0.022721152752637863,
0.03204209357500076,
-0.042084574699401855,
0.06247009336948395,
-0.030287660658359528,
0.06676677614450455,
0.04035501927137375,
-0.011918644420802593,
0.0268852561712265,
0.054219745099544525,
0.08087405562400818,
-0.051880721002817154,
0.014121963642537594,
-0.010047173127532005,
-0.02759275957942009,
-0.006415862124413252,
-0.015358137898147106,
-0.027091002091765404,
-0.0025227379519492388,
0.023511704057455063,
-0.0371255986392498,
0.015523615293204784,
0.050485529005527496,
0.010256562381982803,
0.006432197988033295,
0.018403364345431328,
0.014038342982530594,
-0.0018918643472716212,
-0.05610493943095207,
0.011533875949680805,
0.06084618717432022,
0.054229989647865295,
0.01452793087810278,
0.0006869705975987017,
-0.00036312558222562075,
-0.007688537705689669,
-0.0073628854006528854,
0.018645478412508965,
-0.018336262553930283,
0.06737871468067169,
0.028132673352956772,
-0.0003133098070975393,
0.018204130232334137,
0.0063820513896644115,
0.014168121851980686,
0.008265150710940361,
0.023851921781897545,
-0.022666996344923973,
0.023581497371196747,
-0.010525855235755444,
0.034246478229761124,
-0.04882599785923958,
-0.01634802855551243,
0.031216852366924286,
0.008716623298823833,
0.06739820539951324,
0.06807514280080795,
-0.024018170312047005,
-0.025209520012140274,
-0.03912729024887085,
0.003785228356719017,
0.01910548470914364,
0.014393196441233158,
0.013560604304075241,
0.028364529833197594,
-0.005932108499109745,
-0.016605090349912643,
0.005290530156344175,
-0.03465179726481438,
0.03759493678808212,
-0.010244960896670818,
0.07065925747156143,
0.052855052053928375,
-0.004218507092446089,
-0.0439722016453743,
-0.0035785369109362364,
0.006515895947813988,
-0.0685373842716217,
0.02596767246723175,
0.03262526914477348,
-0.013752821832895279,
-0.015301303938031197,
0.015242258086800575,
-0.012375660240650177,
-0.018522923812270164,
0.018693597987294197,
-0.006530858110636473,
-0.010456625372171402,
-0.027506936341524124,
-0.10342374444007874,
-0.049512237310409546,
0.007235806435346603,
-0.007843396626412868,
-0.02444237284362316,
-0.061116840690374374,
0.030579177662730217,
0.022890394553542137,
0.07188668102025986,
-0.0032806170638650656,
-0.006123772822320461,
0.0033020467963069677,
0.03659823536872864,
-0.013823898509144783,
-0.03491514176130295,
-0.03751949965953827,
0.02310882695019245,
-0.031892936676740646,
-0.00171099160797894,
-0.06257928162813187,
-0.006236635614186525,
-0.002147992607206106,
-0.01899663917720318,
-0.020718274638056755,
-0.006422009784728289,
-0.04585087671875954,
0.002300248946994543,
0.049684666097164154,
0.003989604767411947,
-0.036793146282434464,
0.09971925616264343,
0.005566998850554228,
0.00922555010765791,
0.005681371781975031,
0.0010270884959027171,
0.036469265818595886,
-0.03617796674370766,
0.026316003873944283,
0.010071626864373684,
0.0020221732556819916,
-0.022683855146169662,
0.026875238865613937,
0.03221779689192772,
0.008928236551582813,
-0.05460098013281822,
-0.030798083171248436,
-0.006043256726115942,
-0.008414865471422672,
0.022844048216938972,
0.05123249813914299,
0.019030356779694557,
-0.01799401454627514,
-0.0001351632090518251,
-0.05010578781366348,
-0.0027316557243466377,
-0.02824101597070694,
0.005366824101656675,
-0.014769109897315502,
-0.008913830853998661,
0.026605721563100815,
0.009598649106919765,
0.03035561740398407,
-0.022361040115356445,
-0.028815101832151413,
-0.008394299075007439,
0.03045865334570408,
-0.01326633058488369,
-0.013022870756685734,
0.011775518767535686,
0.06209501996636391,
0.023467261344194412,
-0.012477928772568703,
0.010000946000218391,
-0.06238705292344093,
-0.047150399535894394,
0.015581569634377956,
-0.01053854264318943,
-0.008946796879172325,
0.010429758578538895,
-0.010228261351585388,
0.03277295455336571,
0.0551513247191906,
-0.013927236199378967,
0.023929044604301453,
0.007181717082858086,
0.029547592625021935,
-0.007421713788062334,
-0.03980987146496773,
0.008000765927135944,
0.04782106354832649,
-0.006505576428025961,
0.007702397648245096,
-0.008350980468094349,
-0.0000417386727349367,
-0.06031946465373039,
-0.007906974293291569,
-0.002722715260460973,
0.012180413119494915,
-0.0567261166870594,
0.0012643651571124792,
0.0171209704130888,
0.04574675112962723,
0.016428204253315926,
0.01670614629983902,
-0.011873598210513592,
-0.03560962900519371,
0.028261879459023476,
0.00335299433209002,
0.01191086694598198,
0.02586137317121029,
0.027110299095511436,
0.007162936497479677,
0.05455866828560829,
-0.04859030991792679,
-0.010641122236847878,
0.062367647886276245,
-0.009381623938679695,
0.044633518904447556,
-0.006915162783116102,
0.00667516328394413,
0.019796650856733322,
-0.020538330078125,
0.007232768461108208,
0.002786783967167139,
0.0005892612389288843,
-0.012650107964873314,
-0.05128929018974304,
-0.013214923441410065,
0.009042038582265377,
0.00011533991346368566,
-0.0352494902908802,
-0.03418700024485588,
0.002831402700394392,
-0.021887987852096558,
0.00753852678462863,
0.008548141457140446,
0.0032185728196054697,
-0.05567222088575363,
-0.005714537110179663,
0.006492018233984709,
-0.002086924621835351,
0.041129935532808304,
-0.04636140912771225,
-0.02432199753820896,
-0.026304300874471664,
-0.03077111579477787,
0.006125434301793575,
-0.029502231627702713,
-0.07834033668041229,
0.011980988085269928,
-0.06664838641881943,
-0.056069884449243546,
0.02396603487432003,
-0.011248679831624031,
-0.005526830907911062,
0.027140779420733452,
-0.014888755045831203,
-0.04564061760902405,
-0.005016669165343046,
-0.022105062380433083,
0.012225660495460033,
-0.014787846244871616,
-0.013259242288768291,
0.04314275458455086,
-0.034620922058820724,
-0.022943155840039253,
-0.017623139545321465,
-0.05926819518208504,
-0.05203932523727417,
0.016146721318364143,
-0.05514185130596161,
0.01922198198735714,
-0.01613052375614643,
-0.0034933327697217464,
0.03983880206942558,
-0.05548461526632309,
0.025721292942762375,
-0.007521294988691807,
-0.01021493785083294,
0.004280287306755781,
-0.018014121800661087,
0.03862190991640091,
-0.0012413960648700595,
0.01506433729082346,
0.050353579223155975,
0.03050137683749199,
-0.027658889070153236,
-0.035901982337236404,
0.011735905893146992,
-0.04314742982387543,
-0.07483437657356262,
0.03405839577317238,
0.030847888439893723,
-0.045656636357307434,
0.051268093287944794,
0.014721584506332874,
0.007683685515075922,
0.05131176859140396,
0.022057244554162025,
-0.03193429112434387,
0.01580047234892845,
0.017846856266260147,
-0.013850849121809006,
0.03931783512234688,
0.022536350414156914,
-0.025239506736397743,
0.022538432851433754,
-0.009209617041051388,
0.04145941138267517,
0.027556145563721657,
-0.02781623601913452,
0.06097035109996796,
0.005626609083265066,
0.020937958732247353,
-0.0535578727722168,
0.06769976019859314,
-0.022022511810064316,
-0.009081491269171238,
0.008461141027510166,
0.00654176389798522,
0.049236271530389786,
0.0104869045317173,
0.009473731741309166,
0.05303877219557762,
0.015390620566904545,
-0.0014429353177547455,
-0.004038144834339619,
-0.012404593639075756,
-0.007385461591184139,
0.028434298932552338,
-0.020337451249361038,
0.007574672345072031,
0.08500497043132782,
0.0433887243270874,
0.04214109852910042,
-0.0040600779466331005,
-0.025004398077726364,
-0.007121208589524031,
-0.03101273812353611,
-0.0025570951402187347,
0.012112871743738651,
0.07137712091207504,
-0.007321546785533428,
0.0705992579460144,
0.03087880089879036,
0.0260305218398571,
0.012750615365803242,
0.0026848912239074707,
-0.08483544737100601,
0.020494963973760605,
-0.04394948109984398,
0.010977092199027538,
-0.023555876687169075,
-0.01751311682164669,
-0.021125921979546547,
-0.01800524815917015,
-0.0017566876485943794,
0.011105976067483425,
-0.05805971845984459,
-0.030868057161569595,
-0.0015642462531104684,
-0.008193757385015488,
-0.03966260328888893,
-0.022797085344791412,
0.06623239815235138,
0.007108893245458603,
-0.021936746314167976,
0.0347127728164196,
0.02045026421546936,
-0.02916417270898819,
0.011058439500629902,
-0.045552145689725876,
0.0277786236256361,
0.04720545932650566,
0.03555379807949066,
0.06040729582309723,
0.011175351217389107,
-0.03499726206064224,
0.034065406769514084,
0.040973253548145294,
0.03009987063705921,
-0.021127551794052124,
-0.050123803317546844,
-0.03872969374060631,
-0.08426835387945175,
-0.0142771415412426,
-0.05346382036805153,
0.04792739450931549,
-0.04451969638466835,
0.012842763215303421,
0.015782423317432404,
0.0020280545577406883,
-0.003801560727879405,
-0.01123651023954153,
0.0009940805612131953,
-0.0048244306817650795,
-0.03383287042379379,
0.01867682673037052,
-0.0024717128835618496,
-0.06731223315000534,
0.005167039111256599,
0.008887112140655518,
0.007247445173561573,
0.003087224205955863,
0.01504851970821619,
0.009155520237982273,
0.048852451145648956,
-0.013960988260805607,
-0.012908771634101868,
-0.005903442390263081,
-0.0009522116160951555,
-0.02401871234178543,
-0.018437784165143967,
0.0011441964888945222,
0.058125872164964676,
0.027846748009324074,
-0.035978689789772034,
-0.03741540387272835,
-0.05167997628450394,
-0.003231504000723362,
0.020647622644901276,
0.015175648033618927,
-0.021030504256486893,
-0.01194483507424593,
-0.06631679832935333,
-0.006422166712582111,
0.01026599295437336,
-0.02661522664129734,
0.03309306129813194,
-0.06537862867116928,
-0.006141227204352617,
-0.02329081855714321,
0.009661276824772358,
0.013595398515462875,
0.014059595763683319,
0.003465428948402405,
0.0009461497538723052,
-0.007145734038203955,
-0.007314552552998066,
-0.014151202514767647,
-0.002930249786004424,
0.04595998302102089,
0.008362333290278912,
-0.030233465135097504,
0.023520365357398987,
-0.005212004762142897,
0.008606377057731152,
-0.02802237868309021,
-0.060993365943431854,
-0.012608015909790993,
-0.006210005842149258,
0.010182062163949013,
0.05380111187696457,
-0.020693816244602203,
-0.04925699159502983,
0.041610751301050186,
0.01673636958003044,
-0.02577471360564232,
-0.02637140080332756,
-0.06172245740890503,
0.0008824969409033656,
0.025928279384970665,
-0.03267447650432587,
0.05259259417653084,
0.01394837535917759,
0.001995173981413245,
-0.011515931226313114,
-0.0017887108260765672,
0.04654374718666077,
-0.04580874368548393,
-0.018283048644661903,
-0.03475825861096382,
0.001765022287145257,
-0.010255367495119572,
0.0536884181201458,
0.03352055698633194,
-0.021547384560108185,
-0.003589954925701022,
-0.08470206707715988,
0.0048738340847194195,
0.01927502453327179,
-0.010314364917576313,
0.03450500965118408,
-0.007685203570872545,
0.011013771407306194,
-0.01434094738215208,
-0.0002657111035659909,
0.01585015468299389,
-0.0009981227340176702,
-0.03680938482284546,
0.009988152422010899,
0.027040425688028336,
0.07760107517242432,
-0.03645455464720726,
-0.0015028401976451278,
-0.0021223563235253096,
-0.03035900928080082,
0.007683916017413139,
0.0025108454283326864,
0.04249677062034607,
0.03958122059702873,
-0.0782490149140358,
-0.013346982188522816,
-0.009046145714819431,
-0.04365251213312149,
0.0046763368882238865,
-0.047110654413700104,
0.02492804452776909,
0.02321678213775158,
-0.02331741340458393,
-0.05493823066353798,
-0.03527551144361496,
-0.0170231182128191,
0.022344844415783882,
-0.011925144121050835,
-0.0027017993852496147,
0.022166332229971886,
-0.025395242497324944,
-0.012643937021493912,
0.00286218267865479,
0.02357802353799343,
-0.018639391288161278,
-0.012648342177271843,
0.025092974305152893,
-0.011686759069561958,
0.020804477855563164,
0.00787153746932745,
-0.02859911136329174,
-0.014828061684966087,
-0.02757662907242775,
-0.030947556719183922,
-0.01733643002808094,
0.05419921875,
-0.015503632836043835,
-0.0418953076004982,
-0.007074684835970402,
0.017526401206851006,
0.04034430533647537,
-0.00938994251191616,
0.007795942015945911,
0.00021798968373332173,
0.037299904972314835,
-0.026000460609793663,
-0.03482901677489281,
0.046515412628650665,
0.016296230256557465,
0.012999708764255047,
-0.007593946997076273,
-0.010198486037552357,
-0.04150707274675369,
-0.03822565823793411,
0.0213969424366951,
-0.0013065636157989502,
0.027925636619329453,
0.01905176043510437,
0.09128416329622269,
-0.03782229125499725,
-0.02025209739804268,
0.005012643523514271,
-0.022437959909439087,
0.00408761203289032,
-0.03973788395524025,
-0.015677791088819504,
0.010635306127369404,
0.0008059265092015266,
0.006394652184098959,
-0.01701769419014454,
-0.02263684757053852,
-0.0015497877029702067,
0.04886985570192337,
-0.026876363903284073,
0.06405329704284668,
0.03082014061510563,
0.0007256559329107404,
-0.0062863873317837715,
-0.020707067102193832,
-0.022891297936439514,
-0.014035067521035671,
-0.028316661715507507,
0.05576096847653389,
-0.03324107080698013,
0.015608157031238079,
8.442984267276188e-7,
0.03638796508312225,
0.010686586610972881,
0.02428746037185192,
0.04956572502851486,
0.02661864273250103,
-0.016733655706048012,
0.009385176934301853,
-0.015351914800703526,
0.017883051186800003,
-0.01536643598228693,
0.02589571103453636,
0.02150706760585308,
-0.02135283313691616,
0.05024649202823639,
0.017112456262111664,
0.01403307355940342,
-0.04617360234260559,
-0.0303216390311718,
-0.01685747131705284,
0.013195576146245003,
0.0050399755127727985,
0.07105548679828644,
-0.01293278019875288,
0.023873256519436836,
0.009058861993253231,
0.0035930040758103132,
0.023275909945368767,
-0.004848250653594732,
-0.07720383256673813,
-0.06533490121364594,
-0.036015477031469345,
-0.05130600556731224,
0.07189333438873291,
-0.009220205247402191,
-0.03404271975159645,
0.002989443950355053,
-0.04931095242500305,
0.015574195422232151,
0.01597060076892376,
0.032100461423397064,
0.004503499250859022,
0.03414205461740494,
0.009197243489325047,
0.045468322932720184,
0.029234351590275764,
0.016756247729063034,
0.10168686509132385,
0.027146195992827415,
0.006937813013792038,
-0.06107913702726364,
0.014714506454765797,
-0.035258471965789795,
0.016440413892269135,
-0.039594829082489014,
0.01789303869009018,
-0.03159244358539581,
0.07130783051252365,
0.015063286758959293,
0.03956582769751549,
0.028701385483145714,
-0.01900717057287693,
0.015128204599022865,
-0.04121825844049454,
-0.016337048262357712,
-0.008786298334598541,
0.012850230559706688,
0.001955049578100443,
0.0586753748357296,
-0.04960602521896362,
-0.007989476434886456,
-0.017091771587729454,
0.0008433331386186182,
0.0009735472849570215,
-0.03204929828643799,
0.009434616193175316,
0.002859619213268161,
-0.015520289540290833,
0.022933389991521835,
0.03582397475838661,
-0.030638569965958595,
-0.036386750638484955,
0.01722513884305954,
0.08205393701791763,
-0.010593301616609097,
0.05000091716647148,
-0.0013535880716517568,
0.03356663137674332,
0.012763503938913345,
0.014216537587344646,
0.04935421422123909,
-0.027373580262064934,
-0.01929595321416855,
-0.012888023629784584,
0.044603463262319565,
-0.023858537897467613,
-0.003401894122362137,
0.0075593627989292145,
0.02047889679670334,
-0.006253348197788,
-0.052024297416210175,
0.005892794579267502,
0.031030496582388878,
0.02672049030661583,
-0.012275275774300098,
-0.06152245029807091,
-0.03009229712188244,
0.039695341140031815,
-0.028624100610613823,
0.01579463854432106,
0.030550582334399223,
-0.02301963046193123,
0.004755743779242039,
-0.007934152148663998,
0.028045304119586945,
0.03516860678792,
-0.0027189054526388645,
-0.012068180367350578,
-0.0017240321030840278,
-0.001283237710595131,
-0.03742610663175583,
0.0075784833170473576,
0.03524534031748772,
0.015345832332968712,
-0.03765439987182617,
-0.017542438581585884,
-0.0055763497948646545,
-0.038991715759038925,
-0.004118695389479399,
-0.00953722931444645,
-0.015701282769441605,
-0.034418415278196335,
-0.003062100615352392,
0.0321488156914711,
0.02594856545329094,
0.022443193942308426,
-0.01873805932700634,
0.00042018102249130607,
-0.01971626654267311,
0.04656585678458214,
-0.022797510027885437,
-0.011593201197683811,
0.03875957429409027,
-0.04292773827910423,
-0.02746749110519886,
0.00449864286929369,
0.024176131933927536,
0.025749193504452705,
0.0009731361060403287,
0.021783921867609024,
0.015507814474403858,
-0.023929964751005173,
-0.013999301940202713,
0.002950865775346756,
-0.020298728719353676,
0.03008643537759781,
0.007089458405971527,
-0.03365939110517502,
0.0028117112815380096,
-0.06057189032435417,
0.001733701559714973,
-0.03194349259138107,
0.008739471435546875,
0.0338955819606781,
0.011098508723080158,
-0.028123511001467705,
-0.043183259665966034,
0.033359892666339874,
-0.009997670538723469,
-0.01608634553849697,
-0.04030376300215721,
0.011693664826452732,
0.0016096027102321386,
-0.03250537067651749,
-0.02505376562476158,
0.04782361537218094,
-0.011316287331283092,
-0.022413507103919983,
0.022874830290675163,
0.042156342417001724,
0.010327373631298542,
-0.00015697858179919422,
0.013728762045502663,
0.00018760385864879936,
0.04839446023106575,
0.0014617964625358582,
-0.025711599737405777,
0.05218332260847092,
-0.02897128276526928,
-0.03364754468202591,
0.05084851011633873,
-0.017887508496642113,
0.05622132122516632,
-0.00581509992480278,
0.002834886545315385,
-0.006361769046634436,
0.07711667567491531,
-0.021311508491635323,
-0.038811586797237396,
0.01828630454838276,
-0.02708490379154682,
0.03432658314704895,
-0.01780829206109047,
0.04328742250800133,
-0.010887395590543747,
-0.004468398634344339,
0.06767074018716812,
-0.006012832745909691,
0.006485924124717712,
-0.0028751424979418516,
0.002086816355586052,
0.009211867116391659,
-0.003942920360714197,
0.06494740396738052,
0.005272343289107084,
0.019845057278871536,
0.014981446787714958,
-0.018807776272296906,
0.07601567357778549,
0.013312814757227898,
-0.028057120740413666,
-0.066065713763237,
0.02762657217681408,
0.019727151840925217,
0.017414065077900887,
0.0260639525949955,
-0.0482972115278244,
0.019095737487077713,
0.033766813576221466,
-0.0848899632692337,
0.009893003851175308,
-0.0372362844645977,
-0.031897369772195816,
-0.03749414533376694,
0.013188352808356285,
-0.009784874506294727,
0.03589103743433952,
0.05270995944738388,
0.04651429504156113,
0.030898457393050194,
0.029270583763718605,
-0.014707178808748722,
-0.0006125654326751828,
-0.03180095925927162,
0.046051960438489914,
-0.012194618582725525,
0.012201654724776745,
0.03703266754746437,
0.0016587363788858056,
-0.008317532017827034,
-0.015488406643271446,
-0.0071917870081961155,
0.004125910345464945,
-0.003128086682409048,
-0.00836100708693266,
0.007929476909339428,
-0.01713654398918152,
-0.017341239377856255,
-0.01280107069760561,
-0.027032870799303055,
0.015061178244650364,
0.05387607216835022,
0.011229123920202255,
-0.006076466757804155,
-0.013949747197329998,
0.02256273664534092,
-0.09368135035037994,
-0.037588972598314285,
0.013273726217448711,
0.008402804844081402,
-0.012186216190457344,
0.018748104572296143,
0.06758478283882141,
0.031892262399196625,
-0.045762643218040466,
-0.0023504632990807295,
-0.05207524821162224,
0.005427541211247444,
-0.01596234180033207,
0.02603355050086975,
0.03920965641736984,
0.009869023226201534,
-0.019569598138332367,
-0.022276723757386208,
-0.0009511102107353508,
-0.005719492211937904,
0.004216871690005064,
-0.018986832350492477,
-0.01032988354563713,
0.03554868325591087,
-0.010850033722817898,
-0.0070698438212275505,
0.004118012730032206,
-0.03939690813422203,
-0.009423836134374142,
0.020360631868243217,
-0.014242465607821941,
-0.013618561439216137,
-0.04473439231514931,
-0.05274057760834694,
-0.04021325707435608,
0.03574768826365471,
0.005837147124111652,
-0.026545662432909012,
-0.05936345085501671,
-0.007138851098716259,
-0.04835278168320656,
0.0716136023402214,
0.039425212889909744,
-0.006115194410085678,
-0.026700004935264587,
-0.0018468911293894053,
-0.0005286468658596277,
0.04323011636734009,
-0.014042763039469719,
0.03332791477441788,
-0.014525527134537697,
-0.014097344130277634,
-0.01965855248272419,
-0.0012955169659107924,
0.012876370921730995,
0.027695436030626297,
0.0023169631604105234,
-0.02696378156542778,
0.002372928662225604,
-0.026150956749916077,
-0.04694758355617523,
0.08449999243021011,
0.006407649721950293,
-0.009537558071315289,
0.0641288235783577,
-0.017367396503686905,
-0.008793813176453114,
0.022819919511675835,
-0.010479392483830452,
-0.04396228492259979,
0.04122236371040344,
-0.009649439714848995,
-0.027248216792941093,
0.015050672926008701,
0.0021434102673083544,
0.029938802123069763,
-0.04484492167830467,
0.04892420023679733,
0.043707072734832764,
-0.013388696126639843,
-0.03298744559288025,
0.06484327465295792,
0.002545673167333007,
0.047626085579395294,
-0.0045963069424033165,
-0.002246946794912219,
0.009915300644934177,
-0.03953754901885986,
0.007111750543117523,
0.05529957637190819,
-0.005764904897660017,
0.014705788344144821,
0.03145068138837814,
0.03862034156918526,
0.018402136862277985,
0.006229913327842951,
0.016792919486761093,
0.06743012368679047,
-0.020971087738871574,
0.025504205375909805,
0.007855437695980072,
0.008983377367258072,
0.0023753708228468895,
0.04056297242641449,
-0.0322096161544323,
0.08519860357046127,
-0.04501957446336746,
0.010288723744452,
-0.037829384207725525,
0.01883741095662117,
-0.028671015053987503,
0.009542967192828655,
0.038605134934186935,
0.040021561086177826,
-0.014311281964182854,
0.008159820921719074,
-0.02352994494140148,
-0.003158321138471365,
0.03722422197461128,
-0.0419154018163681,
0.0392334870994091,
-0.03380466625094414,
-0.03974653780460358,
-0.007538612931966782,
-0.00968711357563734,
-0.007788277696818113,
0.003579503856599331,
0.018705280497670174,
0.026665644720196724,
0.03709259256720543,
0.014249462634325027,
-0.004812975414097309,
-0.03922002390027046,
0.0519096814095974,
-0.07518870383501053,
-0.019999364390969276,
-0.013109647668898106,
0.032661307603120804,
-0.023778393864631653,
-0.02187635749578476
] |
<p>It has been claimed (e.g. <a href="http://physics.stackexchange.com/a/36178/10552">here</a>) and apparently already been established, that the interval $x - y$ being (called) "spacelike" implies that $\bigl[\hat O (x),\, \hat O' (y)\bigr]=0$ for any two (not necessarily distinct) operators $\hat O$ and $\hat O'$ corresponding to physical observables evaluated at $x$ or at $y$, respectively: </p>
<p>$$\text{spacelike}( \, x - y \, ) \quad\implies\quad \Bigl( \forall \hat O \, \forall \hat O': \Bigl[\hat O (x),\, \hat O' (y)\Bigr] = 0 \Bigr). $$</p>
<p>Is the converse correct, too, that the vanishing commutators imply (or are sufficient for) the interval $x - y$ to be (called) "spacelike":</p>
<p>$$\Bigl(\forall \hat O \, \forall \hat O': \Big[\hat O (x),\, \hat O' (y)\Bigr] = 0 \Bigr) \quad\implies\quad \text{spacelike}( \, x - y \, ) \, ?$$</p>
| 10,824 |
[
-0.009276804514229298,
-0.02693312056362629,
0.044194381684064865,
-0.02960127219557762,
0.003919726237654686,
0.025417324155569077,
-0.031390514224767685,
-0.06514953076839447,
0.007456204388290644,
-0.013821654953062534,
0.005975660402327776,
-0.0021906867623329163,
0.08964439481496811,
0.059246912598609924,
0.010917670093476772,
-0.002832979429513216,
-0.0447024405002594,
0.025637155398726463,
-0.03154266998171806,
-0.00649550324305892,
0.003448974806815386,
0.040938008576631546,
0.010771107859909534,
0.0031260938849300146,
-0.008243316784501076,
0.011155940592288971,
-0.012082649394869804,
-0.0032000127248466015,
-0.0007900125929154456,
0.059830114245414734,
-0.047636955976486206,
0.00041219781269319355,
-0.0017347196117043495,
0.01774575188755989,
-0.003188662463799119,
0.020076708868145943,
0.03155042231082916,
-0.013832129538059235,
0.03261249512434006,
-0.01195328775793314,
-0.023340614512562752,
-0.02371712401509285,
0.005986564327031374,
0.055955853313207626,
0.022426370531320572,
0.01731462962925434,
-0.004211030434817076,
-0.004937599878758192,
0.0697193518280983,
-0.02930201031267643,
0.07475333660840988,
0.0006267811986617744,
-0.007236995734274387,
0.018400317057967186,
-0.01663057878613472,
0.004857031162828207,
0.07158762961626053,
0.04286353662610054,
0.03215835615992546,
-0.055212777107954025,
-0.0403483584523201,
-0.006438424810767174,
0.008891923353075981,
0.0028652602341026068,
0.014787867665290833,
0.018686359748244286,
0.010704156942665577,
-0.007311811204999685,
-0.005708266049623489,
-0.04113432765007019,
0.023828895762562752,
0.046118345111608505,
0.018406210467219353,
-0.039411529898643494,
0.024224281311035156,
0.008305995725095272,
0.018048200756311417,
0.02050076611340046,
0.032097939401865005,
0.027770616114139557,
-0.0003088182129431516,
0.025967974215745926,
0.021683624014258385,
-0.021830357611179352,
0.03231555595993996,
0.016306564211845398,
0.03613155707716942,
-0.014225075021386147,
0.002403992461040616,
0.021534861996769905,
0.024097520858049393,
0.009733662940561771,
0.048992980271577835,
0.001182066393084824,
-0.03900791332125664,
0.07665542513132095,
0.0030600172467529774,
0.03001200407743454,
-0.01850290596485138,
-0.04292626306414604,
-0.02612403593957424,
-0.0334358736872673,
0.018608104437589645,
0.057164162397384644,
0.01757574826478958,
0.0013571134768426418,
-0.03981897234916687,
0.018821075558662415,
-0.04851381108164787,
-0.02819376438856125,
-0.04555749520659447,
0.015777233988046646,
-0.00971430167555809,
0.03152843564748764,
0.0232704970985651,
-0.03521309047937393,
0.029555361717939377,
0.022551055997610092,
-0.00416520843282342,
0.07810165733098984,
0.0840650126338005,
0.011949187144637108,
0.002658351557329297,
-0.028002971783280373,
-0.08438671380281448,
-0.0018015240784734488,
0.03276994824409485,
0.007722655776888132,
-0.03539849817752838,
0.015361541882157326,
0.019415395334362984,
0.007569082546979189,
0.02628210186958313,
0.015565571375191212,
0.028904138132929802,
-0.009191704913973808,
-0.07215770334005356,
-0.057595353573560715,
0.01795169711112976,
0.01748458668589592,
0.00966025609523058,
-0.05025763064622879,
-0.019827455282211304,
0.01663144677877426,
0.05490599572658539,
-0.002242056652903557,
-0.002161739394068718,
0.00661176024004817,
0.01118890754878521,
-0.012954541482031345,
-0.030614614486694336,
-0.05099749565124512,
0.017761439085006714,
-0.06567467749118805,
-0.020102068781852722,
-0.04558085650205612,
0.025253303349018097,
0.03900892660021782,
0.014167648740112782,
-0.011809449642896652,
0.07793145626783371,
-0.023021871224045753,
-0.004651748575270176,
-0.027842823415994644,
0.019000548869371414,
-0.0343593992292881,
0.07511493563652039,
0.025734419003129005,
0.0344231054186821,
0.028932619839906693,
0.04357043653726578,
0.014127553440630436,
0.005160079803317785,
0.06011752784252167,
0.025804897770285606,
-0.050597112625837326,
-0.039883751422166824,
-0.038291461765766144,
-0.0009169436525553465,
-0.025405680760741234,
-0.07640155404806137,
-0.007685385644435883,
-0.0525188148021698,
-0.009209936484694481,
-0.018968630582094193,
0.03491624817252159,
-0.02161741629242897,
0.010381626896560192,
0.055954087525606155,
-0.054546602070331573,
-0.026409586891531944,
-0.0863269492983818,
-0.021233592182397842,
0.004378630314022303,
-0.06259132921695709,
0.04044991731643677,
0.0008782569202594459,
-0.00028102495707571507,
-0.029413647949695587,
-0.025905558839440346,
0.016088761389255524,
0.038645435124635696,
0.04956711083650589,
-0.002178420312702656,
0.007096153683960438,
0.049991052597761154,
0.05402269959449768,
0.007344868499785662,
0.03620569407939911,
-0.018226152285933495,
-0.06949980556964874,
0.017920169979333878,
-0.011689336970448494,
0.0216661486774683,
0.018872950226068497,
-0.006616903934627771,
0.034158360213041306,
-0.004169601947069168,
-0.025054804980754852,
0.017953353002667427,
-0.036162443459033966,
0.008379778824746609,
0.045898713171482086,
-0.00720483623445034,
-0.005249917507171631,
0.040208783000707626,
0.00007527117122663185,
0.00032019722857512534,
0.018793372437357903,
-0.055574338883161545,
-0.0064798686653375626,
-0.009099692106246948,
0.041125163435935974,
0.052307672798633575,
-0.026382556185126305,
0.06159399077296257,
-0.006518967915326357,
0.07694308459758759,
0.0151954535394907,
0.04969125986099243,
-0.008564243093132973,
-0.028930678963661194,
-0.0028549821581691504,
-0.008736022748053074,
0.0405188649892807,
0.011085505597293377,
-0.005935927852988243,
0.023910386487841606,
0.015404720790684223,
0.003872410161420703,
-0.016892770305275917,
-0.007243304047733545,
0.00950506143271923,
0.0012982244370505214,
0.02139495685696602,
-0.017007214948534966,
-0.004089992493391037,
0.02178468555212021,
0.0074198986403644085,
0.006974885705858469,
-0.012400113046169281,
-0.02076086401939392,
-0.05011734738945961,
-0.0003419479471631348,
0.0342605896294117,
0.012998804450035095,
-0.021384410560131073,
-0.018084336072206497,
0.01492280326783657,
-0.02635921910405159,
-0.020592913031578064,
-0.032518599182367325,
-0.05595795437693596,
-0.004883533343672752,
-0.009421423077583313,
0.06789393723011017,
0.0370032973587513,
0.03909710422158241,
-0.033082764595746994,
0.01366016361862421,
-0.03394157066941261,
0.02212715893983841,
0.025054585188627243,
0.02752968855202198,
-0.0020347735844552517,
0.0221951175481081,
-0.0399589017033577,
-0.03426514193415642,
0.041282691061496735,
-0.03432876244187355,
0.014062763191759586,
-0.007875818759202957,
0.0030784092377871275,
-0.03696024417877197,
-0.017086027190089226,
-0.03694934770464897,
-0.009715139865875244,
-0.013209461234509945,
-0.008815065026283264,
0.03976749628782272,
-0.014873957261443138,
-0.049744606018066406,
0.008476958610117435,
-0.0063375565223395824,
-0.07215985655784607,
-0.010442542843520641,
-0.013035248033702374,
0.02348274365067482,
-0.018903225660324097,
0.004141991958022118,
0.04908393695950508,
-0.013577119447290897,
-0.006547647528350353,
-0.049248263239860535,
-0.06678056716918945,
0.004028614144772291,
0.000788944773375988,
0.021719787269830704,
0.007986404001712799,
-0.0021795874927192926,
0.0694025382399559,
0.004619441460818052,
-0.025434762239456177,
-0.020681381225585938,
0.017813049256801605,
0.001805266598239541,
0.043903350830078125,
-0.00639471085742116,
-0.007379407528787851,
0.020826619118452072,
0.0542016327381134,
0.01750633679330349,
0.025421837344765663,
0.019576512277126312,
0.03156135231256485,
0.023226581513881683,
-0.010156647302210331,
-0.025914419442415237,
0.015671316534280777,
0.021046942099928856,
0.011096419766545296,
-0.02742701768875122,
-0.016864366829395294,
-0.010705769993364811,
-0.027382109314203262,
0.019366411492228508,
-0.05836024507880211,
0.014123300090432167,
-0.002667935797944665,
0.011747758835554123,
0.042489100247621536,
0.039284758269786835,
0.0013864345382899046,
-0.04100429639220238,
-0.05269567295908928,
0.004107232205569744,
0.017990024760365486,
-0.023020396009087563,
-0.005981804337352514,
0.059204794466495514,
0.04088909551501274,
-0.036536019295454025,
-0.012172967195510864,
0.01949307508766651,
-0.043194547295570374,
0.01990540511906147,
-0.040277622640132904,
-0.01977948658168316,
0.06366812437772751,
0.02752990648150444,
-0.005074913147836924,
-0.002359769307076931,
-0.0322197824716568,
-0.005736395251005888,
-0.050122447311878204,
0.03467587009072304,
-0.020285503938794136,
0.013049321249127388,
0.010531353764235973,
0.049044523388147354,
0.029500368982553482,
0.0008450457826256752,
-0.006463603116571903,
0.01156123448163271,
-0.05895703658461571,
0.005419289693236351,
-0.030954904854297638,
-0.014526817947626114,
-0.0027983016334474087,
0.01361910905689001,
0.024537721648812294,
0.04184124991297722,
0.02405637316405773,
-0.03358706459403038,
-0.020333442836999893,
-0.05843821167945862,
0.0293145552277565,
-0.03221816197037697,
-0.07845491170883179,
-0.038538794964551926,
-0.007911027409136295,
0.04757519066333771,
0.004192321095615625,
0.035258859395980835,
-0.005715155508369207,
-0.05685756728053093,
0.010560370050370693,
-0.026811636984348297,
0.03490716591477394,
0.020392317324876785,
-0.015411457046866417,
0.0058311219327151775,
0.026289381086826324,
0.016556188464164734,
0.0072875600308179855,
-0.012685419991612434,
0.07165025919675827,
-0.02363671362400055,
-0.055232204496860504,
-0.029821202158927917,
-0.03624613955616951,
-0.03475361689925194,
0.030474629253149033,
0.07150966674089432,
0.02405935525894165,
0.023008087649941444,
0.02840612642467022,
0.028993656858801842,
0.015201989561319351,
0.04501720890402794,
0.059327129274606705,
0.017012929543852806,
-0.015811167657375336,
-0.032684747129678726,
-0.007205104921013117,
-0.018748991191387177,
-0.0032986770384013653,
0.04406969994306564,
0.0004563489055726677,
-0.011190490797162056,
-0.014865167438983917,
0.019714808091521263,
0.0737718790769577,
-0.013923938386142254,
0.021420883014798164,
0.01324383169412613,
-0.018197298049926758,
-0.026924172416329384,
0.01014536339789629,
0.03274178504943848,
0.03336285427212715,
0.04348079115152359,
0.02780609205365181,
0.009124323725700378,
-0.045747969299554825,
-0.016272688284516335,
0.035439252853393555,
0.0470220148563385,
0.002749713370576501,
0.015157308429479599,
-0.045797236263751984,
-0.010633655823767185,
0.04162970930337906,
-0.016771383583545685,
0.026323124766349792,
-0.06559774279594421,
-0.004583447705954313,
-0.011363059282302856,
-0.009443297050893307,
-0.02178271673619747,
0.02083854004740715,
0.009937717579305172,
-0.003698192071169615,
0.0010363771580159664,
-0.014360851608216763,
-0.021603872999548912,
0.011539191007614136,
-0.013977744616568089,
0.023005573078989983,
0.03772281855344772,
-0.01802048459649086,
-0.010186856612563133,
0.026371728628873825,
-0.011253820732235909,
-0.06311435997486115,
-0.0026532968040555716,
0.03493183106184006,
-0.020844340324401855,
0.07152830064296722,
-0.0076406123116612434,
-0.06576800346374512,
0.01925821229815483,
0.006511380895972252,
0.020140595734119415,
0.03663080558180809,
-0.03139300271868706,
0.0627528503537178,
0.020982826128602028,
0.02028871700167656,
0.0033055762760341167,
0.0014403545064851642,
-0.02216256968677044,
-0.046074751764535904,
0.001551404013298452,
0.01334315910935402,
-0.028777122497558594,
0.03265488147735596,
-0.017643706873059273,
-0.013570219278335571,
-0.023612335324287415,
0.016867633908987045,
-0.03467567637562752,
-0.009221931919455528,
0.004447333049029112,
-0.02665352076292038,
-0.006281943526118994,
0.03482991084456444,
0.0059197572991251945,
-0.017604393884539604,
-0.009443381801247597,
0.044777192175388336,
0.03316498175263405,
-0.006341966800391674,
-0.00007259392441483214,
-0.0042235637083649635,
0.01734691858291626,
0.05948095768690109,
0.0014803169760853052,
0.04279718175530434,
-0.0262946505099535,
0.05027735233306885,
-0.025067150592803955,
-0.03413565456867218,
0.007792625110596418,
-0.03072608821094036,
-0.030372148379683495,
0.021272581070661545,
0.006025980226695538,
-0.05743222311139107,
0.0074503798969089985,
0.010081843473017216,
0.0136851342394948,
-0.0790029838681221,
-0.002462607342749834,
0.04646110162138939,
0.01019752211868763,
-0.08694534003734589,
-0.04817633703351021,
0.013594342395663261,
0.024421537294983864,
-0.017566267400979996,
-0.004944236483424902,
0.016006911173462868,
-0.01793503202497959,
-0.011692964471876621,
-0.006438387557864189,
0.016360485926270485,
-0.06440427154302597,
-0.02235412411391735,
-0.016688812524080276,
0.015266716480255127,
0.030263084918260574,
-0.013205241411924362,
-0.011507296934723854,
0.03167404606938362,
0.001569807413034141,
0.023392025381326675,
0.025303881615400314,
0.05867616459727287,
-0.028879204764962196,
-0.03273322060704231,
-0.022274985909461975,
0.003738256637006998,
0.0017233066027984023,
0.005930630024522543,
-0.04862629622220993,
0.022605760022997856,
0.006937710102647543,
0.020930303260684013,
-0.0015274391043931246,
0.028298942372202873,
-0.023120634257793427,
0.011181673966348171,
0.03274166211485863,
-0.037707164883613586,
-0.027968743816018105,
-0.02002970688045025,
0.0002760032657533884,
-0.006106877699494362,
-0.026594268158078194,
0.006515588145703077,
0.07000455260276794,
0.02522837556898594,
0.006173693109303713,
0.024469027295708656,
-0.008430424146354198,
0.0150143438950181,
-0.0038315702695399523,
-0.006013844627887011,
-0.0012363189598545432,
-0.006087166257202625,
-0.020166045054793358,
-0.011339661665260792,
-0.05368789657950401,
0.046052366495132446,
0.057320691645145416,
-0.0033480538986623287,
0.03929547965526581,
0.02597087062895298,
-0.02157372236251831,
-0.013261580839753151,
-0.004328757990151644,
0.007004397921264172,
-0.025374893099069595,
-0.017257245257496834,
0.010663112625479698,
-0.02593895047903061,
0.020345209166407585,
0.016208838671445847,
0.03745047003030777,
-0.03152860701084137,
-0.007942302152514458,
0.02314791828393936,
0.010993474163115025,
-0.005762261338531971,
-0.04961671680212021,
-0.037349965423345566,
0.042019110172986984,
-0.0602547861635685,
0.02822255715727806,
0.033931925892829895,
-0.02340574562549591,
-0.015022111125290394,
0.017531095072627068,
-0.018376832827925682,
-0.017094356939196587,
-0.04353642463684082,
-0.05204983055591583,
0.020859375596046448,
0.019828597083687782,
0.039674531668424606,
-0.028757503256201744,
-0.015046244487166405,
0.036759115755558014,
0.003854079870507121,
0.013393186032772064,
-0.009818680584430695,
-0.03330378979444504,
0.018948089331388474,
-0.05203643813729286,
-0.03266992047429085,
0.041123803704977036,
0.0024703997187316418,
-0.00793931819498539,
-0.019687024876475334,
-0.05470066890120506,
0.03255205973982811,
0.06227852776646614,
0.04491414502263069,
-0.0320909209549427,
0.03843700885772705,
-0.011611118912696838,
-0.027037687599658966,
-0.032581981271505356,
0.007604584563523531,
0.12953263521194458,
0.055310800671577454,
0.029363509267568588,
-0.0321764275431633,
0.008738316595554352,
0.00883032102137804,
-0.00957685336470604,
-0.03586709871888161,
0.014307158999145031,
-0.02090522088110447,
-0.008793435990810394,
-0.0032166040036827326,
0.04219687730073929,
0.03004216030240059,
-0.006332610733807087,
0.025631481781601906,
-0.04464586451649666,
-0.006910212337970734,
-0.014319435693323612,
0.027248194441199303,
0.01563056744635105,
-0.010911114513874054,
-0.06672684103250504,
-0.007022487930953503,
-0.005577942356467247,
0.031154576689004898,
-0.009459994733333588,
-0.016176193952560425,
0.007262584287673235,
0.010044346563518047,
-0.03734498471021652,
0.01616426557302475,
0.002335015684366226,
0.009510627947747707,
-0.04879413917660713,
-0.03096633031964302,
0.02628188207745552,
-0.013333708047866821,
0.030784297734498978,
0.024080472066998482,
0.012000879272818565,
-0.01751219481229782,
-0.000250129058258608,
0.014815143309533596,
-0.033159784972667694,
-0.008165651932358742,
-0.011313306167721748,
0.061572249978780746,
0.00997532531619072,
0.03059169463813305,
0.004997048061341047,
-0.03881652653217316,
-0.02780345268547535,
-0.05961046367883682,
-0.018513446673750877,
-0.02088843286037445,
0.02511914074420929,
0.010107625275850296,
0.011212006211280823,
0.024290041998028755,
-0.018888821825385094,
0.0027809329330921173,
0.002321631647646427,
-0.02396535687148571,
0.0161972027271986,
-0.012541698291897774,
0.01842576079070568,
0.03819354996085167,
0.018248803913593292,
0.012545449659228325,
-0.0016483458457514644,
-0.0521017424762249,
-0.04484904557466507,
0.006700970698148012,
0.013718770816922188,
-0.00670468807220459,
0.049018051475286484,
-0.003888692008331418,
-0.015617115423083305,
-0.00924643687903881,
-0.05855404958128929,
-0.021803341805934906,
-0.018745694309473038,
-0.03653160482645035,
-0.013884847983717918,
0.02506609633564949,
-0.0026657991111278534,
0.0196220763027668,
0.00469224713742733,
0.004843359347432852,
-0.012743073515594006,
0.05499027296900749,
-0.006938419304788113,
-0.005143832881003618,
-0.056143760681152344,
-0.008108820766210556,
-0.018152181059122086,
0.020943427458405495,
0.006419076584279537,
0.0043149846605956554,
0.019338537007570267,
0.0209093876183033,
0.00036535452818498015,
0.057646095752716064,
-0.010695993900299072,
-0.007080188021063805,
0.019624345004558563,
0.00033784948755055666,
0.011730520986020565,
0.0329199954867363,
0.008111748844385147,
-0.06654302775859833,
-0.047259408980607986,
-0.03516032546758652,
0.01904323138296604,
0.0007453840808011591,
0.021015288308262825,
-0.0367482453584671,
-0.01960807666182518,
0.03460380434989929,
0.023213230073451996,
-0.01400262862443924,
0.009702827781438828,
-0.0476028174161911,
0.03228102996945381,
-0.0047033256851136684,
0.013097455725073814,
0.020970869809389114,
0.06222245842218399,
-0.05967400223016739,
-0.037259478121995926,
0.0030338303185999393,
0.02858482301235199,
-0.0288553349673748,
-0.0072524212300777435,
0.010370601899921894,
0.0248495414853096,
-0.0023066173307597637,
-0.006847302429378033,
-0.04609765112400055,
0.007811715826392174,
-0.047530241310596466,
-0.04378308728337288,
0.033644355833530426,
-0.0004849298857152462,
0.03361906856298447,
0.042274538427591324,
-0.005401222035288811,
-0.0126657048240304,
0.0392654612660408,
-0.039903007447719574,
-0.0008818492060527205,
0.024767395108938217,
-0.033897764980793,
-0.03823485225439072,
0.045019835233688354,
0.018085423856973648,
0.010260109789669514,
0.0005365255055949092,
-0.0010733588133007288,
0.02627902664244175,
-0.011014369316399097,
-0.013762806542217731,
0.008600366301834583,
-0.010096720419824123,
0.010373538359999657,
0.008714740164577961,
-0.02862510085105896,
0.036357346922159195,
0.028233401477336884,
-0.07445571571588516,
0.013601535931229591,
0.021633826196193695,
0.01641438528895378,
-0.10026676207780838,
-0.016887739300727844,
0.02161162719130516,
0.06305556744337082,
0.03981022536754608,
-0.04518544301390648,
0.014834384433925152,
0.017966413870453835,
-0.0628313273191452,
0.05356764420866966,
-0.03707890585064888,
0.0019540940411388874,
-0.03341948240995407,
0.001152616343460977,
-0.06010616198182106,
0.029457928612828255,
0.03317031264305115,
0.017196282744407654,
-0.008606483228504658,
0.057402294129133224,
-0.029875779524445534,
-0.03372815623879433,
-0.034560173749923706,
-0.004107457119971514,
-0.018683474510908127,
-0.045699264854192734,
0.06609901785850525,
0.02346222847700119,
-0.003013734007254243,
0.058729033917188644,
-0.003343197051435709,
-0.02266767807304859,
-0.027675878256559372,
0.04898018389940262,
0.026254212483763695,
-0.010879328474402428,
0.039176613092422485,
-0.009144886396825314,
-0.04020945727825165,
-0.012788031250238419,
0.00028070269036106765,
0.04426146671175957,
-0.007707986980676651,
-0.046903982758522034,
-0.002757305046543479,
-0.07961760461330414,
-0.04558764025568962,
0.026213031262159348,
-0.0019416011637076735,
0.001854347879998386,
0.0056385681964457035,
0.010738443583250046,
-0.003069837111979723,
0.002097387332469225,
0.049102816730737686,
-0.040086135268211365,
-0.02212396264076233,
0.003687899559736252,
-0.007930687628686428,
-0.009838555008172989,
0.014659443870186806,
-0.046510521322488785,
-0.026737840846180916,
0.021631762385368347,
0.001742847729474306,
0.007042439188808203,
-0.06778207421302795,
-0.017638808116316795,
0.009079774841666222,
0.011884821578860283,
0.005497089121490717,
-0.056679949164390564,
-0.04958127439022064,
0.027398420497775078,
-0.01322583295404911,
0.012802605517208576,
-0.002700556768104434,
0.015138235874474049,
-0.04299261420965195,
-0.08242872357368469,
0.01941055804491043,
0.010743861086666584,
0.017647691071033478,
-0.052499521523714066,
-0.005461008287966251,
-0.019334424287080765,
0.026785191148519516,
0.019748546183109283,
0.02476295828819275,
-0.05677270516753197,
0.014231574721634388,
0.001749444636516273,
-0.007841929793357849,
-0.04421383887529373,
0.006143240723758936,
0.01947321556508541,
-0.0009773909114301205,
0.018468201160430908,
-0.03869561478495598,
-0.026287775486707687,
-0.009466148912906647,
0.06425748765468597,
0.005690700840204954,
0.025781624019145966,
0.03051711805164814,
-0.07893930375576019,
0.0009182014036923647,
0.021741818636655807,
-0.0005676043801940978,
0.058667637407779694,
0.009187980554997921,
0.006525915116071701,
-0.0013740549329668283,
-0.020633991807699203,
-0.0536576583981514,
0.03227681666612625,
-0.0017123650759458542,
-0.0316719226539135,
0.00529067637398839,
0.012193539179861546,
-0.0004884458030574024,
-0.021077675744891167,
-0.021191412582993507,
0.06346660852432251,
-0.002330679912120104,
-0.019564416259527206,
0.07234236598014832,
0.028514226898550987,
0.00919263157993555,
0.03069150634109974,
-0.025144826620817184,
0.037830401211977005,
-0.032572224736213684,
0.036960043013095856,
0.02250077947974205,
0.02148864045739174,
0.03925241157412529,
-0.012374899350106716,
0.007997199892997742,
-0.009999207220971584,
0.06407453864812851,
0.05467062070965767,
0.007888615131378174,
-0.021259408444166183,
0.008341142907738686,
0.02447444200515747,
-0.00477411225438118,
-0.010880532674491405,
0.019106630235910416,
-0.002813642844557762,
0.05584986135363579,
-0.004124785773456097,
-0.009470813907682896,
-0.039649903774261475,
-0.011153815314173698,
-0.005531725008040667,
-0.01559683308005333,
0.022798975929617882,
0.02007332816720009,
-0.04069984331727028,
0.005584651604294777,
-0.0328759104013443,
-0.04079102352261543,
0.011507408693432808,
-0.05137748271226883,
-0.008244408294558525,
-0.0020785422530025244,
0.012664180248975754,
0.018906207755208015,
-0.012545817531645298,
-0.027327656745910645,
-0.004064850974828005,
-0.03139451891183853,
0.04390494525432587,
0.037627212703228,
-0.033617809414863586,
0.0095895417034626,
-0.06475137174129486,
0.0018235220341011882,
-0.0483524426817894,
0.009847898967564106,
0.01716766692698002,
0.06279970705509186,
0.010426659137010574,
0.010659461840987206
] |
<p>In a scanning electron microscopy, secondary electrons are defined as the electrons which obey inelastic scattering whereas backscattering electron follow elastic scattering. </p>
<p>Now my question </p>
<blockquote>
<p>Can backscatter electrons produce same level of solution as secondary electrons? </p>
</blockquote>
| 10,825 |
[
-0.037550587207078934,
-0.007744741626083851,
0.007183241657912731,
-0.005622860509902239,
-0.03003571182489395,
-0.005448519717901945,
-0.04147329553961754,
0.00017309145187027752,
0.037456925958395004,
-0.029717983677983284,
0.06437032669782639,
0.006888234056532383,
0.03373377025127411,
-0.0024943442549556494,
0.022273750975728035,
0.021099962294101715,
0.013311361894011497,
0.011131777428090572,
0.01334238238632679,
-0.0036043929867446423,
0.02930418588221073,
0.005626676604151726,
-0.003336486406624317,
-0.021541381254792213,
-0.018535858020186424,
0.0016276567475870252,
0.02487805299460888,
-0.003855713177472353,
0.0264690313488245,
0.020919980481266975,
0.021220950409770012,
-0.03893366456031799,
-0.009478900581598282,
0.0323282890021801,
0.05464144051074982,
-0.03409082815051079,
0.0021655175369232893,
-0.05947455018758774,
-0.01014616433531046,
0.02881666086614132,
-0.004386907909065485,
0.008405056782066822,
-0.00028164254035800695,
0.04624597728252411,
-0.0405847541987896,
-0.006704376544803381,
-0.0063325390219688416,
-0.021185707300901413,
0.02000156044960022,
-0.0559290274977684,
0.04210978373885155,
-0.00005905395664740354,
0.03780006989836693,
0.00033398508094251156,
-0.0019921083003282547,
0.021133802831172943,
0.07000012695789337,
0.05005491152405739,
-0.0023498251102864742,
-0.010235164314508438,
0.01580851897597313,
-0.00534411147236824,
0.002247757278382778,
-0.01516676601022482,
-0.0525791309773922,
0.011709436774253845,
0.013709880411624908,
-0.03062824159860611,
0.026541978120803833,
-0.021373478695750237,
-0.0014324047369882464,
-0.020253390073776245,
-0.00003287521758466028,
-0.01569911278784275,
0.020591583102941513,
-0.05583805963397026,
0.02729630656540394,
0.010125351138412952,
0.003112511010840535,
0.05797496810555458,
0.016543641686439514,
-0.0061458745039999485,
0.030512971803545952,
0.07620539516210556,
-0.015979839488863945,
-0.031675513833761215,
0.07594353705644608,
-0.026356332004070282,
0.02028551883995533,
0.038490671664476395,
0.014191488735377789,
0.04481191188097,
0.03895963728427887,
-0.018000923097133636,
-0.00010552992898738012,
-0.015534592792391777,
-0.030543731525540352,
0.05012691766023636,
0.024057986214756966,
-0.03337143361568451,
0.024842623621225357,
-0.03255666047334671,
0.03617609292268753,
0.08637592196464539,
0.01714002899825573,
-0.01989958994090557,
-0.010320511646568775,
0.04503156617283821,
-0.033222805708646774,
-0.0021860464476048946,
-0.01894996501505375,
0.00390621111728251,
-0.01178724318742752,
0.022663461044430733,
0.011792837642133236,
-0.008676395751535892,
-0.017321405932307243,
-0.018290787935256958,
0.06390371173620224,
0.056725602596998215,
0.011449692770838737,
-0.059688299894332886,
-0.0029623135924339294,
0.001695271348580718,
-0.05949539691209793,
0.01543718297034502,
-0.0021564026828855276,
-0.019067108631134033,
-0.01745663955807686,
0.008670109324157238,
-0.0106341652572155,
0.021574344485998154,
-0.0014524846337735653,
-0.003961876500397921,
0.03226596117019653,
-0.0018301226664334536,
-0.07343211024999619,
-0.07773564755916595,
0.05281224846839905,
-0.016885777935385704,
0.006254925392568111,
-0.09322414547204971,
0.011695274151861668,
0.011874956078827381,
0.04569954052567482,
0.000929147528950125,
0.022726135328412056,
0.008307456970214844,
0.03804803639650345,
0.0322721004486084,
0.009317021816968918,
0.0062181041575968266,
0.023522937670350075,
-0.014299645088613033,
0.0334816537797451,
-0.05491327494382858,
0.012883750721812248,
0.026818042621016502,
0.02011166140437126,
-0.023835718631744385,
0.03829369321465492,
-0.031921397894620895,
0.033604059368371964,
0.01950918510556221,
0.01903454214334488,
-0.05728486552834511,
0.07112828642129898,
-0.004422070924192667,
0.0073247915133833885,
0.033024296164512634,
-0.012383057735860348,
0.0019755475223064423,
-0.02928841859102249,
-0.01069363672286272,
0.03922813758254051,
-0.034562401473522186,
-0.02100088819861412,
-0.02361847460269928,
0.04249183461070061,
0.03467743471264839,
-0.03143884614109993,
-0.010640837252140045,
-0.008861040696501732,
0.025062480941414833,
0.006711619906127453,
0.019197575747966766,
0.011879775673151016,
-0.048161547631025314,
-0.0373917818069458,
-0.04539729282259941,
-0.013020527549088001,
-0.05869854986667633,
0.00868195854127407,
0.021054932847619057,
-0.006729085464030504,
0.05844968929886818,
-0.00414370046928525,
0.02286391891539097,
-0.0354938730597496,
-0.018256237730383873,
-0.030755260959267616,
0.022241326048970222,
-0.015922315418720245,
0.0007615212234668434,
0.0458863340318203,
0.05083002150058746,
0.06216572970151901,
-0.021148012951016426,
-0.000547544623259455,
0.0075570931658148766,
-0.009569838643074036,
-0.019044294953346252,
0.00903101172298193,
0.06028430163860321,
0.015284916386008263,
-0.024519214406609535,
-0.0029967771843075752,
-0.01242954283952713,
0.010796049609780312,
0.08086557686328888,
0.0005437252693809569,
0.07422652095556259,
0.03677967190742493,
0.0121232271194458,
0.00035093771293759346,
-0.0010613504564389586,
0.013495597057044506,
0.050776105374097824,
0.022550858557224274,
-0.01884167082607746,
-0.0403277724981308,
-0.01324820052832365,
0.034146156162023544,
0.026345040649175644,
-0.06370598077774048,
0.021483412012457848,
0.01551774051040411,
-0.006817830726504326,
0.05916549265384674,
0.033353760838508606,
-0.032718461006879807,
-0.05176295340061188,
0.04662685841321945,
-0.005672264378517866,
0.021713221445679665,
0.02711762860417366,
0.03534742444753647,
0.003954137675464153,
0.029634663835167885,
-0.041761983186006546,
0.0032762347254902124,
0.010144408792257309,
-0.051173049956560135,
-0.02502967044711113,
0.00796565692871809,
-0.05060252547264099,
0.024173161014914513,
-0.021592674776911736,
0.0218527652323246,
0.006253525149077177,
-0.010733544826507568,
0.01999172940850258,
-0.025646302849054337,
0.007106882985681295,
0.005127085838466883,
0.005656806286424398,
-0.014380311593413353,
-0.024643821641802788,
0.01030974742025137,
-0.07975553721189499,
0.01580808125436306,
-0.014255881309509277,
-0.030832460150122643,
0.0026158327236771584,
0.02139703743159771,
0.0635119155049324,
-0.026900963857769966,
0.03833150118589401,
-0.03553757816553116,
-0.04120739921927452,
0.01309723500162363,
-0.018153196200728416,
0.013199890963733196,
0.025491369888186455,
-0.01163768395781517,
0.03821218013763428,
-0.04395858943462372,
-0.029404055327177048,
0.0668911561369896,
-0.015560450032353401,
0.00945508386939764,
0.020928962156176567,
-0.0070739202201366425,
0.0032107073348015547,
-0.013549228198826313,
-0.03409707918763161,
0.014804665930569172,
-0.011123494245111942,
-0.005430096294730902,
0.025499843060970306,
-0.003259203629568219,
0.0029221309814602137,
0.0012963538756594062,
-0.030088094994425774,
-0.03796582669019699,
-0.0046845125034451485,
0.0009063278557732701,
0.02053600177168846,
-0.03782849386334419,
0.011815055273473263,
0.023386873304843903,
-0.05759282410144806,
-0.015506511554121971,
-0.05369855836033821,
-0.059364914894104004,
0.03340882062911987,
-0.026718633249402046,
0.008227509446442127,
-0.030118701979517937,
-0.06412675231695175,
0.05677065625786781,
0.018067440018057823,
-0.030554207041859627,
-0.016657650470733643,
-0.024301985278725624,
-0.04069463163614273,
-0.01784549281001091,
-0.017641769722104073,
0.006145949941128492,
-0.029274940490722656,
0.018774041905999184,
0.01581684686243534,
0.046835292130708694,
0.0411541610956192,
-0.011407267302274704,
-0.003511217189952731,
-0.012898505665361881,
0.02127727121114731,
0.0282009057700634,
0.03060724399983883,
-0.012733140029013157,
-0.038739316165447235,
-0.00660342164337635,
0.005278604105114937,
0.05003514140844345,
0.03577357903122902,
-0.05602541193366051,
0.025510113686323166,
0.0194756668061018,
0.004249638877809048,
-0.02757033333182335,
0.034968335181474686,
0.049920376390218735,
0.025246407836675644,
-0.0033056987449526787,
0.0067731947638094425,
0.010817927308380604,
-0.01900966838002205,
-0.012594916857779026,
0.04040417820215225,
0.0686376690864563,
-0.022822357714176178,
-0.03701377287507057,
0.0004117866628803313,
-0.0038412625435739756,
0.03161204606294632,
-0.013140895403921604,
-0.023475073277950287,
0.021069196984171867,
-0.006213274784386158,
0.026574736461043358,
-0.00595431262627244,
-0.021727701649069786,
-0.020903874188661575,
-0.03926336020231247,
-0.01320953480899334,
0.01910746470093727,
0.05394965037703514,
0.01863439567387104,
0.08292658627033234,
0.01989997737109661,
0.043171923607587814,
0.020485006272792816,
0.01320573128759861,
-0.05701056867837906,
0.005255799274891615,
0.00021342193940654397,
-0.007191035430878401,
-0.010022476315498352,
-0.018248843029141426,
-0.056035365909338,
-0.0480831004679203,
-0.027147406712174416,
-0.009457863867282867,
0.016913587227463722,
-0.021786853671073914,
0.014878562651574612,
-0.018891654908657074,
0.000983153353445232,
-0.016807910054922104,
0.021280739456415176,
-0.028326494619250298,
-0.03962608799338341,
0.002802859991788864,
0.02761855162680149,
0.016111688688397408,
0.02204156294465065,
-0.050625916570425034,
0.06136247143149376,
0.013626583851873875,
0.02690020762383938,
0.05111992359161377,
0.014930249191820621,
-0.03876262530684471,
0.03168938681483269,
0.03266046941280365,
0.043503422290086746,
0.011325598694384098,
-0.024708932265639305,
-0.0530724972486496,
-0.059719882905483246,
-0.036379214376211166,
0.013381339609622955,
0.028115492314100266,
0.018088888376951218,
0.012410045601427555,
0.0005152387311682105,
-0.014218456111848354,
-0.008968150243163109,
0.0606878437101841,
0.04103703424334526,
0.04920486733317375,
-0.040872447192668915,
-0.06198853626847267,
-0.05086229369044304,
-0.03759640082716942,
-0.014971441589295864,
0.03780626505613327,
0.03716384992003441,
0.025912215933203697,
-0.017538705840706825,
0.012643678113818169,
0.010280591435730457,
-0.036851588636636734,
-0.010222667828202248,
-0.01567527838051319,
0.002647938672453165,
-0.022156745195388794,
0.019417498260736465,
-0.019249632954597473,
0.018919818103313446,
0.005567323882132769,
0.002416651463136077,
0.0035264105536043644,
-0.09031341224908829,
-0.03991411626338959,
0.027558758854866028,
0.03148197382688522,
-0.02013099566102028,
0.0023492693435400724,
-0.020460737869143486,
-0.018418289721012115,
0.011094159446656704,
-0.024263599887490273,
0.038570016622543335,
-0.01577678695321083,
0.008395482785999775,
-0.010213930159807205,
-0.03378903865814209,
-0.006732984445989132,
0.015593891963362694,
0.01352063100785017,
0.01648653857409954,
-0.025412408635020256,
-0.015865596011281013,
0.0037015890702605247,
0.02915574610233307,
0.015046834014356136,
0.06422978639602661,
0.01257307268679142,
0.0037454438861459494,
0.000739288458134979,
-0.006934446282684803,
-0.01928013376891613,
-0.06878555566072464,
0.018089406192302704,
-0.0023090301547199488,
-0.004347845446318388,
0.039277732372283936,
-0.036316197365522385,
-0.025910789147019386,
0.055330730974674225,
0.02352711744606495,
-0.007605293300002813,
-0.020211482420563698,
-0.025000611320137978,
0.0503590889275074,
0.007051835302263498,
-0.005434300284832716,
0.029720116406679153,
0.021999312564730644,
-0.03468126058578491,
0.0025630698073655367,
-0.04715539515018463,
0.060165662318468094,
-0.07160395383834839,
-0.036484114825725555,
-0.010996082797646523,
0.03160981833934784,
-0.006441397592425346,
0.030049292370676994,
0.0018744496628642082,
0.005095543339848518,
0.007191438693553209,
-0.04465291649103165,
0.005642452277243137,
0.011524888686835766,
0.0005443519330583513,
0.023872120305895805,
-0.005957949906587601,
0.016707131639122963,
-0.006679112557321787,
-0.022190937772393227,
-0.029589377343654633,
-0.032468583434820175,
-0.012985998764634132,
0.010486776940524578,
-0.011024430394172668,
0.016036583110690117,
-0.024615541100502014,
-0.009280798025429249,
0.05997195839881897,
-0.05227430909872055,
0.030423693358898163,
0.005772927775979042,
-0.023679587990045547,
0.014577483758330345,
-0.08311892300844193,
0.023702548816800117,
0.057800572365522385,
-0.015405052341520786,
0.005558728240430355,
-0.05154453217983246,
0.062297523021698,
0.05693723261356354,
0.03383926302194595,
-0.07508283108472824,
-0.044083599001169205,
0.002807937329635024,
0.040353309363126755,
-0.029478801414370537,
0.013048654422163963,
-0.018664255738258362,
-0.014466450549662113,
-0.010407498106360435,
-0.007164337206631899,
0.0188949815928936,
-0.029370738193392754,
-0.00589959230273962,
0.027835674583911896,
0.018304428085684776,
0.035241104662418365,
0.006199896801263094,
0.0016900599002838135,
0.005125256720930338,
-0.03365598991513252,
0.011758585460484028,
-0.00352996657602489,
0.04204011708498001,
-0.0016667157178744674,
-0.026716841384768486,
-0.036558106541633606,
-0.01254020631313324,
0.05710957944393158,
-0.027166875079274178,
-0.0049486905336380005,
0.04408964887261391,
0.00863713026046753,
0.02927776612341404,
-0.006772574968636036,
0.020186137408018112,
-0.028227074071764946,
0.06312143802642822,
0.015238957479596138,
-0.020287485793232918,
-0.007613928522914648,
-0.0018471615621820092,
0.020869357511401176,
0.006145551335066557,
-0.017058394849300385,
-0.0034439312294125557,
0.07431609183549881,
-0.008559411391615868,
-0.011374694295227528,
0.02699717879295349,
-0.009305770508944988,
0.02590051293373108,
-0.03546775504946709,
0.03323322534561157,
0.03033442236483097,
0.03875970095396042,
-0.005733910948038101,
-0.06204927712678909,
-0.015635011717677116,
0.030156195163726807,
0.06574076414108276,
-0.014854911714792252,
0.024434572085738182,
0.013604684732854366,
-0.032373275607824326,
-0.000007419368557748385,
-0.07786831259727478,
0.02384047582745552,
0.01861969381570816,
-0.05586698651313782,
0.03975411504507065,
-0.031189460307359695,
-0.01436146255582571,
0.01502119842916727,
0.04943601414561272,
-0.03170933201909065,
0.030435755848884583,
0.018607746809720993,
-0.024512819945812225,
0.0063971225172281265,
-0.016963336616754532,
-0.04307787865400314,
0.04357065260410309,
-0.03649897128343582,
0.04644318297505379,
-0.01943843625485897,
-0.0339982695877552,
0.061314016580581665,
-0.017849711701273918,
0.020539984107017517,
-0.04778927564620972,
0.000364664796506986,
-0.04741378501057625,
0.02703017368912697,
-0.043885890394449234,
-0.0028906362131237984,
-0.019228197634220123,
0.01977107860147953,
0.00782953854650259,
-0.006467348430305719,
0.018056822940707207,
-0.0201695766299963,
-0.08409286290407181,
-0.008595804683864117,
-0.06800610572099686,
-0.014031946659088135,
0.030687637627124786,
-0.048563651740550995,
0.011589069850742817,
-0.01425329502671957,
-0.05153028666973114,
0.03954339772462845,
0.032106541097164154,
0.005436921492218971,
-0.009666813537478447,
0.018243052065372467,
-0.00454314798116684,
0.07071726024150848,
0.004507557954639196,
-0.0022449225652962923,
0.1332859992980957,
0.06845574826002121,
-0.0019749929197132587,
-0.03182514011859894,
-0.011212355457246304,
-0.004098750185221434,
0.020140275359153748,
0.00017602965817786753,
-0.04492809623479843,
-0.03824765980243683,
-0.01891048066318035,
-0.01787392608821392,
0.04729051515460014,
-0.014583892188966274,
0.023783572018146515,
0.04281510040163994,
-0.056655604392290115,
-0.03279799595475197,
0.011214221827685833,
-0.005918641574680805,
-0.0065554054453969,
0.05956868454813957,
-0.025015704333782196,
0.016338806599378586,
-0.024061840027570724,
-0.016775833442807198,
-0.03392520919442177,
0.0026956135407090187,
0.01922168768942356,
0.012941292487084866,
-0.040937118232250214,
-0.055074382573366165,
0.03632942959666252,
0.010588934645056725,
-0.036757245659828186,
0.012804892845451832,
0.005861775949597359,
-0.026892874389886856,
0.009516931138932705,
0.019475610926747322,
0.033709317445755005,
0.01120738685131073,
0.023155804723501205,
0.04688894376158714,
-0.03538866341114044,
0.044953424483537674,
0.01714976504445076,
0.011100229807198048,
0.0013084376696497202,
-0.024191707372665405,
-0.026580097153782845,
-0.01437300443649292,
0.023430554196238518,
-0.04107396677136421,
-0.03183476999402046,
-0.006004628259688616,
0.012154784053564072,
-0.009635072201490402,
0.001136761624366045,
-0.04435425251722336,
0.03970989212393761,
-0.010880088433623314,
-0.0005271343397907913,
0.05266357585787773,
-0.008718308992683887,
0.004356532823294401,
0.009612763300538063,
0.031227711588144302,
0.018543563783168793,
-0.0444699302315712,
-0.06358148157596588,
0.022602858021855354,
-0.030079752206802368,
-0.010192190296947956,
0.027981368824839592,
0.003799772122874856,
0.0525435209274292,
0.004941447637975216,
-0.01349685899913311,
0.009164419956505299,
-0.05799100920557976,
0.05785807967185974,
0.004296815954148769,
0.020402472466230392,
-0.04473315551877022,
0.03512043133378029,
0.02368147484958172,
0.04219362139701843,
-0.027097532525658607,
0.028872782364487648,
0.04266117885708809,
0.018649872392416,
0.019090527668595314,
-0.044230781495571136,
-0.04286465421319008,
0.039120692759752274,
-0.009708147495985031,
0.017684027552604675,
-0.014470269903540611,
-0.0070596374571323395,
-0.009831208735704422,
0.0022460944019258022,
0.022465858608484268,
0.017186203971505165,
-0.01687171496450901,
-0.029082471504807472,
-0.014734074473381042,
0.02036217786371708,
-0.01702094078063965,
0.0077070025727152824,
-0.009981881827116013,
0.013868492096662521,
0.027233468368649483,
-0.06633839756250381,
0.01594778150320053,
0.04925525560975075,
0.016055554151535034,
-0.0010102264350280166,
0.03678359091281891,
-0.001749010756611824,
0.007829135283827782,
-0.027586722746491432,
-0.019697993993759155,
-0.005841350182890892,
0.0070724282413721085,
0.004871827084571123,
0.010349511168897152,
-0.03141308203339577,
0.024288346990942955,
-0.004896755795925856,
-0.016864735633134842,
0.03816775977611542,
0.04183201119303703,
0.01727401278913021,
-0.033553335815668106,
0.038527000695466995,
0.008618208579719067,
0.06123968958854675,
-0.01811865158379078,
-0.035756368190050125,
0.03758087754249573,
-0.028161564841866493,
-0.03729122132062912,
0.007847554981708527,
-0.04214378818869591,
-0.010716473683714867,
0.059293653815984726,
-0.0015313387848436832,
0.007045662496238947,
0.05808740854263306,
0.02027164399623871,
0.007605378516018391,
0.019576966762542725,
-0.0539521649479866,
0.01211499609053135,
-0.017468471080064774,
0.01845904439687729,
-0.006148166488856077,
0.016247883439064026,
0.058485209941864014,
0.0007749706855975091,
0.0076046413742005825,
-0.03914375603199005,
-0.0006238557398319244,
0.02414950355887413,
-0.005873566027730703,
0.017181292176246643,
-0.034727372229099274,
0.02476898953318596,
0.019596833735704422,
-0.010521105490624905,
0.034557487815618515,
0.018277987837791443,
0.00028301513521000743,
-0.0709507018327713,
0.00035682349698618054,
-0.016810012981295586,
0.012037013657391071,
-0.009860781952738762,
-0.020772142335772514,
0.022258300334215164,
-0.011790976859629154,
-0.10155629366636276,
0.020311016589403152,
-0.0029666610062122345,
-0.031078260391950607,
-0.04335055127739906,
0.029088223353028297,
-0.028573891147971153,
0.024436283856630325,
0.0031634997576475143,
0.09465532749891281,
0.04970231279730797,
0.019163040444254875,
0.03890535980463028,
-0.004913137294352055,
-0.08684904128313065,
0.048192959278821945,
0.02148761786520481,
-0.015185627155005932,
0.054477959871292114,
-0.04542895406484604,
-0.03398533910512924,
0.019306857138872147,
0.024244535714387894,
0.005314915906637907,
-0.008249294012784958,
0.028491070494055748,
0.02040807530283928,
0.05713144689798355,
-0.006653523538261652,
-0.011669743806123734,
0.013176280073821545,
0.007973430678248405,
0.020800428465008736,
0.02543966844677925,
0.004342387430369854,
-0.009092472493648529,
0.016421185806393623,
-0.04521847143769264,
-0.041751038283109665,
0.025059372186660767,
-0.056533124297857285,
-0.05059977248311043,
-0.007442750968039036,
-0.0032080505043268204,
0.043229199945926666,
0.03567937761545181,
-0.020001064985990524,
-0.07312656193971634,
-0.0038160423282533884,
0.003985119052231312,
0.02735959179699421,
-0.014200619421899319,
0.037459325045347214,
-0.02155284583568573,
-0.023829109966754913,
-0.006330390460789204,
-0.003251276444643736,
-0.004177443217486143,
-0.05089721456170082,
-0.004243088886141777,
0.005193919874727726,
0.0017080603865906596,
-0.022889677435159683,
-0.03854740411043167,
-0.02862568013370037,
0.07049091905355453,
-0.001442998880520463,
0.03293149173259735,
0.027632733806967735,
-0.004685035441070795,
-0.011345315724611282,
-0.054500870406627655,
0.00471443822607398,
-0.000775244552642107,
-0.02189784310758114,
-0.04131186008453369,
-0.0448867492377758,
0.025397151708602905,
0.04014391079545021,
0.060182973742485046,
0.0026519279927015305,
0.003301002085208893,
0.00904364325106144,
-0.060044750571250916,
0.011428364552557468,
-0.04869220033288002,
0.008509064093232155,
0.0032979778479784727,
-0.01512024737894535,
-0.03251485526561737,
0.01148594357073307,
-0.018025629222393036,
0.022911565378308296,
-0.001060002134181559,
0.014058878645300865,
-0.023532330989837646,
-0.05383126810193062,
-0.018412217497825623,
0.03447601571679115,
0.022898145020008087,
-0.05092596262693405,
0.08528480678796768,
-0.010673425160348415,
0.0062184641137719154,
-0.0010904704686254263,
-0.014340726658701897,
-0.018277233466506004,
0.0012099678860977292,
-0.03495882824063301,
-0.01932132989168167,
0.0022613699547946453,
-0.01582666113972664,
0.031057223677635193,
-0.0427231565117836,
-0.02160724438726902,
0.027368653565645218,
0.008912691846489906,
0.02479146420955658,
0.03688397258520126,
-0.014247405342757702,
-0.01496981456875801,
-0.0010212082415819168,
0.01856384426355362,
-0.008533892221748829,
0.00928871612995863,
-0.023756420239806175,
0.03410260006785393,
-0.013119461014866829,
-0.0031720770057290792,
0.016064750030636787,
-0.013008334673941135,
-0.011906669475138187,
0.00981987826526165,
0.01562667265534401,
-0.002402397571131587,
0.028488200157880783,
-0.007024554070085287,
0.013149458914995193,
-0.015696339309215546,
0.022855747491121292,
-0.021631529554724693,
-0.016520477831363678,
0.054236773401498795,
-0.05670226365327835,
0.017004722729325294,
-0.024673394858837128,
0.020490091294050217,
-0.026028335094451904,
0.0032142067793756723,
0.009461507201194763,
0.03410235419869423,
-0.003779191756621003,
-0.07348821312189102,
-0.021462684497237206,
0.005031614098697901,
0.025258643552660942,
-0.039814673364162445,
0.012196035124361515,
-0.04388795793056488,
-0.01221904344856739,
-0.0034542656503617764,
0.009577548131346703,
-0.028202438727021217,
0.01211165077984333,
0.015136424452066422,
-0.01145787164568901,
0.0018078474095091224,
0.007838401943445206,
-0.024357125163078308,
-0.02901671826839447,
0.05295942351222038,
-0.0358523465692997,
-0.03842402994632721,
-0.005730943288654089,
-0.020245537161827087,
-0.003707129042595625,
-0.04888702183961868
] |
<p>I think I have learned in physics that escape velocity is defined as the speed at which objects going ballistic in the opposite direction of the main gravitational force are able to finally overcome that force (assuming the simplest case with two directly opposing forces).</p>
<p>This means objects ballistically moving away from Earth slower than that velocity would never be able to escape and will finally fall back to Earth.</p>
<p>I have heard in many documentaries that this is the reason that spacecraft must accelerate to that velocity to get into deeper space at all.</p>
<p>However, as far as I understand it, spacecraft are not purely ballistic objects and could be controlled and accelerated step by step as needed, so why is it not possible to escape from Earth with lower speed and just "keep going", i.e. "accelerating" (exerting force) only to not come to a halt ?</p>
| 10,826 |
[
-0.030427370220422745,
0.007044117897748947,
-0.016028374433517456,
-0.010402974672615528,
0.009279568679630756,
-0.0036288462579250336,
-0.005144666880369186,
0.004442291799932718,
0.01223277859389782,
-0.04829319193959236,
-0.02020375244319439,
0.0679623931646347,
0.03521404415369034,
-0.0016809547087177634,
0.01313832774758339,
0.016213979572057724,
0.002637401921674609,
-0.001175142009742558,
0.0031576433684676886,
-0.031554725021123886,
0.003967252094298601,
0.0028710782062262297,
0.0013942308723926544,
0.014584101736545563,
-0.02459772489964962,
0.005724429152905941,
0.030204303562641144,
-0.008513052947819233,
0.026010874658823013,
0.049649689346551895,
0.026754947379231453,
0.0310191847383976,
0.0015478564891964197,
0.013176649808883667,
0.01807122305035591,
0.035330213606357574,
-0.03785980865359306,
-0.02923821099102497,
-0.012000897899270058,
0.018253810703754425,
-0.06711035966873169,
-0.017960382625460625,
-0.01649492233991623,
0.08137976378202438,
-0.031568873673677444,
0.00310402805916965,
0.024085745215415955,
-0.025124596431851387,
0.031940434128046036,
-0.05197425186634064,
0.04807504639029503,
-0.011552111245691776,
0.0488358736038208,
0.02844061702489853,
0.0550549253821373,
-0.005093398969620466,
0.10130765289068222,
0.08206939697265625,
-0.025460513308644295,
-0.01446879468858242,
-0.01081815641373396,
-0.006807078141719103,
0.0004458596813492477,
-0.004446534439921379,
-0.005543826147913933,
0.0585605725646019,
-0.026584964245557785,
-0.016788728535175323,
0.011773592792451382,
0.04025515541434288,
0.001995775615796447,
-0.01285446248948574,
0.014384050853550434,
0.0005310162669047713,
0.022396588698029518,
-0.046338360756635666,
0.035576753318309784,
-0.0065146079286932945,
0.02488291822373867,
0.07091443240642548,
-0.019435591995716095,
-0.0018219848861917853,
0.049407150596380234,
0.03209792450070381,
-0.0006260956870391965,
0.041625261306762695,
0.07159847766160965,
-0.01178875844925642,
0.02650752104818821,
0.04770887643098831,
0.0002510649792384356,
0.015127432532608509,
0.008154151029884815,
0.0062641566619277,
-0.031125204637646675,
0.06071973592042923,
0.027164623141288757,
0.06669408828020096,
0.025856386870145798,
-0.04480987414717674,
-0.005023816134780645,
0.00858391635119915,
0.021852929145097733,
0.038616035133600235,
0.033248186111450195,
-0.01448867842555046,
-0.07417774945497513,
0.0077147395350039005,
-0.025041023269295692,
-0.013622007332742214,
-0.016474297270178795,
0.03273233026266098,
0.014452601782977581,
-0.01371093187481165,
-0.011445664800703526,
-0.0193423330783844,
-0.008159839548170567,
-0.035345494747161865,
0.030289916321635246,
0.043584492057561874,
0.04100111499428749,
-0.0004939211648888886,
0.057838499546051025,
-0.013795042410492897,
-0.0269693061709404,
-0.025662604719400406,
0.03760211542248726,
0.012838794849812984,
0.0032796296291053295,
0.007907380349934101,
0.021045543253421783,
-0.03854093328118324,
-0.0031877702567726374,
-0.007909301668405533,
0.07267014682292938,
-0.0015345514984801412,
-0.08510642498731613,
-0.07743345946073532,
0.05965782701969147,
0.02103583514690399,
-0.0051778387278318405,
-0.09280078858137131,
0.005849780049175024,
0.036942243576049805,
0.07510922849178314,
-0.022836221382021904,
-0.014043307863175869,
-0.020312443375587463,
-0.005564047489315271,
0.022861875593662262,
-0.017885571345686913,
-0.011272738687694073,
-0.014191273599863052,
-0.05606240779161453,
0.015263973735272884,
-0.09844088554382324,
0.025294968858361244,
0.008704113774001598,
0.008351248688995838,
-0.014966816641390324,
0.04703729599714279,
-0.046355314552783966,
-0.013480564579367638,
-0.03743205592036247,
0.012168793007731438,
0.006964000407606363,
0.10369300097227097,
0.03236045688390732,
-0.024532770738005638,
0.04783419892191887,
0.06219608709216118,
0.026769151911139488,
0.03006863407790661,
0.0033983939792960882,
0.0243703443557024,
-0.06338505446910858,
-0.026735078543424606,
-0.03680909425020218,
-0.01784389838576317,
-0.0305025652050972,
-0.01608618162572384,
-0.027247050777077675,
0.012371016666293144,
-0.02574683353304863,
0.020940056070685387,
0.021462906152009964,
0.0051564984023571014,
0.019423708319664,
-0.008981195278465748,
-0.0033287990372627974,
-0.006266205105930567,
-0.06176794692873955,
0.025479957461357117,
0.01496603712439537,
0.018456796184182167,
0.007320560049265623,
0.009268352761864662,
0.02976979687809944,
-0.012064019218087196,
0.006968740373849869,
0.0008678094018250704,
0.03641495481133461,
-0.02508147805929184,
-0.01462814211845398,
-0.027575358748435974,
0.05771379917860031,
0.04567086324095726,
0.011660383082926273,
0.009085838682949543,
0.02065213769674301,
-0.05901878699660301,
-0.027150457724928856,
-0.004738789517432451,
-0.0018664808012545109,
0.02664005756378174,
-0.003433799836784601,
0.04235771670937538,
-0.009982815012335777,
0.00606194045394659,
0.02764766477048397,
0.002693908056244254,
0.12395213544368744,
0.032808393239974976,
0.04006456956267357,
-0.010324926115572453,
0.03312725946307182,
0.0188994649797678,
-0.016515597701072693,
-0.0031228046864271164,
-0.015538712963461876,
-0.01465122401714325,
-0.001069727004505694,
0.013321030884981155,
-0.006956588942557573,
-0.049370262771844864,
0.014192705042660236,
0.017988398671150208,
0.03125770762562752,
0.029031574726104736,
0.047175776213407516,
-0.023907102644443512,
0.000379126169718802,
0.0391596183180809,
0.01116078719496727,
0.020583830773830414,
0.011991220526397228,
0.0382266491651535,
0.0013452197890728712,
-0.04307851567864418,
-0.02942293882369995,
-0.024670468643307686,
0.025703586637973785,
0.03965413570404053,
-0.019211137667298317,
0.010649536736309528,
-0.04718932509422302,
0.01774122193455696,
-0.02107943594455719,
0.0406763069331646,
0.019458597525954247,
0.0142141692340374,
0.02196568064391613,
-0.06241430342197418,
0.034574538469314575,
0.024285119026899338,
-0.009814676828682423,
-0.016705283895134926,
-0.0017349645495414734,
0.02235807292163372,
-0.05375400185585022,
0.016164768487215042,
-0.03060217574238777,
-0.001647153403609991,
-0.009781389497220516,
-0.012269983999431133,
0.0004619136161636561,
-0.0027726097032427788,
0.0383160375058651,
-0.005917845759540796,
-0.031211359426379204,
-0.006542298477143049,
-0.05301303789019585,
-0.0023353344295173883,
0.02177293226122856,
-0.019125215709209442,
0.057223182171583176,
-0.03940499946475029,
-0.07212129980325699,
0.07120325416326523,
0.006803059484809637,
0.0576719269156456,
0.03979584574699402,
-0.022616561502218246,
-0.052796173840761185,
0.010815727524459362,
-0.02082137018442154,
0.0014397973427549005,
-0.005162139888852835,
-0.006511612329632044,
0.0799299106001854,
-0.02460147626698017,
-0.014062143862247467,
0.03384237736463547,
-0.06744478642940521,
-0.048502009361982346,
-0.011365487240254879,
0.03637721762061119,
0.00019709233311004937,
-0.007526038680225611,
0.010914885438978672,
-0.00717152701690793,
-0.04716915637254715,
-0.01529762800782919,
-0.03879847377538681,
-0.04021696001291275,
-0.01174608152359724,
0.02504158392548561,
0.020653484389185905,
-0.02270541526377201,
-0.033443816006183624,
0.07315964251756668,
0.038186971098184586,
0.014419430866837502,
-0.03771049156785011,
-0.032952699810266495,
-0.011242764070630074,
0.01005232147872448,
-0.006393628194928169,
0.01636483520269394,
-0.015402530319988728,
-0.012871289625763893,
-0.0033933427184820175,
0.024484027177095413,
0.0030080846045166254,
-0.035504478961229324,
0.004120807163417339,
0.010225804522633553,
0.017844945192337036,
0.0035186614841222763,
0.017847498878836632,
0.03134728595614433,
-0.038272518664598465,
0.05033271014690399,
0.009570113383233547,
0.0628790482878685,
-0.00039206561632454395,
-0.055673982948064804,
0.02417738363146782,
-0.008324068039655685,
0.006021046079695225,
0.006093256641179323,
0.0197581984102726,
-0.011187799274921417,
0.012412304058670998,
0.009534870274364948,
0.014191865921020508,
0.0556466244161129,
-0.0032978004310280085,
-0.024769602343440056,
-0.008769030682742596,
0.05855267867445946,
-0.02807501330971718,
-0.01160251721739769,
-0.0011533719953149557,
-0.00865161046385765,
-0.006191228982061148,
-0.0033323236275464296,
-0.012647459283471107,
0.048181816935539246,
0.014743811450898647,
0.007209830917418003,
0.007980156689882278,
-0.01058149989694357,
0.019829725846648216,
-0.0694962814450264,
0.01082976721227169,
-0.026286745443940163,
0.04981470853090286,
0.0013235235819593072,
0.05237521976232529,
0.03775497153401375,
0.04815395548939705,
0.0025854783598333597,
0.01614462584257126,
-0.11518393456935883,
0.028369644656777382,
-0.048069193959236145,
-0.048705458641052246,
-0.02863440103828907,
-0.007433572318404913,
-0.024394415318965912,
-0.033877868205308914,
-0.022698916494846344,
-0.03129013255238533,
0.028424086049199104,
-0.04940428584814072,
-0.0058742705732584,
-0.02518334425985813,
-0.011622399091720581,
-0.027482133358716965,
0.033594533801078796,
0.03894224762916565,
-0.010101617313921452,
0.021630341187119484,
0.03266650438308716,
-0.020791737362742424,
-0.01579831726849079,
-0.01564663089811802,
-0.014367648400366306,
0.032260194420814514,
0.0024923833552747965,
-0.004705528263002634,
0.022871965542435646,
-0.0012547537917271256,
-0.016505872830748558,
0.027389751747250557,
0.014389283955097198,
-0.04127253592014313,
0.032055456191301346,
-0.048397090286016464,
-0.040232524275779724,
-0.021182255819439888,
0.029793018475174904,
0.021672947332262993,
-0.012718203477561474,
0.016610711812973022,
0.029771937057375908,
0.014288813807070255,
-0.00042639434104785323,
0.02805284969508648,
0.03253047913312912,
-0.011184957809746265,
0.00046102903434075415,
-0.04031972959637642,
-0.05021117255091667,
-0.04594859853386879,
-0.02714459039270878,
0.004231066443026066,
-0.01401928998529911,
-0.03565433248877525,
0.0033862018026411533,
0.028573481366038322,
-0.014351500198245049,
-0.01519241277128458,
-0.0072731198742985725,
-0.013699658215045929,
0.04164235293865204,
0.003993663005530834,
0.015554193407297134,
0.024304412305355072,
0.014475210569798946,
0.029530411586165428,
0.0009655713802203536,
0.010690941475331783,
-0.04086993262171745,
-0.02047141082584858,
0.0009350040345452726,
0.028078917413949966,
0.013012849725782871,
0.0018663863884285092,
-0.062232762575149536,
-0.02912251465022564,
-0.0007881020428612828,
-0.003282180754467845,
0.027949271723628044,
-0.022886544466018677,
0.013520820997655392,
0.006112086586654186,
-0.04822560399770737,
-0.016514666378498077,
-0.013296633027493954,
-0.0017491698963567615,
-0.007016042713075876,
-0.013503795489668846,
0.046546079218387604,
-0.02176186814904213,
-0.0014053191989660263,
0.007726872805505991,
0.04251228645443916,
0.009666269645094872,
0.017382526770234108,
0.004092897288501263,
-0.010170958004891872,
-0.01765376888215542,
-0.055211424827575684,
-0.032241836190223694,
-0.0026115919463336468,
-0.005148882046341896,
0.01395163033157587,
-0.06356889754533768,
-0.028135402128100395,
0.019557245075702667,
0.000996398157440126,
0.02299511805176735,
-0.021277019754052162,
-0.03146186098456383,
-0.01823987066745758,
0.02704012766480446,
-0.009893459267914295,
0.02681654691696167,
0.020519237965345383,
-0.0051300195045769215,
-0.012151433154940605,
-0.02737804688513279,
0.03003447875380516,
-0.06562693417072296,
-0.02554798498749733,
-0.014432576484978199,
0.00784328579902649,
-0.04413177818059921,
0.061354294419288635,
0.0004320086445659399,
0.006247013341635466,
0.0032249365467578173,
-0.04744220897555351,
0.00149490253534168,
0.014552518725395203,
0.016445117071270943,
-0.013601909391582012,
-0.003308090614154935,
0.024486877024173737,
-0.02433479018509388,
-0.025272049009799957,
-0.011664084158837795,
0.009750056080520153,
-0.011681323871016502,
0.053718481212854385,
-0.027868499979376793,
-0.016487615182995796,
-0.016025785356760025,
-0.01780877634882927,
0.03359290957450867,
-0.036565184593200684,
0.04842497780919075,
-0.03319864347577095,
-0.026167485862970352,
0.025377977639436722,
-0.03136540949344635,
-0.0037697581574320793,
-0.008528538048267365,
-0.02934885211288929,
0.010927439667284489,
-0.07602590322494507,
0.05241487920284271,
0.0038873590528964996,
0.043120335787534714,
-0.08058461546897888,
-0.045830439776182175,
0.033334728330373764,
-0.0035329540260136127,
-0.03547212854027748,
-0.026426615193486214,
-0.01287967897951603,
-0.05425417050719261,
-0.04872620850801468,
-0.006182226352393627,
0.0629497841000557,
0.009860129095613956,
-0.004400975536555052,
0.01889197900891304,
0.018964461982250214,
0.021001381799578667,
-0.011785241775214672,
-0.03207603842020035,
0.00033062315196730196,
-0.0022609771694988012,
0.0170662309974432,
-0.023800160735845566,
0.09114205092191696,
-0.010787568986415863,
-0.0506962351500988,
-0.011900690384209156,
-0.040971800684928894,
-0.00494327861815691,
-0.015974629670381546,
0.0024037633556872606,
0.0756571814417839,
-0.0018585023935884237,
0.013157377019524574,
0.0023706904612481594,
0.04453470930457115,
-0.007362800184637308,
0.02507532574236393,
0.01181078515946865,
0.009554633870720863,
-0.04417967051267624,
-0.04070200398564339,
0.04024417698383331,
-0.014810364693403244,
0.030899105593562126,
-0.020104750990867615,
0.0420730859041214,
0.012452388182282448,
-0.01735011860728264,
0.010679686442017555,
0.007691631093621254,
0.013824423775076866,
-0.02200031466782093,
-0.021451398730278015,
0.02879468910396099,
0.015408312901854515,
-0.04145486652851105,
-0.014993209391832352,
-0.01431630551815033,
0.022708823904395103,
0.034586768597364426,
-0.07402890175580978,
0.032567281275987625,
-0.0062391310930252075,
0.0051405043341219425,
-0.015132848173379898,
-0.04530158266425133,
-0.0032844676170498133,
0.0212444718927145,
-0.0008177492418326437,
0.00641802279278636,
-0.0056834290735423565,
0.004344087094068527,
0.025298506021499634,
0.05529394745826721,
-0.02327411063015461,
-0.015095972456037998,
0.026137810200452805,
-0.009496993385255337,
0.0004946612170897424,
-0.0042040650732815266,
-0.009024979546666145,
0.022305963560938835,
-0.020214052870869637,
0.023439494892954826,
0.018496116623282433,
-0.002431117231026292,
0.043484486639499664,
0.004751117900013924,
-0.012807007879018784,
-0.07330841571092606,
-0.028610603883862495,
-0.050450216978788376,
0.03386063128709793,
0.016167523339390755,
0.003375230124220252,
0.02741609700024128,
-0.009435810148715973,
0.010245149955153465,
-0.005177404265850782,
-0.01938416250050068,
0.009664605371654034,
-0.05164896324276924,
-0.04575372487306595,
-0.05755656957626343,
-0.03569462522864342,
0.017939526587724686,
0.017390703782439232,
-0.0001550777378724888,
-0.02115512266755104,
0.008611196652054787,
-0.005038789473474026,
-0.012727644294500351,
0.04939112812280655,
-0.011390638537704945,
0.07071429491043091,
0.0038320310413837433,
-0.0032273498363792896,
-0.04607192426919937,
0.02519826777279377,
0.11894619464874268,
0.03394973278045654,
-0.0009680463699623942,
-0.03041910193860531,
0.011624016799032688,
-0.0461704395711422,
0.027818623930215836,
-0.04058757796883583,
0.029046611860394478,
0.041037172079086304,
0.0151876425370574,
-0.0022273038048297167,
0.06293044984340668,
-0.04235773906111717,
-0.019728101789951324,
0.057172998785972595,
-0.029932145029306412,
-0.00040052077383734286,
-0.00560044078156352,
0.006556201260536909,
-0.018308568745851517,
0.003992779646068811,
-0.0033864611759781837,
0.018227601423859596,
-0.024186180904507637,
-0.03995409980416298,
-0.015845030546188354,
-0.023868879303336143,
0.01847103238105774,
-0.02095482312142849,
-0.042079854756593704,
0.004614939913153648,
0.015735048800706863,
-0.04186112433671951,
-0.018184620887041092,
0.03564347326755524,
0.019700493663549423,
-0.028413135558366776,
-0.025833917781710625,
0.03339989483356476,
0.0255753081291914,
0.02755914069712162,
0.0046671731397509575,
0.005940182600170374,
-0.03096669912338257,
0.02948445826768875,
-0.015121977776288986,
0.048799965530633926,
-0.0176019798964262,
0.019531790167093277,
0.027913253754377365,
0.012627187184989452,
0.03239017352461815,
-0.045764438807964325,
-0.01909988932311535,
-0.03575985133647919,
0.024536438286304474,
0.03699309006333351,
-0.01705746166408062,
-0.020288724452257156,
-0.00035790918627753854,
0.027712030336260796,
0.00941910408437252,
-0.004693213850259781,
0.010954475030303001,
0.027313387021422386,
-0.02662820555269718,
0.028846990317106247,
-0.04544994235038757,
-0.006449675653129816,
-0.02983228862285614,
0.02637861855328083,
-0.0560651458799839,
0.0012781867990270257,
0.029211534187197685,
0.02483384869992733,
-0.0037450247909873724,
0.015058760531246662,
-0.0021653410512953997,
-0.03269831836223602,
-0.04768666625022888,
0.06763555109500885,
-0.016778480261564255,
-0.014234738424420357,
-0.020168263465166092,
0.004030698910355568,
0.045380525290966034,
0.03706938400864601,
-0.039244960993528366,
0.016354640945792198,
-0.03404424712061882,
0.025626245886087418,
-0.008961889892816544,
0.0012682050000876188,
-0.025473563000559807,
-0.0027946685440838337,
0.0007528430433012545,
0.019496671855449677,
0.00494433892890811,
0.04225819185376167,
0.027880553156137466,
0.00026834383606910706,
0.0001626377779757604,
0.003074312349781394,
-0.029046611860394478,
0.03415263816714287,
0.03503189608454704,
-0.018453583121299744,
-0.02018982730805874,
0.010609785094857216,
0.025489576160907745,
-0.0030043781735002995,
-0.033169180154800415,
-0.04474485665559769,
-0.01365450955927372,
-0.012165863998234272,
0.03070720098912716,
-0.007139910478144884,
0.033834680914878845,
-0.0015129059320315719,
0.011077585630118847,
-0.06577255576848984,
0.01789999008178711,
-0.04149891808629036,
0.02083018608391285,
-0.047212276607751846,
-0.037676893174648285,
-0.03473234921693802,
0.0017025310080498457,
-0.04956034943461418,
-0.02155044674873352,
0.021592704579234123,
0.019160525873303413,
-0.01807117834687233,
-0.0008208265644498169,
0.037472669035196304,
-0.009880615398287773,
0.0402449332177639,
-0.022361867129802704,
0.001630978542380035,
0.01571962982416153,
-0.032941095530986786,
-0.08082199841737747,
0.002014392986893654,
-0.017585035413503647,
0.032838281244039536,
0.0182975884526968,
-0.020605744794011116,
-0.03890146315097809,
0.08824805170297623,
-0.016075046733021736,
-0.003875056514516473,
0.0005823473911732435,
0.002399152610450983,
-0.03378124535083771,
-0.0026529585011303425,
0.018333638086915016,
-0.06287416070699692,
0.0007510261493735015,
0.010090316645801067,
0.004348676186054945,
0.000611260300502181,
0.0050088101997971535,
-0.008281323127448559,
0.018403591588139534,
0.00801001489162445,
0.014573291875422001,
0.003911053761839867,
0.043157197535037994,
0.048374149948358536,
-0.007323169149458408,
0.027016913518309593,
0.02471073344349861,
0.004830946214497089,
-0.07141997665166855,
0.01651490479707718,
-0.03308168426156044,
0.01983026973903179,
0.008991328999400139,
-0.07152853161096573,
-0.00041545782005414367,
0.02226213552057743,
-0.048567306250333786,
0.005282403435558081,
-0.0673888623714447,
-0.018265118822455406,
-0.04997522011399269,
0.0024319139774888754,
0.008604351431131363,
0.07219003140926361,
0.05860954150557518,
0.018290381878614426,
0.010502669960260391,
-0.01805596612393856,
-0.02587950974702835,
-0.0019075465388596058,
0.021514877676963806,
-0.004159496631473303,
-0.02629757858812809,
0.025450395420193672,
0.07452370971441269,
-0.008863160386681557,
-0.02337358333170414,
0.03548212721943855,
0.03745495527982712,
0.020466426387429237,
0.003424285678192973,
0.029523424804210663,
0.021726392209529877,
0.009040987119078636,
0.02781505137681961,
-0.015181579627096653,
-0.009404823184013367,
0.03405759856104851,
0.005455647129565477,
0.014885282143950462,
-0.027476118877530098,
-0.007543343119323254,
0.007136414293199778,
-0.029357558116316795,
-0.02671399898827076,
-0.00906948558986187,
-0.006902244873344898,
0.02494204416871071,
0.005662376061081886,
0.001877004629932344,
0.02701285481452942,
-0.027299560606479645,
0.005933740641921759,
-0.038913629949092865,
-0.04401734098792076,
0.010766618885099888,
-0.008827775716781616,
-0.007524142041802406,
0.03898704797029495,
-0.011255045421421528,
-0.0279222521930933,
-0.004396996460855007,
-0.001852610963396728,
0.0033143176697194576,
-0.030373452231287956,
0.014598510228097439,
-0.01405587512999773,
-0.040747545659542084,
-0.020475925877690315,
-0.045224763453006744,
0.0019401090685278177,
0.07758679240942001,
-0.005070995539426804,
0.03554827347397804,
0.01470562070608139,
-0.04156144708395004,
-0.026397883892059326,
-0.06999338418245316,
0.03898034244775772,
-0.0338904932141304,
-0.003136241342872381,
-0.04100897163152695,
-0.05869536101818085,
0.02624371647834778,
-0.02774921804666519,
0.06294690072536469,
-0.03805446997284889,
0.03517784923315048,
0.0466059073805809,
-0.006312496028840542,
-0.008296332322061062,
-0.05297400429844856,
0.01893763616681099,
0.012512825429439545,
-0.055975887924432755,
-0.008267435245215893,
-0.00692186551168561,
-0.043071579188108444,
0.01052064448595047,
0.02333238162100315,
-0.006497150752693415,
0.048760779201984406,
0.03330637887120247,
-0.020749161019921303,
0.03192654624581337,
0.04037138447165489,
-0.004182213451713324,
0.07502413541078568,
-0.01248530950397253,
0.003118228865787387,
0.03836255148053169,
-0.0175304152071476,
-0.02622884325683117,
0.04837368428707123,
0.005266172811388969,
-0.010372379794716835,
-0.023828767240047455,
-0.02366507425904274,
0.007850851863622665,
-0.047994453459978104,
0.0025421015452593565,
0.055483628064394,
-0.03730332851409912,
0.014823269098997116,
0.038520071655511856,
0.021140260621905327,
0.038743190467357635,
-0.05075608566403389,
0.03550559654831886,
0.004131391178816557,
0.001362582086585462,
-0.00645647244527936,
0.03585916385054588,
0.03926987200975418,
-0.008990813978016376,
0.02267644740641117,
0.04022349417209625,
0.012557129375636578,
0.012912719510495663,
0.017040256410837173,
0.04425730183720589,
-0.02730381488800049,
-0.017196113243699074,
-0.0005670149112120271,
-0.03647555038332939,
0.014712996780872345,
0.020520001649856567,
-0.04833730310201645,
0.07229236513376236,
-0.012860814109444618,
0.008056625723838806,
0.051166463643312454,
-0.00005392481034505181,
-0.02495773322880268,
0.015127819962799549,
-0.035910382866859436,
0.014488693326711655,
0.02386198379099369,
-0.02874036692082882,
0.0019820970483124256,
0.0017544995062053204,
0.06488803774118423,
0.044201262295246124,
0.030465906485915184,
-0.015096541494131088,
0.0007651164778508246,
-0.030489157885313034,
-0.009205163456499577,
-0.025073109194636345,
-0.02104780077934265,
0.009564202278852463,
0.025317896157503128,
0.012035530060529709,
0.0015331683680415154,
-0.016394849866628647,
-0.0031334487721323967,
0.043613046407699585,
-0.07149302214384079,
-0.010611601173877716,
-0.003437157953158021,
0.020068207755684853,
-0.015558908693492413,
0.01270854752510786
] |
<p>My understanding of weak gravitational lensing is that it assumes random alignment distribution of galaxies in order to estimate statistical shear and convergences, which are used to estimate matter distributions. This might be subject to noise that depends on the granularity and presence of galaxies, and the expected ellipticity of the galaxies.</p>
<p>matter sources will deflect light in several wavelengths in different amounts. Also, there are different backgrounds at different wavelengths that should be deflected consistently by real matter sources, specially dark matter.</p>
<p>Is such kind of multi-spectral, multi-background correlation analysis a standard procedure to validate dark matter concentrations? I'm particularly interested in the case of the Bullet Cluster, which is kind of <em>the</em> pivotal example to support dark matter.</p>
<p>For instance, CMB light should be deflected by dark matter just like far-away galaxies. I'm guessing without much knowledge about the subject that convergence of CMB is hard to estimate because it is mostly undistinguishable from thermal fluctuations (possibly with the exception of polarization of the CMB, which I won't discuss). But if we could correlate lensing/fluctuations of the CMB with galactic lensing (which is at different wavelengths, and at a different background), then one could in principle tell what features of the CMB are due to fluctuations and which one are due to actual lensing effects. Only real dark matter concentrations will persist across the spectrum and across the background. Measurement noise should be substantially reduced if done properly.</p>
<p>Does this analysis sounds accurate?</p>
| 10,827 |
[
-0.015318269841372967,
0.008617966435849667,
0.032365087419748306,
-0.06411237269639969,
0.06777146458625793,
0.050741638988256454,
-0.009164839051663876,
-0.06381285190582275,
-0.006860273890197277,
-0.04813897982239723,
0.030996287241578102,
0.0249718576669693,
0.06420807540416718,
0.026088573038578033,
0.029136482626199722,
-0.0008216964779421687,
0.019326023757457733,
-0.012239002622663975,
-0.01401145663112402,
-0.04310823231935501,
0.008439673110842705,
0.05047864094376564,
0.011617361567914486,
0.0014435179764404893,
-0.025991521775722504,
0.0047578588128089905,
-0.005707149393856525,
-0.004426090512424707,
0.003712174016982317,
0.06461482495069504,
-0.025496037676930428,
0.022468166425824165,
0.0008317339816130698,
0.06399811804294586,
0.009143901988863945,
-0.004193446133285761,
-0.026625515893101692,
-0.042448822408914566,
-0.007147118914872408,
0.026429789140820503,
-0.04947447031736374,
-0.002050569513812661,
0.0013308146735653281,
0.04209723696112633,
-0.027382265776395798,
0.0013513551093637943,
-0.007324023637920618,
0.004543669987469912,
0.07300684601068497,
-0.04455205425620079,
0.07145045697689056,
0.019020793959498405,
0.021488923579454422,
0.052622560411691666,
-0.03335507959127426,
-0.012620976194739342,
0.07307878881692886,
0.08123014122247696,
-0.015160317532718182,
-0.032887447625398636,
-0.03581584244966507,
-0.022453563287854195,
0.019790399819612503,
0.0032339596655219793,
-0.005266634281724691,
0.05891702324151993,
-0.03436409309506416,
-0.007707361131906509,
0.019710909575223923,
0.005531127564609051,
0.034096721559762955,
-0.0015333079500123858,
0.01365837175399065,
-0.013511433266103268,
0.005433350335806608,
-0.005263058468699455,
0.011960456147789955,
0.0058776577934622765,
0.007354480214416981,
0.030252451077103615,
0.0016307260375469923,
-0.017433440312743187,
-0.018475083634257317,
0.017497459426522255,
0.0294321421533823,
0.008250512182712555,
0.08381596207618713,
-0.06729727238416672,
-0.00348792877048254,
0.023965809494256973,
-0.0015851488569751382,
0.012191197834908962,
0.038397956639528275,
-0.009381033480167389,
-0.06250908970832825,
0.037571653723716736,
-0.008021215908229351,
0.03261717036366463,
-0.0005582293961197138,
-0.014109250158071518,
-0.012290313839912415,
-0.00971372239291668,
-0.01058237999677658,
0.06912031024694443,
-0.029619598761200905,
-0.023680005222558975,
-0.02997838333249092,
0.006903056055307388,
-0.05705716460943222,
-0.008422168903052807,
-0.021333303302526474,
0.006833036430180073,
0.01705440878868103,
-0.03043478913605213,
0.03360743820667267,
-0.0013912790454924107,
0.012168584391474724,
-0.04019153490662575,
0.06565047800540924,
0.06838636845350266,
0.023114556446671486,
0.009326654486358166,
-0.002505919197574258,
-0.07051381468772888,
-0.026846518740057945,
0.026321301236748695,
0.09347661584615707,
0.007894368842244148,
-0.04015548154711723,
0.027240749448537827,
0.03873775899410248,
-0.0058823153376579285,
0.012442594394087791,
0.010816331952810287,
0.021939506754279137,
-0.026395251974463463,
-0.07070174068212509,
-0.08084997534751892,
0.052851419895887375,
-0.012214620597660542,
-0.0013504644157364964,
-0.0038639456033706665,
-0.014472872018814087,
0.039854805916547775,
0.07616227865219116,
0.020437762141227722,
0.03393610194325447,
-0.025806987658143044,
0.04897890239953995,
0.0021148305386304855,
-0.05125052109360695,
0.010998640209436417,
-0.024071935564279556,
-0.016467638313770294,
-0.0382552295923233,
-0.11599864065647125,
0.01597891002893448,
0.026745563372969627,
0.020270876586437225,
-0.03283906728029251,
0.07051560282707214,
0.005173377692699432,
0.011904335580766201,
-0.011507812887430191,
0.006097792182117701,
-0.017898840829730034,
0.04110238701105118,
0.005312593188136816,
0.029754724353551865,
0.0372794009745121,
-0.014547297731041908,
0.026072930544614792,
0.03434503450989723,
0.01639602892100811,
0.01403873972594738,
-0.05308934673666954,
0.005259084049612284,
-0.012114018201828003,
-0.013229011557996273,
0.014115937054157257,
-0.023204049095511436,
-0.0083873076364398,
-0.02484903670847416,
-0.01731039397418499,
0.02236800082027912,
0.018384110182523727,
0.009695745073258877,
-0.026251859962940216,
0.03228824585676193,
-0.03765739127993584,
0.004193547647446394,
-0.057836417108774185,
-0.010727821849286556,
-0.03675344958901405,
0.003014928661286831,
0.035757288336753845,
0.0023061812389642,
0.012430870905518532,
0.01954391598701477,
-0.03802410885691643,
-0.004480615723878145,
0.025788933038711548,
-0.011083493940532207,
-0.0007866120431572199,
-0.009442346170544624,
-0.02166479453444481,
0.018447333946824074,
-0.015106543898582458,
-0.005280415527522564,
-0.005099037662148476,
-0.03966398164629936,
-0.002611808478832245,
-0.024784987792372704,
0.008096841163933277,
-0.01568990759551525,
0.01143326424062252,
0.013765391893684864,
0.012157744728028774,
0.00277445325627923,
0.016460390761494637,
-0.046416886150836945,
0.07148899883031845,
0.027399640530347824,
-0.0038147110026329756,
-0.04916578158736229,
0.0308495182543993,
-0.00793355330824852,
-0.007634577341377735,
-0.014460276812314987,
-0.028609316796064377,
-0.09514549374580383,
-0.018155336380004883,
0.028199922293424606,
0.05942842364311218,
-0.013155338354408741,
0.05306203290820122,
0.05818675830960274,
0.050263140350580215,
-0.017056768760085106,
-0.00823628343641758,
-0.05166499316692352,
-0.026347631588578224,
0.013397241942584515,
0.0407203733921051,
0.024509096518158913,
0.01687251776456833,
0.0014255486894398928,
-0.005794487427920103,
-0.023467442020773888,
-0.02519761212170124,
-0.020107686519622803,
0.01973687671124935,
0.015527724288403988,
-0.011572541669011116,
-0.011707939207553864,
-0.017782844603061676,
0.03180612623691559,
0.022369608283042908,
0.017104757949709892,
0.05232653021812439,
0.019495675340294838,
-0.022395571693778038,
-0.0326981395483017,
-0.025609716773033142,
0.0251669492572546,
0.012867742218077183,
-0.0748983770608902,
-0.031639400869607925,
0.015433341264724731,
-0.0390191487967968,
0.003865101607516408,
-0.01813920959830284,
0.00024701253278180957,
-0.03731655329465866,
0.022352954372763634,
0.018661735579371452,
0.024639876559376717,
0.022869115695357323,
-0.05376918986439705,
-0.043530162423849106,
0.03618055209517479,
0.030779751017689705,
-0.003640830982476473,
0.006027198862284422,
-0.036718133836984634,
0.017039945349097252,
-0.019577639177441597,
0.007060473784804344,
0.01382431946694851,
0.005335526075214148,
0.016992101445794106,
0.01148973684757948,
0.027982482686638832,
-0.06705072522163391,
0.010048282332718372,
0.019212141633033752,
0.00820247270166874,
-0.010557871311903,
0.006934672128409147,
0.03385242447257042,
0.006544495467096567,
-0.026615066453814507,
0.03202509880065918,
-0.025269661098718643,
-0.04153886437416077,
-0.028779249638319016,
0.0011921949917450547,
0.008882788941264153,
-0.03574664518237114,
0.04568447172641754,
0.02751537226140499,
-0.031213633716106415,
0.01208723708987236,
-0.03339361399412155,
-0.05607070401310921,
0.034295693039894104,
-0.02348906174302101,
0.04220160096883774,
-0.024021875113248825,
-0.0014266108628362417,
0.04924317076802254,
0.04846153035759926,
-0.015268526040017605,
-0.015192256309092045,
0.022154731675982475,
-0.04374886676669121,
-0.012633394449949265,
0.00783617328852415,
0.0014377827756106853,
0.03620145842432976,
0.037213243544101715,
0.055729977786540985,
0.011585087515413761,
0.04333892837166786,
-0.0018016649410128593,
-0.004483055789023638,
0.020430410280823708,
-0.019646991044282913,
0.00028561169165186584,
0.023155000060796738,
0.036285798996686935,
-0.0020466132555156946,
0.006932377349585295,
-0.01477113924920559,
0.02124032936990261,
0.0038708236534148455,
-0.05403035879135132,
0.03567621111869812,
-0.028632083907723427,
-0.005298867356032133,
-0.022858593612909317,
0.008545758202672005,
0.01692049577832222,
-0.008006841875612736,
0.0024614145513623953,
-0.006752012763172388,
0.053346484899520874,
0.016036737710237503,
-0.0017917834920808673,
0.042182788252830505,
0.038221005350351334,
0.01652589440345764,
-0.02530524879693985,
0.010472903959453106,
-0.005628820043057203,
0.012551882304251194,
-0.0465083047747612,
-0.01449735276401043,
0.01527728047221899,
0.03450973704457283,
0.006642050109803677,
-0.02437387779355049,
-0.013923050835728645,
0.03430714085698128,
-0.04078816622495651,
0.025927536189556122,
-0.023231199011206627,
0.014910439029335976,
0.003716327017173171,
0.044793758541345596,
0.03361765667796135,
-0.016881732270121574,
0.010251789353787899,
-0.003093454986810684,
-0.05953901633620262,
0.0059351846575737,
-0.030880307778716087,
-0.02228526584804058,
-0.012766779400408268,
-0.02417728304862976,
-0.003295835107564926,
-0.032510485500097275,
0.006734247785061598,
-0.04505014792084694,
0.012349230237305164,
-0.024037498980760574,
-0.003464855719357729,
-0.039359066635370255,
-0.07699841260910034,
0.006900570821017027,
0.029483018442988396,
0.035330839455127716,
0.02025783807039261,
0.04612186551094055,
0.015421034768223763,
0.00032346980879083276,
-0.028124362230300903,
-0.011463135480880737,
0.03205409646034241,
-0.03577824681997299,
0.05781523510813713,
-0.020500751212239265,
0.03419532626867294,
-0.024175843223929405,
0.0016499690245836973,
0.06428457051515579,
0.043019041419029236,
0.034844156354665756,
-0.00678588729351759,
0.016767747700214386,
-0.022021761164069176,
-0.030938751995563507,
0.03570910170674324,
0.030589843168854713,
0.002240668283775449,
-0.0008361481013707817,
0.0384281724691391,
0.03796303644776344,
-0.02991269715130329,
0.03152284026145935,
0.05175625532865524,
-0.029940515756607056,
-0.03624251112341881,
-0.06337547302246094,
-0.03350354731082916,
0.021274229511618614,
0.013360103592276573,
0.05224098265171051,
-0.017269304022192955,
-0.0009002059232443571,
0.007614622358232737,
0.0014190683141350746,
0.004037636332213879,
-0.029144421219825745,
0.005762570537626743,
-0.005872273817658424,
0.012311183847486973,
-0.008540159091353416,
0.0258975550532341,
0.04095529764890671,
0.07589354366064072,
0.053617507219314575,
0.031376857310533524,
-0.020497480407357216,
-0.07096365094184875,
0.019960299134254456,
0.021961122751235962,
0.016264688223600388,
-0.02876269817352295,
-0.0011978762922808528,
-0.05745970457792282,
-0.029132381081581116,
0.07046210765838623,
0.0019597350619733334,
0.02655387483537197,
0.018097616732120514,
0.010525630787014961,
-0.00710296630859375,
-0.001186183886602521,
-0.026303807273507118,
0.014300464652478695,
-0.012118586339056492,
-0.018669432029128075,
-0.038130857050418854,
0.00435011787340045,
-0.037929147481918335,
0.004901209846138954,
0.032674744725227356,
0.04687514528632164,
0.013051874004304409,
-0.015664787963032722,
-0.004902040585875511,
-0.014123272150754929,
0.021574243903160095,
-0.09170567244291306,
0.02000034786760807,
-0.014587326906621456,
-0.03398958221077919,
0.03329315036535263,
-0.007216610945761204,
-0.003806689288467169,
0.03051728941500187,
-0.00543783325701952,
0.011877965182065964,
0.023735567927360535,
-0.024433620274066925,
0.03569146245718002,
0.02626628987491131,
0.013852535746991634,
0.0651927962899208,
0.027939356863498688,
-0.0005675129941664636,
0.028419751673936844,
-0.01468371506780386,
0.04677576199173927,
-0.04985526204109192,
0.0006190326530486345,
-0.002971433801576495,
-0.015886550769209862,
-0.027750074863433838,
0.04861829802393913,
0.0289080198854208,
0.01846303418278694,
0.03350256383419037,
-0.01566595397889614,
0.011608071625232697,
0.027319591492414474,
0.01512460969388485,
0.0316489115357399,
0.02577032893896103,
0.03979765623807907,
-0.0022792776580899954,
0.006059848237782717,
0.036180514842271805,
0.00127335824072361,
-0.011290906928479671,
-0.0017823830712586641,
-0.014793464913964272,
-0.006531380582600832,
0.00842259917408228,
0.0012809361796826124,
-0.015989333391189575,
-0.0038369689136743546,
0.05618591606616974,
0.0022922030184417963,
0.03464367985725403,
0.047594744712114334,
-0.06386957317590714,
-0.02935347892343998,
0.007172817829996347,
-0.03396473452448845,
0.03285413235425949,
-0.03821307420730591,
-0.00663779815658927,
-0.008300622925162315,
0.028613056987524033,
-0.08390554040670395,
0.008035942912101746,
-0.03403380513191223,
0.038995835930109024,
-0.010094336234033108,
-0.013000241480767727,
0.018969060853123665,
-0.032529234886169434,
-0.020990196615457535,
-0.030868278816342354,
0.04965990036725998,
-0.01425869669765234,
-0.008222728967666626,
-0.009463937021791935,
0.01713710092008114,
0.05561777204275131,
-0.012731972150504589,
-0.012874254956841469,
0.03313539922237396,
-0.0038641691207885742,
0.010612938553094864,
0.009553859010338783,
0.02389952726662159,
-0.020732618868350983,
-0.031250014901161194,
-0.0585622563958168,
-0.00011092048225691542,
0.014534332789480686,
-0.05603180080652237,
-0.011973727494478226,
0.03219810128211975,
0.0031343691516667604,
0.0044443923979997635,
-0.0053563364781439304,
0.020421933382749557,
-0.04562069848179817,
0.01727946102619171,
0.00937390886247158,
-0.005743810907006264,
0.012961730360984802,
-0.03715142235159874,
0.07441416382789612,
-0.0029905205592513084,
0.0005339720519259572,
0.03443796932697296,
0.05446603149175644,
0.022456016391515732,
-0.016496066004037857,
0.002891442272812128,
-0.017145894467830658,
0.010409250855445862,
-0.037520382553339005,
0.05001911520957947,
0.018992867320775986,
-0.0008474191417917609,
-0.023461727425456047,
-0.06554959714412689,
-0.006137077696621418,
-0.02001757174730301,
0.07525172084569931,
0.013943318277597427,
0.032261963933706284,
0.013330580666661263,
-0.029319727793335915,
-0.01236228458583355,
-0.048142753541469574,
0.005162044428288937,
-0.0032028928399086,
0.005642212461680174,
0.02438725344836712,
-0.06766863167285919,
-0.030116166919469833,
0.010472860187292099,
0.04428380727767944,
-0.007746543735265732,
0.01452653855085373,
0.018664350733160973,
0.026288777589797974,
0.013967830687761307,
-0.0213901586830616,
-0.07105504721403122,
0.017184797674417496,
-0.04525389149785042,
0.024791980162262917,
0.009626566432416439,
0.0007858117460273206,
0.04440741986036301,
0.025321807712316513,
-0.004379849415272474,
-0.02586410567164421,
-0.028868181630969048,
-0.05493801459670067,
0.024498948827385902,
0.02576051838696003,
0.01623961143195629,
-0.006881624925881624,
-0.007899226620793343,
0.01652262732386589,
0.006688258145004511,
0.003244072664529085,
-0.0036722554359585047,
-0.09934592992067337,
-0.04976552724838257,
0.00040100186015479267,
-0.04650005325675011,
0.048229068517684937,
-0.03694071248173714,
-0.0395243838429451,
0.018782243132591248,
-0.014997717924416065,
0.010636714287102222,
0.024876493960618973,
0.003293639048933983,
-0.045476771891117096,
0.04579496011137962,
-0.02227214351296425,
0.009398490190505981,
-0.05265660583972931,
-0.003671735292300582,
0.12113425880670547,
0.043462418019771576,
0.020079532638192177,
-0.06207192689180374,
-0.02784840576350689,
-0.015049822628498077,
0.00215861015021801,
-0.0435299426317215,
-0.0021118419244885445,
-0.04317585378885269,
0.04154352471232414,
0.005705974996089935,
0.0639304518699646,
0.006855260580778122,
-0.0328582301735878,
0.04871334135532379,
-0.020106619223952293,
-0.029640834778547287,
0.04923219606280327,
0.02132258377969265,
-0.02621101401746273,
0.028107590973377228,
-0.04809548333287239,
0.022851046174764633,
0.010895061306655407,
-0.02280174195766449,
-0.01999470964074135,
-0.018387554213404655,
-0.03488661348819733,
-0.0010322695598006248,
-0.03225331753492355,
0.006564523559063673,
-0.005730197299271822,
-0.018901243805885315,
-0.006451368797570467,
0.016145022585988045,
0.014862019568681717,
-0.022054709494113922,
0.03695202246308327,
0.010268163867294788,
-0.01389292348176241,
-0.0056271846406161785,
-0.0012673846213147044,
-0.03311879187822342,
-0.014120840467512608,
-0.03285199776291847,
-0.0035880140494555235,
0.056783951818943024,
-0.03512661159038544,
-0.012544038705527782,
0.0013614350464195013,
0.008371548727154732,
0.017524681985378265,
-0.02801114320755005,
0.013720528222620487,
-0.023216497153043747,
0.0002978131524287164,
-0.05144153907895088,
-0.028876109048724174,
-0.01003525871783495,
0.029720837250351906,
0.00966194923967123,
0.01724918745458126,
-0.02511230669915676,
0.031106751412153244,
-0.03972744569182396,
-0.01348506286740303,
0.0687294751405716,
-0.0028371575754135847,
0.0035515795461833477,
-0.04098822548985481,
0.0032267477363348007,
-0.034680917859077454,
-0.0016245252918452024,
0.005723212845623493,
-0.010411056689918041,
0.045111458748579025,
0.011414360255002975,
0.01267267856746912,
-0.0011120109120383859,
-0.08011183142662048,
0.035707682371139526,
-0.013293035328388214,
-0.013645988889038563,
-0.021083524450659752,
0.00793822668492794,
0.021468162536621094,
0.040119655430316925,
0.03609586879611015,
-0.010906433686614037,
-0.04561305418610573,
0.021599536761641502,
0.019420532509684563,
-0.020830323919653893,
-0.028706612065434456,
0.005547935143113136,
-0.010232563130557537,
-0.016309749335050583,
-0.0344468355178833,
0.016751863062381744,
-0.016141321510076523,
0.02237827517092228,
-0.009348594583570957,
0.010143551044166088,
-0.009177378378808498,
0.012375916354358196,
-0.009412228129804134,
-0.027030162513256073,
-0.01979420706629753,
0.033033039420843124,
0.01968163624405861,
-0.012034581042826176,
-0.021416442468762398,
-0.05334007740020752,
-0.01328881923109293,
0.04061569646000862,
-0.01449740119278431,
-0.06312775611877441,
-0.010208764113485813,
0.014312741346657276,
-0.00006142681377241388,
-0.07909026741981506,
0.016468767076730728,
-0.014266390353441238,
0.012843484058976173,
0.013667013496160507,
-0.003681852715089917,
0.0531059168279171,
0.019313808530569077,
-0.027875859290361404,
-0.07757405191659927,
0.03293544799089432,
-0.016460983082652092,
0.002334887394681573,
0.016145115718245506,
0.019390318542718887,
-0.003165678819641471,
0.043865181505680084,
-0.0017637426499277353,
-0.04407196119427681,
0.020641973242163658,
-0.05123400688171387,
-0.061014048755168915,
0.03843921422958374,
-0.0069198161363601685,
0.025764424353837967,
-0.0005301733035594225,
-0.0041490960866212845,
-0.02714255452156067,
0.027230050414800644,
-0.027542203664779663,
-0.019088102504611015,
0.00037945149233564734,
0.015468047931790352,
0.0363013856112957,
0.006172755733132362,
0.0401541106402874,
-0.026680536568164825,
-0.006107047200202942,
0.049332719296216965,
0.009421207010746002,
0.0041015916503965855,
-0.03252910077571869,
0.009765944443643093,
-0.07563919574022293,
0.0064026243053376675,
-0.02131224051117897,
0.03600884974002838,
0.017651017755270004,
0.045263923704624176,
-0.04155423864722252,
0.04768417775630951,
0.04260054975748062,
0.011355506256222725,
-0.08604401350021362,
-0.0033548364881426096,
-0.0014575584791600704,
0.00978538766503334,
0.025561703369021416,
-0.03977767378091812,
0.014441906474530697,
-0.0061425259336829185,
-0.05662019923329353,
0.007184070535004139,
-0.026878921315073967,
-0.040706414729356766,
-0.027714621275663376,
0.02413569577038288,
-0.02346494048833847,
0.014558403752744198,
0.027430318295955658,
0.025901425629854202,
-0.013200964778661728,
0.035190388560295105,
-0.006626935210078955,
0.008964085020124912,
-0.022614875808358192,
-0.0010544240940362215,
0.04186391085386276,
0.004089773632586002,
0.08095743507146835,
0.007341962307691574,
-0.03413674607872963,
0.02628718875348568,
0.004480699542909861,
0.00864097848534584,
-0.016097068786621094,
-0.015809115022420883,
0.002604447538033128,
0.009349660947918892,
-0.0024827877059578896,
-0.004017062019556761,
-0.000647161272354424,
0.0326373316347599,
0.009689349681138992,
0.04787185788154602,
-0.014174962416291237,
0.01260128989815712,
-0.00031548007973469794,
-0.05698610842227936,
-0.029340067878365517,
0.01859860122203827,
-0.0026021949015557766,
-0.0016510996501892805,
0.00888015702366829,
0.019242724403738976,
0.01762424409389496,
0.010018594563007355,
0.040349896997213364,
-0.05372938886284828,
-0.007299104239791632,
0.03815366327762604,
0.052189167588949203,
-0.048536352813243866,
0.015540285035967827,
0.011537197977304459,
-0.0595780648291111,
0.019266290590167046,
-0.009032277390360832,
-0.03783690556883812,
0.0084762554615736,
-0.0006691024755127728,
0.003780463943257928,
-0.011080232448875904,
0.02496969699859619,
-0.03447557985782623,
-0.03700890392065048,
0.07830093801021576,
-0.038212329149246216,
0.019379766657948494,
-0.0186480600386858,
-0.04768367484211922,
-0.036125972867012024,
-0.04634512960910797,
-0.0007420626352541149,
-0.011540931649506092,
0.026230433955788612,
0.004983784630894661,
-0.02818572334945202,
-0.026469102129340172,
0.0011727031087502837,
0.02907479554414749,
-0.010946475900709629,
-0.0015207440592348576,
0.026163605973124504,
-0.02989199012517929,
0.019076207652688026,
-0.06753439456224442,
0.006105202715843916,
0.009819811210036278,
0.029289230704307556,
-0.009483085945248604,
-0.02484061010181904,
0.004898045212030411,
-0.0014742860803380609,
0.04069497808814049,
-0.011256004683673382,
0.014126099646091461,
0.022802291437983513,
-0.03466697409749031,
0.07904426753520966,
0.018569674342870712,
-0.03261188417673111,
0.05838194862008095,
-0.0022584358230233192,
0.012641625478863716,
0.023321790620684624,
0.023032359778881073,
-0.049029525369405746,
0.013223977759480476,
-0.011411458253860474,
-0.04091919586062431,
0.014490344561636448,
0.06686407327651978,
-0.003713867859914899,
-0.03003007546067238,
-0.014708858914673328,
0.0037307143211364746,
-0.04093310236930847,
-0.009251045063138008,
0.02868526056408882,
-0.026581475511193275,
0.04485411196947098,
0.016365258023142815,
-0.029063409194350243,
0.005342074204236269,
-0.0002046838926617056,
-0.023555926978588104,
0.029672134667634964,
0.05266944691538811,
0.03343365341424942,
0.01391162071377039,
-0.0008199914009310305,
-0.01469044853001833,
0.000058055080444319174,
-0.035969819873571396,
0.03201698511838913,
-0.0721190944314003,
-0.01882478967308998,
0.015475397929549217,
0.0043699112720787525,
-0.015267395414412022,
-0.006071606185287237,
0.011486977338790894,
0.08292187750339508,
-0.030214481055736542,
-0.029092855751514435,
-0.01952480711042881,
-0.06765758991241455,
-0.024425985291600227,
0.040450118482112885,
-0.015622356906533241,
0.030769681558012962,
0.034250129014253616,
0.0030642584897577763,
-0.01833326369524002,
0.019961442798376083,
0.04488804563879967,
-0.049716562032699585,
-0.002888899529352784,
-0.008393796160817146,
-0.030570654198527336,
0.0166215430945158,
0.02728157676756382,
-0.01879664696753025,
-0.04140869900584221,
0.023414507508277893,
0.025456322357058525,
0.023410692811012268,
-0.020623518154025078,
0.010468876920640469,
-0.035199929028749466,
0.013985168188810349,
-0.04138132184743881,
0.010632061399519444,
-0.033212028443813324,
0.02706291154026985,
0.00382880587130785,
-0.011625579558312893
] |
<p>I have always pictured <a href="http://en.wikipedia.org/wiki/Volume_element" rel="nofollow">volume element</a> as a small cuboid in with volume $dx dy dz$. however in <a href="http://en.wikipedia.org/wiki/Curvilinear_coordinates" rel="nofollow">curvilinear system</a>, how would the shape of this volume element be?</p>
<p>I mean in spherical polar coordinate system, how the shape of this volume element be visualized (is it a small sphere whose integration give the volume of object or same), or my idea of 3D Cartesian coordinate absolutely wrong.</p>
| 10,828 |
[
-0.03583230823278427,
-0.003502350766211748,
0.010136251337826252,
-0.007314902264624834,
0.07229536771774292,
0.036518193781375885,
-0.022930234670639038,
-0.04819519445300102,
0.05326421186327934,
-0.04075853154063225,
0.043491218239068985,
0.025543026626110077,
0.08491399884223938,
0.0440702848136425,
0.029132874682545662,
-0.02098405733704567,
-0.03546690195798874,
-0.011293168179690838,
0.004638844635337591,
-0.02623598277568817,
0.021847033873200417,
0.0056734709069132805,
-0.0014359545893967152,
0.0188409723341465,
0.016298718750476837,
0.05811174958944321,
0.03386138379573822,
-0.011836333200335503,
0.015525132417678833,
0.07249205559492111,
-0.0348794050514698,
-0.037397243082523346,
0.021745305508375168,
0.0013991211308166385,
0.01121272798627615,
0.0015132622793316841,
-0.018211888149380684,
-0.016208168119192123,
0.00013980553194414824,
0.01945437304675579,
-0.03809129446744919,
-0.012842999771237373,
-0.030679019168019295,
0.07519526779651642,
-0.012450826354324818,
0.022181708365678787,
-0.02282240241765976,
-0.024649137631058693,
0.005818437784910202,
-0.06435788422822952,
0.056911833584308624,
0.023979535326361656,
0.013901243917644024,
0.038930635899305344,
0.008862724527716637,
-0.001973823644220829,
0.0442228801548481,
0.07754621654748917,
-0.01877598464488983,
-0.04655136168003082,
-0.0036411667242646217,
-0.021331049501895905,
0.016226671636104584,
-0.01666812226176262,
-0.014444487169384956,
0.018816284835338593,
-0.001381120877340436,
-0.02870803512632847,
-0.00606033019721508,
-0.0003198741178493947,
0.019506746903061867,
0.010758942924439907,
0.017863929271697998,
-0.040134724229574203,
0.009288656525313854,
-0.01941108889877796,
0.027491111308336258,
0.030704136937856674,
0.06895998865365982,
-0.0207748394459486,
-0.00822362955659628,
0.014408853836357594,
0.020395498722791672,
0.025231361389160156,
-0.002189239952713251,
0.04020461440086365,
0.056868381798267365,
-0.023459147661924362,
-0.0018007924081757665,
0.030727211385965347,
-0.0129843819886446,
0.009810351766645908,
0.012890649959445,
-0.03360721096396446,
0.003090683836489916,
0.011406105943024158,
-0.008596411906182766,
0.03943298012018204,
0.019104275852441788,
-0.050234731286764145,
0.02498360350728035,
-0.024071630090475082,
-0.012120441533625126,
0.06019001454114914,
0.010872185230255127,
-0.003437543986365199,
-0.03785902261734009,
0.020766740664839745,
-0.009967345744371414,
-0.027422280982136726,
-0.053904272615909576,
0.035001419484615326,
0.0036638870369642973,
0.015195177868008614,
0.02138480730354786,
-0.02175506204366684,
-0.020485632121562958,
-0.021074457094073296,
0.04434995353221893,
0.03475436568260193,
0.05964706093072891,
-0.011711809784173965,
0.023407267406582832,
-0.04110972583293915,
-0.07761190086603165,
0.015196169726550579,
0.03440188616514206,
0.013588469475507736,
0.0016338219866156578,
0.025000164285302162,
0.04885271191596985,
-0.038968704640865326,
0.02740117534995079,
0.0047127120196819305,
0.027531644329428673,
-0.011608115397393703,
-0.05102573335170746,
-0.04553760960698128,
0.03511990234255791,
0.012526044622063637,
-0.011034827679395676,
-0.06308212876319885,
0.007791955955326557,
0.04025133699178696,
0.03523285314440727,
0.0013138002250343561,
-0.022448785603046417,
0.051953960210084915,
0.06806062161922455,
-0.005649682134389877,
-0.029366111382842064,
0.0134019386023283,
-0.027952583506703377,
-0.04399769380688667,
0.03424924239516258,
-0.05841600149869919,
0.04233773425221443,
0.031084129586815834,
0.0435795858502388,
-0.039482686668634415,
0.05226055532693863,
-0.04718130826950073,
0.013274118304252625,
0.016106879338622093,
-0.027788760140538216,
-0.020776066929101944,
0.05001052841544151,
-0.010571302846074104,
0.025600258260965347,
0.03254516422748566,
0.02152099832892418,
0.0252390056848526,
-0.007372547406703234,
0.033721502870321274,
0.06452639400959015,
-0.02394562028348446,
-0.02930423617362976,
-0.012874079868197441,
-0.024627914652228355,
0.022562962025403976,
-0.06131613627076149,
-0.041071817278862,
0.010210924781858921,
0.02240254543721676,
0.008121875114738941,
0.05338739976286888,
-0.011193880811333656,
-0.016685141250491142,
0.012782490812242031,
-0.046372879296541214,
-0.01943950541317463,
-0.058521293103694916,
0.01958710327744484,
-0.010999542661011219,
-0.029131602495908737,
0.07796800881624222,
0.0073243253864347935,
0.004577108193188906,
-0.025202512741088867,
0.01915648765861988,
-0.03868112713098526,
0.038227301090955734,
0.003965211566537619,
-0.02114134654402733,
0.02412397228181362,
0.04124562442302704,
0.04657348245382309,
-0.006144564598798752,
-0.0009587019449099898,
-0.02108292654156685,
-0.007423748262226582,
-0.00017657206626608968,
-0.009430781938135624,
0.007852233946323395,
-0.0073000346310436726,
-0.029074113816022873,
-0.04276330769062042,
0.024565020576119423,
-0.00791134126484394,
0.04024939239025116,
-0.04285765439271927,
0.05320703610777855,
0.08160664886236191,
0.005584581755101681,
-0.02725326083600521,
0.031066788360476494,
0.004063038621097803,
0.02535632625222206,
0.010204926133155823,
-0.03273075073957443,
-0.033211346715688705,
0.013570545241236687,
0.06979864090681076,
0.030547471717000008,
-0.035320937633514404,
-0.012216421775519848,
0.03716885298490524,
0.015567999333143234,
0.04796842858195305,
-0.024124637246131897,
0.0024194978177547455,
-0.02562103047966957,
-0.013497753068804741,
0.01909126155078411,
0.03168690949678421,
-0.008115614764392376,
-0.0142134390771389,
0.0011213974794372916,
0.042104076594114304,
0.009176578372716904,
-0.027972795069217682,
0.039198119193315506,
-0.03806529566645622,
0.01027478463947773,
-0.0017171693034470081,
0.007162916474044323,
0.03517117723822594,
-0.03373747318983078,
-0.013360892422497272,
0.037415266036987305,
0.005089327692985535,
-0.012447123415768147,
-0.007604534737765789,
0.02019575797021389,
0.0244633536785841,
0.06092686951160431,
-0.02469681017100811,
-0.023677727207541466,
0.014515219256281853,
-0.04116005077958107,
0.0063232178799808025,
-0.02780378982424736,
-0.008495491929352283,
-0.030564529821276665,
0.0013045382220298052,
0.009960183873772621,
0.003203954780474305,
-0.03609824553132057,
0.00529857911169529,
-0.05981290340423584,
-0.04268292710185051,
-0.023894373327493668,
-0.0073244571685791016,
0.021985327824950218,
-0.04522043839097023,
-0.001592460204847157,
-0.05614308640360832,
-0.006465632934123278,
0.01776280254125595,
0.016456706449389458,
0.011426229029893875,
0.012995698489248753,
-0.022078877314925194,
-0.07418352365493774,
-0.032870400696992874,
-0.007668058853596449,
0.0647357776761055,
-0.02591453678905964,
0.0044614095240831375,
0.009259055368602276,
-0.009994535706937313,
-0.0020919833332300186,
0.00013293490337673575,
-0.02521178312599659,
-0.035081613808870316,
-0.014653410762548447,
-0.004538676701486111,
0.024914544075727463,
-0.020527176558971405,
-0.00899172481149435,
0.04023388400673866,
-0.02155771479010582,
-0.0019591853488236666,
-0.060030341148376465,
-0.05157618224620819,
0.00898668635636568,
-0.00835634395480156,
0.026277268305420876,
-0.028577636927366257,
-0.04452107101678848,
0.08182287961244583,
-0.018244946375489235,
-0.07047894597053528,
-0.017641078680753708,
-0.002076206263154745,
-0.011488569900393486,
-0.014256944879889488,
0.008476746268570423,
-0.006252241786569357,
0.008167296648025513,
0.03407936915755272,
0.015802714973688126,
0.019741076976060867,
-0.00595275079831481,
0.05763350799679756,
-0.004267962649464607,
0.020118724554777145,
0.00831093080341816,
-0.028247300535440445,
0.04511840268969536,
0.022495970129966736,
-0.020305052399635315,
0.011011616326868534,
-0.04304056242108345,
0.03142132610082626,
0.04102790355682373,
-0.03011297807097435,
-0.0015034809475764632,
-0.00479541253298521,
-0.017786361277103424,
0.0028889570385217667,
0.028446150943636894,
0.011853431351482868,
0.003540146630257368,
-0.010102388449013233,
0.041935693472623825,
0.04590645059943199,
-0.012891406193375587,
-0.037825699895620346,
0.014695018529891968,
0.030652105808258057,
-0.025718074291944504,
-0.0024940911680459976,
-0.01179912406951189,
0.0419725626707077,
0.005570938345044851,
0.009377581998705864,
-0.014843177050352097,
0.034114234149456024,
0.032624807208776474,
0.011674297973513603,
0.007966158911585808,
-0.024062877520918846,
0.022815242409706116,
-0.07160990685224533,
0.017442289739847183,
0.01022869348526001,
0.023191386833786964,
0.004953295923769474,
0.03580210730433464,
0.0069683874025940895,
0.00215960037894547,
0.020373784005641937,
-0.002949118847027421,
-0.04410674050450325,
0.0124100586399436,
-0.04349932819604874,
0.016453269869089127,
-0.020887257531285286,
-0.02395719848573208,
-0.034971933811903,
-0.0062644220888614655,
-0.04310637339949608,
0.020121106877923012,
-0.020056838169693947,
-0.06462609767913818,
0.029126005247235298,
-0.009637873619794846,
0.0014649142976850271,
-0.0281682088971138,
0.04603137820959091,
0.03404109925031662,
-0.034193579107522964,
0.032660502940416336,
0.0679868534207344,
-0.011075953021645546,
0.04117024689912796,
0.002122781705111265,
0.00226915767416358,
0.04849633201956749,
0.0035396849270910025,
-0.014759257435798645,
-0.0007360836025327444,
0.03269980847835541,
0.03344276174902916,
-0.0011149159399792552,
0.09253021329641342,
-0.009676840156316757,
0.025492241606116295,
-0.022707713767886162,
-0.05476920306682587,
0.02605665847659111,
-0.015618236735463142,
0.03209472447633743,
-0.009241809137165546,
0.04573693871498108,
0.06477542221546173,
-0.011445671319961548,
-0.018262287601828575,
0.030206365510821342,
0.03569057583808899,
0.0043863775208592415,
-0.017287397757172585,
-0.04952148348093033,
-0.019070789217948914,
-0.03231797739863396,
-0.051396358758211136,
0.05103219300508499,
0.007027897518128157,
-0.02317006140947342,
-0.006902340799570084,
-0.0011931462213397026,
-0.010305695235729218,
-0.04717687889933586,
-0.003572053276002407,
0.013494933024048805,
-0.004410740919411182,
-0.028747420758008957,
-0.0073099285364151,
0.042594071477651596,
0.03428230434656143,
0.02170347236096859,
0.012211077846586704,
-0.019858568906784058,
-0.08019185811281204,
-0.011305760592222214,
0.03463765233755112,
0.024476537480950356,
-0.016374291852116585,
-0.019645825028419495,
-0.06557479500770569,
-0.02457743138074875,
0.06945205479860306,
-0.052932772785425186,
0.008388962596654892,
-0.026241974905133247,
0.016294922679662704,
-0.005347300320863724,
-0.005312591325491667,
-0.025504805147647858,
-0.0085751386359334,
-0.0002651145914569497,
-0.010597645305097103,
-0.018000898882746696,
0.003384459065273404,
0.004164515063166618,
0.03831182420253754,
-0.0035902170930057764,
0.018793458119034767,
0.04346437379717827,
-0.005014658439904451,
0.006204518489539623,
0.04683368280529976,
-0.027808666229248047,
-0.05987013131380081,
-0.000007571197329525603,
0.025614624843001366,
-0.030710911378264427,
0.00009971320105250925,
-0.008436924777925014,
-0.045250311493873596,
0.023971306160092354,
-0.00361352670006454,
0.03053702600300312,
0.03519367799162865,
-0.043572112917900085,
0.0665758028626442,
0.024261990562081337,
-0.004855026490986347,
0.03837219998240471,
0.00648739468306303,
-0.0007902201032266021,
-0.04027542099356651,
-0.03039875067770481,
0.033931173384189606,
0.0035916368942707777,
-0.029752448201179504,
-0.0523834154009819,
0.02638261951506138,
-0.01955295354127884,
0.046976782381534576,
-0.03070632740855217,
-0.011109750717878342,
-0.050682734698057175,
-0.011671624146401882,
0.0049051265232264996,
0.026067208498716354,
0.039926670491695404,
0.005976508837193251,
0.03309693932533264,
0.003785476554185152,
0.005661960691213608,
-0.00015095830895006657,
0.022388480603694916,
-0.040434762835502625,
0.012843525037169456,
0.024269063025712967,
0.0036510895006358624,
0.002861948683857918,
-0.0029933706391602755,
-0.024874629452824593,
0.010756458155810833,
-0.05290598049759865,
0.060046255588531494,
-0.02613980881869793,
0.0001356273132842034,
0.045559126883745193,
-0.08065459877252579,
-0.013330013491213322,
0.0027993901167064905,
-0.0021654784213751554,
0.05700148269534111,
-0.07226473838090897,
0.019951799884438515,
0.015724115073680878,
0.05176997557282448,
-0.050004854798316956,
-0.05759396404027939,
0.05064266547560692,
0.02556576207280159,
-0.024898840114474297,
-0.0021150601096451283,
0.01315049547702074,
-0.01835368573665619,
-0.02848619967699051,
-0.01079961284995079,
0.051325950771570206,
-0.05125376582145691,
-0.027968630194664,
0.006227692123502493,
0.03483590856194496,
0.049126382917165756,
0.00663991691544652,
0.005983208771795034,
0.004378192126750946,
-0.0014055089559406042,
-0.00869657937437296,
-0.0011691615218296647,
0.059544533491134644,
-0.03226175159215927,
-0.032114967703819275,
-0.01369378250092268,
-0.016883425414562225,
0.041487738490104675,
-0.029774636030197144,
0.008488301187753677,
0.030261678621172905,
0.008240333758294582,
-0.03388015553355217,
0.007821706123650074,
0.006673980969935656,
-0.012927569448947906,
0.01564309000968933,
-0.05822478234767914,
-0.01231243647634983,
-0.019212599843740463,
-0.0108021330088377,
-0.000044133266783319414,
0.01108330488204956,
0.013082988560199738,
-0.04210708290338516,
0.047406960278749466,
-0.017598377540707588,
0.030748682096600533,
-0.0033690056297928095,
-0.0018608749378472567,
0.01883736066520214,
0.022661270573735237,
-0.013161596842110157,
0.07114159315824509,
0.03062349371612072,
-0.020476611331105232,
-0.016718795523047447,
-0.05572367459535599,
0.051662322133779526,
0.06799988448619843,
-0.03999868035316467,
0.02897108905017376,
0.030723026022315025,
-0.012611879967153072,
0.005049366503953934,
-0.02394690364599228,
-0.032751619815826416,
0.019048212096095085,
-0.0049974857829511166,
0.04027029871940613,
-0.02203983999788761,
0.0066664451733231544,
0.005165510345250368,
0.03265133500099182,
-0.033091917634010315,
0.04299609363079071,
0.008042397908866405,
-0.006281107198446989,
0.012828069739043713,
0.02790355496108532,
-0.032837703824043274,
0.0673491358757019,
-0.009064002893865108,
0.02874103933572769,
-0.004955163225531578,
-0.025883547961711884,
0.03891368955373764,
-0.02202465943992138,
0.001405555522069335,
-0.04608365148305893,
-0.029290534555912018,
-0.020512502640485764,
0.03312111645936966,
0.012006212025880814,
0.015716910362243652,
-0.04462536424398422,
-0.014145398512482643,
0.03259710967540741,
0.004218115005642176,
0.0012425963068380952,
-0.025874409824609756,
-0.08119413256645203,
0.00795536395162344,
-0.003840217599645257,
-0.022331135347485542,
0.021884895861148834,
0.037846289575099945,
-0.016446761786937714,
-0.010507799685001373,
-0.028436459600925446,
-0.011446845717728138,
-0.0025228075683116913,
0.003005379345268011,
-0.009402431547641754,
0.06495101004838943,
-0.009597131051123142,
0.004513411317020655,
-0.023654649034142494,
0.023895736783742905,
0.10308466106653214,
0.03145981952548027,
-0.030976610258221626,
-0.06280375272035599,
0.02503296174108982,
-0.036983672529459,
-0.008521560579538345,
-0.028227200731635094,
0.0484960563480854,
0.011023355647921562,
0.0015629956033080816,
0.03133424371480942,
0.04139309003949165,
-0.013640464283525944,
0.0020347179379314184,
0.044486500322818756,
-0.025647414848208427,
-0.0365849994122982,
-0.006899022031575441,
0.044725071638822556,
-0.042261119931936264,
0.03089130111038685,
-0.038898665457963943,
0.013786835595965385,
-0.0056417882442474365,
0.005475429818034172,
-0.06514859199523926,
-0.049080923199653625,
0.047859907150268555,
0.01272508129477501,
-0.041873883455991745,
0.0006040573352947831,
0.0044791242107748985,
0.005297208670526743,
-0.03289610892534256,
0.018169116228818893,
0.03934213146567345,
0.006550689227879047,
0.012944920919835567,
0.04646700620651245,
-0.007812957279384136,
-0.007215189281851053,
-0.0042873858474195,
0.026353897526860237,
-0.023016592487692833,
-0.0352790430188179,
-0.040705785155296326,
0.04901078715920448,
-0.029535729438066483,
0.0452091246843338,
-0.02455352060496807,
0.019040631130337715,
0.012220432050526142,
-0.08349758386611938,
0.016913704574108124,
0.0041247024200856686,
0.008150086738169193,
-0.005036249756813049,
-0.02138448879122734,
0.025402672588825226,
0.02102864533662796,
-0.019979694858193398,
0.03439182788133621,
-0.026215974241495132,
-0.027744079008698463,
0.024357784539461136,
0.008832314983010292,
0.048248399049043655,
-0.021607013419270515,
-0.0004898538463748991,
-0.034187063574790955,
0.014497153460979462,
-0.04379000887274742,
-0.0168925654143095,
0.019766630604863167,
0.03018318861722946,
0.025403913110494614,
0.0039808847941458225,
-0.004211431369185448,
0.01646464504301548,
-0.0603201650083065,
0.02049221284687519,
0.018009455874562263,
-0.03342226892709732,
-0.036736804991960526,
0.022862447425723076,
0.02614990435540676,
0.03719937801361084,
0.004197956062853336,
0.012466369196772575,
-0.03834770992398262,
0.011907586827874184,
0.02822522446513176,
-0.021743733435869217,
-0.046112168580293655,
0.03633879870176315,
-0.05085824802517891,
-0.0138419633731246,
-0.0008801397052593529,
0.024414049461483955,
0.028020039200782776,
0.0002562316367402673,
-0.02913878858089447,
0.03940197452902794,
-0.018788745626807213,
0.002279317006468773,
0.0333247072994709,
-0.022769005969166756,
0.006943744141608477,
0.019979000091552734,
-0.019890164956450462,
-0.05220003053545952,
0.00019635423086583614,
-0.04614408686757088,
-0.039086904376745224,
-0.026940932497382164,
0.012280996888875961,
-0.019807051867246628,
0.025952300056815147,
-0.02849455736577511,
0.016115767881274223,
0.0028370970394462347,
-0.018981171771883965,
-0.01899789646267891,
-0.006137429736554623,
0.03305875509977341,
-0.009152480401098728,
-0.014190985821187496,
0.046568650752305984,
-0.028016500174999237,
-0.01147865317761898,
0.0011059045791625977,
0.019325673580169678,
0.00025450403336435556,
-0.024217473343014717,
-0.014193836599588394,
0.025298800319433212,
0.04609576612710953,
-0.029833106324076653,
-0.05434063822031021,
-0.0010202248813584447,
-0.018331503495573997,
-0.06069548428058624,
-0.006433889269828796,
-0.026815662160515785,
0.041212111711502075,
0.013977709226310253,
0.002680986188352108,
-0.024937981739640236,
0.038803428411483765,
-0.010053183883428574,
0.029069161042571068,
-0.0036399904638528824,
-0.034550730139017105,
-0.007298877462744713,
-0.03759622946381569,
0.01508951187133789,
-0.007395254448056221,
-0.006621505133807659,
0.010928577743470669,
0.015278780832886696,
-0.01427588053047657,
-0.0007001609192229807,
0.00694187032058835,
-0.025323640555143356,
-0.00035599584225565195,
0.017413364723324776,
0.0021841097623109818,
0.026172958314418793,
0.04255026951432228,
-0.0733923688530922,
0.04330507665872574,
0.02710822969675064,
0.006148442160338163,
-0.08993038535118103,
-0.03529246523976326,
0.03790604695677757,
-0.015271983109414577,
0.055906303226947784,
-0.07091677933931351,
-0.01224531326442957,
0.01850990019738674,
-0.07191132009029388,
0.010950815863907337,
-0.03997890278697014,
-0.04543877765536308,
-0.02807961031794548,
-0.04547128826379776,
0.00484446668997407,
0.0598653107881546,
-0.019986463710665703,
0.027230149134993553,
0.032056309282779694,
-0.01699965074658394,
-0.028381235897541046,
-0.029229149222373962,
-0.022160591557621956,
0.03824165090918541,
-0.004788315389305353,
-0.02169264294207096,
0.06294464319944382,
-0.01858970709145069,
-0.03318530693650246,
0.03818323835730553,
-0.007542558014392853,
0.008775302208960056,
0.01184169016778469,
-0.005175602622330189,
-0.02575896866619587,
0.021668285131454468,
0.0474063865840435,
0.0040609994903206825,
-0.03767623007297516,
-0.00676400400698185,
0.017490224912762642,
-0.010716231539845467,
0.005287468433380127,
0.015137719921767712,
0.015723172575235367,
0.0205264650285244,
0.006463456433266401,
0.03843960538506508,
-0.012924419716000557,
-0.01210029050707817,
-0.043407339602708817,
-0.015437901020050049,
0.0179628673940897,
-0.03594404458999634,
0.03250593692064285,
-0.032704584300518036,
-0.013087095692753792,
0.012171268463134766,
-0.01755918748676777,
0.01657470501959324,
0.015113248489797115,
-0.01602553203701973,
-0.04559030383825302,
0.01429769117385149,
0.006889132782816887,
-0.02200445905327797,
-0.05466529726982117,
-0.0012559875613078475,
0.01566585712134838,
-0.03815114498138428,
0.008058440871536732,
-0.03319472819566727,
-0.048012472689151764,
0.06112053990364075,
0.032184720039367676,
0.022945256903767586,
0.013459506444633007,
-0.03687852621078491,
-0.054303403943777084,
-0.07092364877462387,
0.03958067670464516,
0.0028120744973421097,
-0.0646643191576004,
-0.013596903532743454,
0.004373994190245867,
0.006486542522907257,
0.03066207654774189,
0.0447012260556221,
0.0027831385377794504,
0.024619439616799355,
-0.006716291885823011,
0.0250399149954319,
0.037443190813064575,
-0.041555460542440414,
-0.025221457704901695,
0.007776251062750816,
-0.0050507038831710815,
0.04156658425927162,
-0.027859337627887726,
0.002828118856996298,
0.003971893340349197,
0.03963572159409523,
-0.03082243911921978,
0.007429799064993858,
0.0038160693366080523,
-0.04561711102724075,
0.00016806188796181232,
-0.004808700643479824,
0.004219628870487213,
0.06676431000232697,
-0.01606222242116928,
-0.011471987701952457,
0.020529842004179955,
0.003547663800418377,
-0.012769358232617378,
-0.01339756604284048,
-0.03947053849697113,
-0.01757083646953106,
-0.015813186764717102,
-0.014232030138373375,
0.05743927136063576,
-0.06901256740093231,
-0.008159728720784187,
0.049161069095134735,
-0.04997767135500908,
0.020038451999425888,
0.046688057482242584,
0.013874620199203491,
0.02236802875995636,
0.006035982631146908,
0.05498731881380081,
0.033892594277858734,
-0.016236230731010437,
0.008352318778634071,
0.008374500088393688,
0.05789714679121971,
0.013011899776756763,
-0.016973184421658516,
0.021692102774977684,
-0.03370308130979538,
0.033325519412755966,
0.005186615511775017,
0.027067869901657104,
-0.036367446184158325,
-0.014490288682281971,
0.02799157239496708,
-0.01765224151313305,
0.03130374103784561,
-0.011980262584984303,
-0.012868105433881283,
0.05082385987043381,
-0.026097562164068222,
-0.00642980495467782,
-0.048139747232198715,
-0.011968767270445824,
-0.044896602630615234,
0.022031735628843307,
0.03816383332014084,
0.0429159440100193,
0.00693286769092083,
-0.00024073840177152306,
-0.02083739824593067,
-0.011325142346322536,
0.050361569970846176,
0.019338442012667656,
-0.025635024532675743,
-0.03589693456888199,
0.002545616589486599,
0.008444116450846195,
-0.020935140550136566,
-0.034932419657707214,
-0.0025542895309627056,
0.03320181369781494,
0.034589581191539764,
0.06819756329059601,
0.027734750881791115,
-0.010599610395729542,
-0.00811510905623436,
0.04902903735637665,
-0.09366778284311295,
-0.001115900930017233,
0.023225151002407074,
0.03312230110168457,
0.028057878836989403,
0.007056010887026787
] |
<p>Is there a difference in <a href="http://en.wikipedia.org/wiki/Binet_equation" rel="nofollow">Binet's equation</a> when the force acting on a body is attractive and repulsive? </p>
<p>I mean, if the force has a magnitude $F(r)$, is it Binet's equation always $$\frac{d^2u}{d\theta ^2}+u=-\frac{F(u^{-1})}{mh^2u^2}, u=r^{-1},$$ no matter if the force is attractive or impulsive?</p>
| 10,829 |
[
-0.040341854095458984,
0.0022287454921752214,
-0.04201481491327286,
-0.010409305803477764,
0.011849042028188705,
-0.027410408481955528,
-0.024754038080573082,
-0.019606806337833405,
0.03713350370526314,
-0.027746595442295074,
-0.0018391367048025131,
0.025401420891284943,
0.05190761014819145,
-0.008599037304520607,
0.015198725275695324,
0.004188272170722485,
-0.04358059912919998,
0.008734526112675667,
0.02482556737959385,
0.010335948318243027,
-0.0150480130687356,
-0.004433540627360344,
0.06416005641222,
-0.009566684253513813,
-0.01874076947569847,
0.03779153153300285,
0.0386350154876709,
-0.021146710962057114,
-0.01238205749541521,
0.04894690215587616,
0.005343705881386995,
-0.016069993376731873,
-0.007856177166104317,
0.04724538326263428,
-0.004829675890505314,
0.02922593057155609,
-0.024782927706837654,
-0.025250490754842758,
-0.03616504743695259,
0.008324072696268559,
-0.03250288963317871,
-0.059566840529441833,
0.00823681615293026,
0.042491454631090164,
-0.019890405237674713,
-0.016794145107269287,
0.03125271201133728,
-0.011665445752441883,
0.039235249161720276,
-0.08131343871355057,
0.06738989800214767,
0.014189241454005241,
0.032392553985118866,
0.006868715398013592,
0.0033666363451629877,
-0.055245377123355865,
0.05127401277422905,
0.07242030650377274,
-0.03564812242984772,
-0.048457249999046326,
-0.012471355497837067,
-0.0012683381792157888,
-0.033182159066200256,
0.01811041496694088,
0.008040295913815498,
0.06253132224082947,
-0.00519929826259613,
-0.034024983644485474,
0.05495459958910942,
0.005393650382757187,
0.018094409257173538,
0.018784767016768456,
0.019034545868635178,
-0.024354925379157066,
0.006203565746545792,
-0.028447162359952927,
0.016562391072511673,
0.01957586593925953,
0.015827026218175888,
0.07228797674179077,
-0.04094354435801506,
0.01763048954308033,
0.04206480085849762,
0.045986518263816833,
0.014181225560605526,
-0.0015659687342122197,
0.060311414301395416,
-0.01047992892563343,
-0.0010766173945739865,
0.006033510901033878,
-0.015355023555457592,
0.005110384896397591,
0.019213281571865082,
-0.016044175252318382,
-0.000919853278901428,
0.022210849449038506,
-0.004860083106905222,
0.048526663333177567,
0.0176963172852993,
-0.0465330071747303,
-0.044491246342659,
-0.015061582438647747,
0.006173224654048681,
0.06877636164426804,
-0.016003914177417755,
-0.023880483582615852,
-0.044030316174030304,
0.010201632976531982,
-0.04367036372423172,
0.004808278754353523,
-0.01951499469578266,
0.01937919482588768,
-0.015409287065267563,
-0.009315659292042255,
0.006024994421750307,
0.0004646397428587079,
0.02488158456981182,
0.013460405170917511,
0.048719823360443115,
0.07635144889354706,
0.052494116127491,
-0.02808457612991333,
0.031247958540916443,
-0.02503223344683647,
-0.044471751898527145,
0.008269882760941982,
0.033998847007751465,
-0.016224419698119164,
-0.02125360071659088,
0.006217334885150194,
-0.005574135575443506,
-0.018180308863520622,
-0.012683389708399773,
0.0327899344265461,
0.038538601249456406,
0.02010456472635269,
-0.09539531171321869,
-0.06888588517904282,
0.005451573990285397,
0.011787320487201214,
0.0034709786996245384,
-0.04780522733926773,
0.03228689730167389,
0.054537609219551086,
0.06686735153198242,
0.0320427305996418,
0.005211966577917337,
0.03798458352684975,
0.039030689746141434,
0.020909428596496582,
0.01632053218781948,
0.006419679615646601,
0.029910529032349586,
-0.053154293447732925,
-0.0055119977332651615,
-0.07749374210834503,
0.04364795610308647,
0.01150287501513958,
0.03591684624552727,
-0.03930562362074852,
0.0827675461769104,
-0.03167292848229408,
-0.02050662599503994,
0.014587766490876675,
0.030243132263422012,
0.021164419129490852,
0.07241062819957733,
-0.013496908359229565,
0.028945930302143097,
0.03312812000513077,
0.026486415416002274,
0.038288719952106476,
0.005610004998743534,
0.03801092132925987,
0.02225595712661743,
-0.04360968992114067,
-0.04357564076781273,
-0.049530044198036194,
-0.011504216119647026,
-0.017085948958992958,
-0.04840124025940895,
-0.045333459973335266,
-0.025617655366659164,
-0.028449201956391335,
-0.04119560122489929,
0.06732245534658432,
0.02073434367775917,
-0.022121304646134377,
0.01952149160206318,
-0.017430897802114487,
-0.005491964053362608,
-0.02253248728811741,
0.04331345111131668,
-0.010896923020482063,
0.011208557523787022,
0.05276389420032501,
0.01583109237253666,
0.025614991784095764,
-0.020233463495969772,
0.034745488315820694,
-0.019847635179758072,
0.02880912832915783,
-0.03600702062249184,
-0.03840810805559158,
0.0019230229081586003,
0.02418728731572628,
0.00520367082208395,
0.029698140919208527,
0.04245590791106224,
-0.0025295675732195377,
0.001209054491482675,
-0.007172289304435253,
-0.02919495850801468,
0.02978275716304779,
-0.0015419471310451627,
-0.005353495944291353,
0.01728176884353161,
-0.018366090953350067,
-0.018854310736060143,
0.061078108847141266,
-0.04932161048054695,
0.07634516060352325,
0.04045329615473747,
0.04627269506454468,
0.05068325996398926,
0.08017563074827194,
0.01973535679280758,
0.021139970049262047,
-0.0036467534955590963,
-0.04791448265314102,
-0.036136604845523834,
0.03772672265768051,
0.014198580756783485,
-0.000535682775080204,
-0.03325655311346054,
0.040970493108034134,
0.019489971920847893,
0.022100355476140976,
0.06161775439977646,
0.04526014253497124,
-0.018574198707938194,
-0.051007214933633804,
0.06344089657068253,
0.03536268323659897,
0.01149696484208107,
0.007481034845113754,
0.018298346549272537,
-0.006102371960878372,
0.04144721478223801,
-0.01700161024928093,
-0.002237695502117276,
0.03349601477384567,
-0.013085251674056053,
-0.007699203677475452,
-0.00644151633605361,
0.01632106490433216,
0.041324108839035034,
-0.006553009618073702,
0.01973441243171692,
0.015725314617156982,
0.0031730192713439465,
-0.014180109836161137,
-0.01995457522571087,
0.0106919901445508,
0.006424050312489271,
0.006596382241696119,
0.0037261503748595715,
-0.027485869824886322,
0.011067844927310944,
-0.026102891191840172,
-0.013219629414379597,
-0.017343079671263695,
-0.019665801897644997,
-0.045818354934453964,
-0.028146181255578995,
0.007114625070244074,
0.008695601485669613,
0.02238473854959011,
0.018900960683822632,
-0.010399130173027515,
-0.025265615433454514,
-0.04181016609072685,
-0.006748064886778593,
0.019173184409737587,
-0.03148757293820381,
0.00978854950517416,
-0.05624806135892868,
-0.010512885637581348,
0.07217057049274445,
0.020775718614459038,
0.006820254493504763,
-0.004248647019267082,
-0.00044826374505646527,
-0.044018011540174484,
-0.0029809698462486267,
-0.047458045184612274,
0.015291568823158741,
0.032688699662685394,
-0.03351211175322533,
0.04368283227086067,
-0.0006378029356710613,
-0.020804325118660927,
0.0069754780270159245,
-0.04831567406654358,
-0.04593509063124657,
-0.04025577753782272,
0.010647284798324108,
0.043904565274715424,
0.007711779326200485,
0.025980807840824127,
0.03401472419500351,
-0.047970421612262726,
0.002637590514495969,
-0.06137274205684662,
-0.02749238722026348,
0.006929734256118536,
0.006482578348368406,
0.029122188687324524,
-0.007974355481564999,
-0.02157650515437126,
0.041879717260599136,
0.02635069563984871,
0.0004939195932820439,
-0.0377422459423542,
-0.018393661826848984,
-0.035805150866508484,
0.007357767783105373,
0.002500845119357109,
0.04486783593893051,
0.007710047997534275,
0.00015043182065710425,
0.003310314379632473,
0.017496811226010323,
0.010229691863059998,
0.03415127471089363,
-0.022936154156923294,
0.008730512112379074,
0.03229987248778343,
-0.024048957973718643,
0.04698048159480095,
0.019952405244112015,
-0.009040501900017262,
0.00853300467133522,
0.0016187668079510331,
0.05011005327105522,
0.03277849778532982,
-0.04021088778972626,
0.036568790674209595,
-0.022408928722143173,
0.02868741936981678,
-0.018952855840325356,
0.03211238607764244,
-0.013992446474730968,
0.002029906027019024,
-0.02972474694252014,
0.02051505260169506,
0.055267084389925,
-0.04501989483833313,
-0.0181169081479311,
0.0171591155230999,
0.004832095932215452,
-0.02974689193069935,
-0.01041897851973772,
-0.0009896699339151382,
-0.0053609320893883705,
0.07344763725996017,
-0.009745174087584019,
-0.0010580624220892787,
0.04543619602918625,
-0.010283121839165688,
0.04661452770233154,
0.00032825861126184464,
-0.017220541834831238,
0.0162754338234663,
-0.06260690093040466,
0.0038935882039368153,
-0.019523851573467255,
0.02296728827059269,
0.0038046184927225113,
0.05434636399149895,
-0.0020395147148519754,
0.04976404830813408,
0.004390563815832138,
0.002804323798045516,
-0.08442142605781555,
0.02221163734793663,
-0.04727700352668762,
-0.015246113762259483,
-0.022480664774775505,
-0.005148536991328001,
-0.029277317225933075,
-0.03744759410619736,
0.003847961314022541,
-0.012277886271476746,
0.004452801775187254,
-0.06284945458173752,
0.025030583143234253,
-0.05085889250040054,
-0.02563103288412094,
0.0014707930386066437,
0.04211367294192314,
0.017222872003912926,
-0.05386845022439957,
0.03531908243894577,
0.03010813146829605,
0.00034579570638015866,
0.006591083947569132,
-0.053495705127716064,
-0.024364834651350975,
-0.004149635788053274,
0.015412823297083378,
-0.002054863376542926,
0.02447526343166828,
-0.0015106184873729944,
0.007531582377851009,
0.01405285857617855,
0.02306636981666088,
0.02751474641263485,
-0.013518080115318298,
-0.053920477628707886,
-0.09831400215625763,
-0.004064376465976238,
-0.015975767746567726,
0.045967116951942444,
-0.007972133345901966,
-0.000031319923436967656,
0.03212365135550499,
-0.024648865684866905,
0.02123183384537697,
0.04016090929508209,
0.01904636062681675,
-0.0197122972458601,
-0.012920082546770573,
-0.0635082945227623,
0.028158606961369514,
-0.03129879757761955,
-0.002867273287847638,
0.04285479336977005,
0.027671802788972855,
-0.055273376405239105,
-0.005787194706499577,
0.031697340309619904,
0.025716204196214676,
-0.04161187261343002,
-0.019331198185682297,
-0.0026034885086119175,
0.026593634858727455,
-0.04633917286992073,
-0.006797068286687136,
0.03710554540157318,
0.03754446655511856,
0.02325398288667202,
-0.0165993794798851,
0.006363581866025925,
-0.07137448340654373,
0.00452361861243844,
0.04553075134754181,
-0.01019167061895132,
-0.026410095393657684,
-0.012448308989405632,
-0.0642753392457962,
-0.00847284309566021,
0.04744017869234085,
-0.03270198777318001,
0.0408109687268734,
-0.020221788436174393,
0.012685823254287243,
0.02538888156414032,
-0.0016107213450595737,
-0.03209352865815163,
-0.007183718029409647,
-0.005601942539215088,
-0.014901607297360897,
-0.009310212917625904,
0.011146451346576214,
-0.004681809339672327,
0.030343540012836456,
0.026628470048308372,
0.06255865097045898,
-0.01020297221839428,
-0.023489415645599365,
-0.009273477829992771,
-0.01868126168847084,
-0.03919776901602745,
-0.07071015983819962,
-0.03922537714242935,
0.022645609453320503,
0.03050648421049118,
0.05146579071879387,
-0.037165187299251556,
-0.05080021172761917,
0.011618576012551785,
-0.0023892188910394907,
-0.007997038774192333,
0.014676141552627087,
-0.034156110137701035,
-0.0010588915320113301,
0.0378560945391655,
-0.023289252072572708,
0.050061535090208054,
0.03700932860374451,
-0.022068433463573456,
-0.031992144882678986,
-0.044699132442474365,
0.0043632048182189465,
-0.009995713829994202,
-0.03738000988960266,
-0.04854276403784752,
-0.021442314609885216,
-0.03953688591718674,
0.054886020720005035,
-0.0051949345506727695,
-0.01298508234322071,
-0.05599326640367508,
-0.027111459523439407,
-0.03144310042262077,
0.04769672080874443,
0.0015099761076271534,
0.019122213125228882,
0.02322324924170971,
0.024243174120783806,
0.014367255382239819,
-0.017503976821899414,
-0.016951866447925568,
-0.044250763952732086,
0.0017349544214084744,
0.01958007924258709,
-0.03200845792889595,
0.0004815911815967411,
-0.021793516352772713,
-0.011572866700589657,
0.013470752164721489,
-0.03735504299402237,
0.04922867938876152,
-0.010057435370981693,
-0.0028052297420799732,
0.013491541147232056,
-0.0375845767557621,
-0.0045118797570466995,
0.008662332780659199,
-0.00828271172940731,
0.06053696945309639,
-0.04423145949840546,
0.03862893581390381,
0.01807125099003315,
-0.02334176003932953,
-0.06073892116546631,
-0.039820682257413864,
0.01961352862417698,
-0.03467977046966553,
0.00362402549944818,
0.015183803625404835,
-0.005876797251403332,
0.010746701620519161,
-0.035970088094472885,
-0.01656130887567997,
0.06855446845293045,
-0.01534423790872097,
-0.019756080582737923,
-0.03264198452234268,
0.00018641259521245956,
0.045514386147260666,
-0.0030554512050002813,
-0.00160436041187495,
-0.015782421454787254,
-0.03004482202231884,
0.004982244223356247,
0.020041683688759804,
0.07938148826360703,
-0.02780754491686821,
-0.01560757402330637,
-0.002195097040385008,
-0.042924582958221436,
0.030453916639089584,
-0.020898783579468727,
-0.016555748879909515,
0.03534181788563728,
0.017788399010896683,
-0.011284350417554379,
-0.027865957468748093,
-0.009895560331642628,
-0.02448250912129879,
0.004315184894949198,
-0.00465722382068634,
-0.017698828130960464,
-0.03775327280163765,
-0.030799422413110733,
0.0148704769089818,
0.0062763020396232605,
-0.009315540082752705,
-0.012704594060778618,
0.05277149751782417,
-0.012300084345042706,
-0.02895505353808403,
0.012907424010336399,
0.0004313618701416999,
0.051062554121017456,
-0.040135037153959274,
-0.022667570039629936,
0.03987298905849457,
0.049603044986724854,
-0.014663280919194221,
-0.02998916432261467,
-0.03437883406877518,
0.048270367085933685,
0.06970766931772232,
-0.018145687878131866,
0.025541679933667183,
0.00478357495740056,
0.007519378326833248,
-0.008428272791206837,
-0.06197385862469673,
-0.001060329843312502,
0.023611851036548615,
-0.0035497930366545916,
0.04295652359724045,
-0.01363725308328867,
0.025402896106243134,
0.0011067389277741313,
0.05222700163722038,
0.014746631495654583,
-0.009397885762155056,
0.01993933692574501,
0.024735622107982635,
0.01157777477055788,
0.021343186497688293,
-0.022421633824706078,
0.03721672669053078,
-0.006818958558142185,
0.02015097439289093,
-0.01774510182440281,
-0.017003849148750305,
0.03032863885164261,
0.015757575631141663,
-0.008177749812602997,
-0.09594062715768814,
-0.0022241901606321335,
0.029916642233729362,
0.022758666425943375,
0.00970379263162613,
0.0334322415292263,
0.0003508306108415127,
0.0026321434415876865,
0.022133884951472282,
-0.00412188982591033,
0.0005179792642593384,
0.001143667846918106,
-0.031584933400154114,
0.001182290376164019,
-0.045386284589767456,
-0.0698137879371643,
0.024754302576184273,
-0.011936397291719913,
-0.02565881982445717,
-0.0016056561144068837,
-0.02188033238053322,
0.03883921355009079,
0.03729260340332985,
0.006713982205837965,
-0.0026991653721779585,
0.0910114124417305,
-0.023480389267206192,
0.0018527703359723091,
-0.02526957541704178,
0.004444589372724295,
0.12253310531377792,
0.01776486448943615,
0.024058310315012932,
-0.03200346603989601,
-0.008319376967847347,
-0.021605856716632843,
-0.02469436451792717,
-0.04085187986493111,
0.015987757593393326,
0.020304594188928604,
-0.006785636302083731,
0.022282429039478302,
0.04798348620533943,
-0.004444030113518238,
-0.03337003290653229,
0.037663783878088,
-0.014119593426585197,
-0.006668371148407459,
-0.009722316637635231,
-0.004293288104236126,
-0.017637334764003754,
0.02469472959637642,
-0.01636345684528351,
-0.0013629907043650746,
-0.015290999785065651,
-0.009950111620128155,
-0.04345221072435379,
0.010713120922446251,
0.03462716192007065,
0.00820180308073759,
-0.07356946915388107,
-0.01686093769967556,
-0.020559081807732582,
-0.018410833552479744,
-0.030054934322834015,
0.024102186784148216,
0.007462926674634218,
-0.046944644302129745,
0.03684256598353386,
0.036813151091337204,
0.012492788024246693,
0.01952247880399227,
0.0380077101290226,
-0.006733567453920841,
-0.04641415923833847,
0.056401100009679794,
-0.02204113081097603,
0.0335635207593441,
-0.0010777023853734136,
0.004897763952612877,
-0.005772722419351339,
0.001314571825787425,
0.0038216111715883017,
-0.07336686551570892,
-0.04018818214535713,
-0.011816679500043392,
0.03058905154466629,
-0.006857594940811396,
-0.020655564963817596,
-0.03136255592107773,
0.008496525697410107,
0.025904037058353424,
0.026957113295793533,
-0.0283226165920496,
-0.008552533574402332,
0.010837041772902012,
0.011282051913440228,
0.04255172237753868,
-0.0076980204321444035,
-0.01773957535624504,
-0.002909688279032707,
-0.024751560762524605,
-0.04376840963959694,
-0.02431679703295231,
-0.0035943470429629087,
0.020291611552238464,
0.026984618976712227,
-0.028968090191483498,
-0.009154494851827621,
-0.015469791367650032,
-0.08201971650123596,
0.025574512779712677,
0.005491966847330332,
-0.018691353499889374,
0.02033352665603161,
0.01183745451271534,
0.016835901886224747,
0.009190489538013935,
-0.02046959660947323,
0.010337872430682182,
0.0020266142673790455,
0.029755057767033577,
0.006483616307377815,
-0.03553726524114609,
-0.05335940048098564,
0.00883760116994381,
-0.02660858817398548,
0.002570005366578698,
-0.031612738966941833,
-0.027512239292263985,
0.019883574917912483,
0.026549173519015312,
-0.04638010263442993,
0.0425342358648777,
-0.015452809631824493,
0.02287481725215912,
0.013306763954460621,
-0.034199438989162445,
-0.0004534819454420358,
0.006339531857520342,
-0.002473478903993964,
-0.017393553629517555,
-0.02060074917972088,
-0.05016538128256798,
-0.013861561194062233,
0.010385265573859215,
-0.000998161151073873,
-0.03218236565589905,
-0.03568468615412712,
0.007220844272524118,
0.01232207752764225,
-0.025756457820534706,
-0.02896750159561634,
-0.059505101293325424,
0.03437642753124237,
0.030195284634828568,
-0.019044896587729454,
-0.009193816222250462,
0.03279219567775726,
-0.02023141458630562,
0.0033004586584866047,
0.009998878464102745,
0.00781475380063057,
-0.01920505240559578,
-0.007039504125714302,
0.056100163608789444,
-0.03842780739068985,
0.03828296437859535,
-0.010881124064326286,
-0.0157280582934618,
0.04814358428120613,
-0.02723633125424385,
-0.0031502714846283197,
0.040317729115486145,
-0.0020983796566724777,
0.009694982320070267,
0.010678261518478394,
0.002762438030913472,
-0.006998654454946518,
0.09474434703588486,
0.004775597248226404,
-0.023454995825886726,
0.03280393034219742,
-0.04362744092941284,
-0.003243344370275736,
-0.023601165041327477,
-0.009912113659083843,
-0.02862859144806862,
-0.0032920953817665577,
0.011468544602394104,
0.024917377158999443,
0.012157028540968895,
-0.00974739994853735,
-0.001110757002606988,
0.030838891863822937,
0.03969782590866089,
0.013951930217444897,
-0.0035442891530692577,
0.023417619988322258,
0.044620368629693985,
-0.002296231919899583,
0.014179839752614498,
0.01577848196029663,
0.027041632682085037,
-0.11157574504613876,
-0.010291479527950287,
0.020141568034887314,
0.015777722001075745,
0.024729259312152863,
-0.044905152171850204,
0.0337984673678875,
-0.002348795300349593,
-0.0014048253651708364,
-0.013886538334190845,
-0.03394244983792305,
-0.008611789904534817,
-0.009068680927157402,
0.006544771138578653,
-0.00471630459651351,
0.031787045300006866,
0.006214592140167952,
0.021064329892396927,
0.0262970682233572,
-0.03783334419131279,
-0.023883644491434097,
0.014554270543158054,
0.0006659954669885337,
0.04151648283004761,
-0.0026165659073740244,
-0.023860018700361252,
0.07017911970615387,
-0.010363462381064892,
-0.03957339748740196,
0.041948288679122925,
0.005526458844542503,
-0.01473100483417511,
-0.029018407687544823,
0.05344908684492111,
0.02901368774473667,
0.04632813110947609,
0.0040326835587620735,
-0.0278586708009243,
0.0007698358385823667,
0.05308346822857857,
0.004919256549328566,
0.04859847575426102,
-0.044649187475442886,
-0.015674863010644913,
0.002868711482733488,
-0.030452294275164604,
-0.024594677612185478,
0.04322226345539093,
-0.010027531534433365,
-0.014821013435721397,
-0.04110714793205261,
-0.047514528036117554,
0.025832727551460266,
-0.01018466241657734,
0.01143707800656557,
-0.060007963329553604,
0.006454401183873415,
0.03038371540606022,
-0.0629112720489502,
0.01519859116524458,
0.0279401708394289,
-0.004497849848121405,
-0.027124974876642227,
0.0008240843890234828,
-0.008028946816921234,
0.013106183148920536,
-0.038238491863012314,
-0.029478203505277634,
0.0007659003022126853,
0.008003800176084042,
-0.03451555222272873,
-0.01787942461669445,
-0.026667168363928795,
0.03502950072288513,
0.00794177409261465,
0.008017570711672306,
-0.0040176622569561005,
-0.028810670599341393,
-0.07009587436914444,
-0.07064861059188843,
0.025525983422994614,
0.017421292141079903,
-0.025254031643271446,
-0.04465676471590996,
-0.020024726167321205,
-0.011132804676890373,
0.004800628405064344,
0.06052079051733017,
-0.023362483829259872,
-0.03126220405101776,
0.026761885732412338,
-0.022468356415629387,
-0.012983659282326698,
-0.026219099760055542,
-0.0040487321093678474,
0.019835233688354492,
0.02819877117872238,
0.009041612036526203,
0.016877712681889534,
-0.03187761455774307,
0.03972674533724785,
-0.0322653092443943,
0.0034374985843896866,
0.0352775864303112,
0.005207513924688101,
-0.01835026405751705,
0.059382613748311996,
0.02159901335835457,
-0.027019521221518517,
0.08429213613271713,
-0.010139651596546173,
0.06847652047872543,
-0.027138348668813705,
-0.03080153651535511,
-0.028913460671901703,
0.0367673859000206,
-0.03463372215628624,
-0.014759805984795094,
0.006386305671185255,
-0.020197570323944092,
0.022647753357887268,
-0.03783533349633217,
-0.006745023652911186,
0.02875647321343422,
-0.055641286075115204,
-0.002083040773868561,
0.036453694105148315,
0.006380544975399971,
0.05484243854880333,
-0.004176919814199209,
0.007380770053714514,
0.041352272033691406,
0.0035837760660797358,
-0.005135548301041126,
0.03844888135790825,
0.025971753522753716,
0.01908283680677414,
-0.013786799274384975,
0.017975011840462685,
-0.003857644507661462,
0.03730613365769386,
0.045466210693120956,
0.029484089463949203,
0.01917511224746704,
-0.004664129111915827,
0.001321481540799141,
-0.007104550022631884,
0.02553701214492321,
0.027010023593902588,
-0.005227476824074984,
0.06665157526731491,
-0.022290468215942383,
0.04717588424682617,
-0.05036872625350952,
0.00577126769348979,
-0.005887863226234913,
0.016247091814875603,
0.027507033199071884,
0.04868292063474655,
0.021384594962000847,
-0.041660815477371216,
-0.009179449640214443,
0.01393154263496399,
0.03637876361608505,
-0.024691440165042877,
-0.008112762123346329,
0.002124297898262739,
0.024989187717437744,
-0.018745673820376396,
-0.01984577625989914,
-0.03809564188122749,
-0.026471620425581932,
0.04492529109120369,
0.006551161874085665,
0.04502588510513306,
-0.002929364563897252,
0.009043257683515549,
0.003100377507507801,
0.05218249931931496,
-0.07954426109790802,
-0.0450701043009758,
0.0025454871356487274,
0.007078356109559536,
0.014100595377385616,
-0.014984501525759697
] |
<p>Can the vacuum be understood as a physical/chemical/material substance? </p>
<p>Remark: Vacuum has a density energy (so it has a density "mass" equivalence due to $E=mc^2$). Vacuum is quantum (but not classically!) polarizable (vacuum polarization effects are essential in QED or QCD).</p>
<p>Remark (II): A chemical substance is a form of matter that has constant chemical composition and characteristic properties.It can be solid, liquid, gas, or plasma. If vacuum is some kind of "substance" with some "physical" constant features (like density energy, polarizability,...), we can understand from elementary QFT principles that every particle is excitation from "a ground" state. Should we understand the SM as the vacuum composition or "states" at certain energy ranges ("temperature") just as a solid, liquid or gas (even a plasma) are just states at certain "temperature"?</p>
<p>Remark (III): Vacuum has "a structure" or "features" just as the state of matter show certain properties at certain temperatures. Is this just a useless analogy?</p>
| 10,830 |
[
-0.009034328162670135,
-0.008534171618521214,
0.011074680835008621,
-0.0003393132355995476,
0.025648083537817,
0.034524042159318924,
-0.010094542987644672,
-0.027250148355960846,
0.007792247924953699,
-0.030170392245054245,
0.035494763404130936,
0.015523187816143036,
0.06533593684434891,
-0.005308239255100489,
-0.003801973070949316,
-0.01081411074846983,
0.035046134144067764,
-0.026853708550333977,
-0.010274965316057205,
-0.029324743896722794,
0.039388008415699005,
0.03398121893405914,
0.00448246905580163,
0.031854964792728424,
-0.016243046149611473,
0.034627918154001236,
-0.015922371298074722,
-0.00043101541814394295,
0.02345578745007515,
0.016824036836624146,
0.011394383385777473,
-0.024766501039266586,
-0.009965846315026283,
-0.0029095516074448824,
0.024798516184091568,
-0.022574488073587418,
-0.04995792731642723,
-0.019534913823008537,
-0.008288252167403698,
0.005323737859725952,
-0.03535587713122368,
-0.0099628996104002,
0.008363073691725731,
0.02317250706255436,
-0.0056889671832323074,
-0.03540068864822388,
0.027765078470110893,
-0.0013649399625137448,
0.03003726154565811,
-0.08221515268087387,
0.031889479607343674,
0.04626922681927681,
0.01986238919198513,
0.015508435666561127,
-0.017529422417283058,
-0.029626216739416122,
0.05757395178079605,
0.06287849694490433,
-0.008982490748167038,
-0.04496169835329056,
-0.0506102591753006,
-0.003564215498045087,
-0.014380819164216518,
-0.021461518481373787,
-0.042275577783584595,
0.01300434023141861,
-0.015619915910065174,
0.00257588061504066,
0.011377701535820961,
0.018640626221895218,
0.020167186856269836,
0.006519280839711428,
0.0052306861616671085,
0.0012963269837200642,
-0.008251377381384373,
-0.012978050857782364,
0.037544045597314835,
0.019246317446231842,
0.01961684785783291,
0.03147691488265991,
0.001494891126640141,
0.0005507339956238866,
0.013746633194386959,
0.042416367679834366,
0.010569208301603794,
-0.010327620431780815,
0.06822847574949265,
-0.03389326483011246,
0.01695513352751732,
0.046881627291440964,
0.005728290416300297,
0.013107676059007645,
0.03784238174557686,
-0.0016625121934339404,
-0.036493975669145584,
0.0017739887116476893,
0.00814899243414402,
0.03587111830711365,
0.004785051103681326,
-0.009485519491136074,
-0.015557951293885708,
0.03750578314065933,
0.05887390300631523,
0.07031005620956421,
0.01836892031133175,
-0.023238347843289375,
-0.028484022244811058,
0.038460467010736465,
-0.0119238356128335,
-0.0190432108938694,
-0.03951982408761978,
0.0019315435783937573,
0.01836482062935829,
0.0016282383585348725,
0.018950605764985085,
-0.049518048763275146,
0.011086742393672466,
-0.03918907791376114,
0.040517330169677734,
0.0723491907119751,
0.05623874440789223,
-0.043967634439468384,
0.03558683022856712,
-0.01468199584633112,
-0.08927604556083679,
0.0050033824518322945,
0.015840623527765274,
-0.009425523690879345,
-0.017225045710802078,
-0.033997543156147,
-0.008077006787061691,
-0.01561114750802517,
0.029740819707512856,
-0.015371972694993019,
0.06281816959381104,
-0.010528994724154472,
-0.08728024363517761,
-0.049791596829891205,
0.012041470967233181,
0.011921345256268978,
-0.037729986011981964,
-0.06996699422597885,
0.016947276890277863,
0.030920706689357758,
0.06054969131946564,
-0.004032042808830738,
-0.05400967597961426,
-0.003468497423455119,
0.07611624151468277,
0.012409397400915623,
-0.03382410481572151,
-0.03458932042121887,
-0.01709059439599514,
-0.0854354277253151,
0.008555157110095024,
-0.054620858281850815,
0.027249319478869438,
0.05528835952281952,
0.01184648834168911,
0.0011893636547029018,
0.04835784062743187,
-0.06326260417699814,
0.0015326864086091518,
0.048060446977615356,
0.03307557478547096,
-0.03849933296442032,
0.035716619342565536,
0.01474994607269764,
0.04759375378489494,
0.052759405225515366,
0.02717548981308937,
0.004131107125431299,
0.03217998147010803,
0.023179005831480026,
0.025004377588629723,
-0.032418712973594666,
-0.020847341045737267,
0.016451049596071243,
0.023177726194262505,
-0.00788938719779253,
-0.0721469596028328,
-0.045367687940597534,
-0.03463409096002579,
0.019419891759753227,
-0.008234824053943157,
0.01592828519642353,
-0.011351966299116611,
-0.02297986112535,
-0.016537604853510857,
-0.06949155032634735,
-0.02194671891629696,
-0.06874355673789978,
-0.029736898839473724,
-0.009713925421237946,
-0.00874809268862009,
0.030261937528848648,
-0.008750376291573048,
0.013957329094409943,
-0.058294571936130524,
-0.050808247178792953,
0.013173367828130722,
0.04765484482049942,
0.014286783523857594,
-0.0220553707331419,
0.0018016808899119496,
0.01390849519520998,
0.034739259630441666,
-0.005101349204778671,
-0.007363061886280775,
-0.028110483661293983,
-0.07820960134267807,
-0.014393641613423824,
-0.00964190624654293,
0.0497424341738224,
-0.028952250257134438,
-0.005601099692285061,
0.013364652171730995,
-0.02554190531373024,
-0.005117119289934635,
0.05619450658559799,
-0.03329839929938316,
0.07032690197229385,
0.021188559010624886,
0.024101117625832558,
-0.0032788091339170933,
0.049907129257917404,
-0.001127351657487452,
0.01592835783958435,
-0.008084631524980068,
-0.036668092012405396,
-0.035597145557403564,
-0.03537123277783394,
0.029736775904893875,
0.03377045691013336,
-0.030331220477819443,
0.04270443692803383,
0.009355048649013042,
0.05767485126852989,
0.043892163783311844,
-0.002438025316223502,
-0.026139890775084496,
-0.00008206391066778451,
0.02592071332037449,
-0.009267997927963734,
0.030064066872000694,
0.0014487514272332191,
-0.00044094515033066273,
0.031624700874090195,
0.014466649852693081,
-0.005541382823139429,
0.013010527938604355,
0.0779002234339714,
-0.016428766772150993,
0.009886251762509346,
0.009402638301253319,
-0.030226921662688255,
0.0325532890856266,
-0.021728649735450745,
0.013435129076242447,
0.04157308116555214,
-0.05080298334360123,
-0.0021680439822375774,
-0.04715120419859886,
-0.01464913785457611,
-0.004757217597216368,
-0.0029359953477978706,
-0.03085213527083397,
0.005672970321029425,
0.01596369780600071,
-0.03194468468427658,
0.020596789196133614,
0.003776532830670476,
0.0057855346240103245,
-0.0005980719579383731,
0.019306398928165436,
0.023036247119307518,
-0.018596630543470383,
0.017263952642679214,
-0.027153929695487022,
-0.05950302258133888,
0.018635401502251625,
-0.020385628566145897,
-0.02678423747420311,
0.019589824602007866,
-0.03636954352259636,
0.00893140397965908,
-0.0398046150803566,
-0.04268030822277069,
0.022574052214622498,
0.004307562950998545,
-0.011328534223139286,
0.0008400355582125485,
-0.026335617527365685,
-0.048249345272779465,
0.021048424765467644,
-0.02019623853266239,
0.02022704668343067,
-0.016390396282076836,
-0.004524489399045706,
0.019427547231316566,
-0.010635077022016048,
-0.024293754249811172,
0.019619017839431763,
-0.0026551492046564817,
-0.058032963424921036,
-0.029940642416477203,
-0.017299193888902664,
0.02437395602464676,
-0.028273988515138626,
0.04117950424551964,
0.07346999645233154,
-0.06068611517548561,
0.013482261449098587,
-0.016232483088970184,
-0.039651915431022644,
0.019217083230614662,
0.009031221270561218,
0.05483795702457428,
0.01990012638270855,
-0.038670096546411514,
0.054508306086063385,
0.023947084322571754,
-0.03767167776823044,
0.009984269738197327,
-0.012242141179740429,
-0.04141489043831825,
0.003913856577128172,
-0.0159197635948658,
0.0005214946577325463,
0.009925272315740585,
0.005407574586570263,
0.044256363064050674,
0.04263400286436081,
-0.011969872750341892,
0.014466813765466213,
-0.02694633975625038,
0.021920040249824524,
0.03396317735314369,
-0.0017624999163672328,
0.06129365414381027,
0.005684303119778633,
-0.0027980520389974117,
0.020527474582195282,
-0.00016551141743548214,
0.02581605687737465,
0.02881704829633236,
-0.029546689242124557,
0.06474702060222626,
0.006936140824109316,
0.018318040296435356,
-0.03032108210027218,
0.039998285472393036,
0.0030463039875030518,
-0.02009827271103859,
-0.0050786323845386505,
0.024843480437994003,
-0.007486084010452032,
-0.003913617227226496,
-0.014528441242873669,
0.024795664474368095,
0.06483547389507294,
-0.048894286155700684,
-0.036535631865262985,
0.018628140911459923,
-0.04675665125250816,
0.006441870704293251,
-0.026002390310168266,
0.009947095066308975,
0.04004128649830818,
0.03745244815945625,
0.0513540618121624,
-0.029681526124477386,
-0.049670685082674026,
-0.0041494122706353664,
-0.06104421988129616,
-0.032949160784482956,
0.014951401390135288,
0.0027903274167329073,
-0.005565992556512356,
0.06369665265083313,
0.009705222211778164,
0.01680290326476097,
0.0036536420229822397,
0.006965250708162785,
-0.1005217656493187,
-0.01921890489757061,
-0.046194709837436676,
0.02418760024011135,
-0.031041642650961876,
0.014848087914288044,
-0.029223572462797165,
-0.009939798153936863,
-0.0408126525580883,
0.028701387345790863,
0.0006588407559320331,
-0.047850627452135086,
0.02131250873208046,
-0.05923712998628616,
-0.041175130754709244,
-0.009613704867661,
0.015668999403715134,
0.034872353076934814,
-0.010875513777136803,
0.005737746134400368,
0.04176224768161774,
-0.05381220951676369,
0.03853178396821022,
-0.0076137930154800415,
0.002529564080759883,
0.048995573073625565,
0.01475420780479908,
0.03309322148561478,
-0.00448036240413785,
-0.009100767783820629,
0.004453922156244516,
0.040369827300310135,
0.03428926691412926,
-0.010861176997423172,
-0.03107367269694805,
-0.018766969442367554,
-0.05476754158735275,
-0.03502515330910683,
0.029198767617344856,
0.04938504472374916,
0.003720885841175914,
0.01960170827805996,
0.011693346314132214,
-0.025877514854073524,
-0.018760651350021362,
0.05809428170323372,
0.054243117570877075,
0.009264040738344193,
-0.03187530115246773,
-0.03234252706170082,
0.020492084324359894,
-0.04628138244152069,
-0.01968531310558319,
0.027172349393367767,
-0.004679394420236349,
-0.013085736893117428,
0.00741158239543438,
-0.056373775005340576,
-0.010841108858585358,
-0.035756342113018036,
-0.01745978184044361,
0.0031677738297730684,
0.003629039041697979,
-0.025630369782447815,
-0.02625630982220173,
-0.005242640618234873,
0.04470231384038925,
0.019576359540224075,
-0.002365339081734419,
-0.02809947542846203,
-0.10319484025239944,
-0.011723069474101067,
0.043821025639772415,
0.04211033135652542,
0.020334746688604355,
-0.01811816543340683,
-0.0430966280400753,
-0.012270993553102016,
0.022691411897540092,
-0.02083374559879303,
0.015189227648079395,
-0.02301103062927723,
-0.02479086071252823,
-0.016736416146159172,
-0.020699040964245796,
0.030663568526506424,
0.01243983581662178,
0.015598533675074577,
0.007727433927357197,
-0.016293440014123917,
-0.006796946749091148,
-0.006053563207387924,
0.007342899683862925,
0.0029616181273013353,
-0.010171591304242611,
0.02750902622938156,
0.001668863114900887,
-0.02986060455441475,
-0.020412014797329903,
-0.031095776706933975,
-0.06799261271953583,
-0.016607681289315224,
0.029583550989627838,
-0.017231082543730736,
-0.003831624984741211,
0.005712699610739946,
-0.04652419313788414,
0.032975465059280396,
0.02055962383747101,
0.0024414488580077887,
0.0074351211078464985,
-0.023485785350203514,
0.06324057281017303,
0.0018026597099378705,
-0.0031790160574018955,
0.03442050516605377,
0.015245734713971615,
-0.007109073922038078,
0.0044639273546636105,
-0.023816490545868874,
0.039016854017972946,
-0.02565290592610836,
0.012575644999742508,
-0.038677945733070374,
0.014395800419151783,
-0.030325600877404213,
0.070070780813694,
0.00955189485102892,
-0.023416686803102493,
-0.016650129109621048,
-0.028039103373885155,
0.0028731771744787693,
-0.0065049114637076855,
0.005835902411490679,
-0.023144176229834557,
-0.011370024643838406,
0.025375204160809517,
-0.018145382404327393,
-0.002276898128911853,
0.015307479538023472,
0.024167297407984734,
-0.005494551733136177,
0.02731531485915184,
-0.0038415086455643177,
0.04413128271698952,
-0.017645686864852905,
0.012141978368163109,
0.025439295917749405,
-0.0721367672085762,
0.04953811690211296,
-0.02763081155717373,
0.0037138029001653194,
0.015412922017276287,
-0.04948195815086365,
-0.008833336643874645,
0.00014492387708742172,
0.002784264739602804,
0.002374105853959918,
-0.0415356270968914,
0.023248868063092232,
0.026603318750858307,
0.009426451288163662,
-0.08033260703086853,
-0.05053534358739853,
-0.0042449114844202995,
0.006793338805437088,
-0.015017993748188019,
-0.01789957284927368,
0.0336797833442688,
-0.05235498398542404,
-0.043577227741479874,
-0.006932066287845373,
0.04877634719014168,
-0.03865627571940422,
-0.02819814532995224,
0.014728590846061707,
0.07280350476503372,
0.045039594173431396,
0.004402737598866224,
-0.002670892747119069,
-0.02186359278857708,
0.02352573722600937,
0.022027375176548958,
0.0248966496437788,
0.039306990802288055,
-0.020073961466550827,
-0.0319950245320797,
-0.025492092594504356,
0.00160790525842458,
0.03129275515675545,
-0.014297712594270706,
-0.022458810359239578,
0.04125272482633591,
0.014173422940075397,
0.008910938166081905,
-0.013377108611166477,
0.025830747559666634,
0.015799246728420258,
0.036812856793403625,
0.008200682699680328,
0.008000007830560207,
0.026202425360679626,
-0.040043905377388,
0.018819991499185562,
-0.015810994431376457,
0.015241187065839767,
0.036142852157354355,
0.03892409801483154,
0.004160032141953707,
0.029710352420806885,
0.017307249829173088,
-0.017866183072328568,
0.01126246340572834,
0.014255034737288952,
0.0009802044369280338,
0.031260062009096146,
0.01189865730702877,
-0.0024233702570199966,
-0.021617958322167397,
-0.048751749098300934,
-0.030758844688534737,
0.03547830134630203,
0.004090776666998863,
0.0051360661163926125,
-0.0020476984791457653,
-0.019735997542738914,
0.021067481487989426,
-0.039039526134729385,
0.004038651008158922,
0.01974230259656906,
-0.021376805379986763,
0.030343905091285706,
-0.004078584257513285,
0.006713204085826874,
0.014599082060158253,
0.04643869772553444,
-0.04655104875564575,
0.020930876955389977,
0.054405275732278824,
0.02875065617263317,
0.023828914389014244,
-0.001737495418637991,
-0.07634123414754868,
0.04264779016375542,
-0.02012811228632927,
0.0011646646307781339,
0.024208229035139084,
-0.017386434599757195,
0.022166026756167412,
-0.025031685829162598,
0.025847019627690315,
-0.04151681810617447,
-0.02412394993007183,
-0.06638625264167786,
0.04344820976257324,
0.020629795268177986,
0.027304042130708694,
0.013233255594968796,
-0.002542713424190879,
0.0032490442972630262,
0.008484899066388607,
-0.011454928666353226,
0.022216400131583214,
-0.0478782057762146,
-0.005903583951294422,
-0.03646917641162872,
-0.03378735110163689,
0.036451131105422974,
-0.018777471035718918,
-0.05421530827879906,
-0.009589183144271374,
-0.04259314388036728,
0.042174942791461945,
-0.000646681000944227,
0.023420549929142,
-0.007472039200365543,
0.032295603305101395,
-0.04724159836769104,
0.008866285905241966,
-0.04217061400413513,
0.026965217664837837,
0.11640691012144089,
0.042796339839696884,
0.03248967230319977,
-0.02392181195318699,
-0.004332695156335831,
-0.017765335738658905,
0.023114759474992752,
-0.0025427835062146187,
0.04618033021688461,
-0.01382528804242611,
0.022084102034568787,
0.0018850044580176473,
0.07583507150411606,
0.010279064998030663,
0.05125122517347336,
0.05065302923321724,
-0.04584714397788048,
-0.010057216510176659,
-0.04022017493844032,
0.01756453700363636,
-0.04123937338590622,
0.04941816255450249,
-0.001453824108466506,
0.007618789095431566,
-0.005460129585117102,
0.03903781995177269,
-0.01892244443297386,
-0.018733294680714607,
0.018462173640727997,
-0.023437272757291794,
-0.04309999942779541,
-0.005315676331520081,
-0.016159584745764732,
-0.020275674760341644,
-0.053330156952142715,
-0.009299730882048607,
0.027220100164413452,
-0.0005065005389042199,
0.013286060653626919,
0.023170264437794685,
0.027489420026540756,
0.024304434657096863,
0.009316816926002502,
0.03694361820816994,
-0.02832435816526413,
0.008686846122145653,
-0.0027125736232846975,
0.03444218635559082,
-0.009253655560314655,
-0.012545140460133553,
-0.00674758804962039,
0.007238513324409723,
0.009176474995911121,
-0.03711730241775513,
-0.014935355633497238,
-0.02628306671977043,
0.052147265523672104,
-0.01553137693554163,
-0.005300378426909447,
-0.0465606190264225,
0.06370899081230164,
-0.01980874501168728,
0.027114741504192352,
-0.012505373917520046,
-0.004751783795654774,
0.029104191809892654,
0.009774059057235718,
0.027116810902953148,
-0.037369366735219955,
0.005511467345058918,
-0.028071260079741478,
-0.0049387491308152676,
-0.0389745831489563,
-0.015592969954013824,
0.004462274257093668,
0.04447150230407715,
0.0644771084189415,
-0.019433336332440376,
0.029725225642323494,
-0.005480628926306963,
-0.06177763268351555,
0.0614684522151947,
-0.012496153824031353,
-0.03275668993592262,
-0.012379493564367294,
0.019236024469137192,
-0.0018071779049932957,
0.05940947309136391,
-0.06544437259435654,
-0.00763727119192481,
0.004876085557043552,
0.03965168073773384,
0.019062183797359467,
-0.0329105518758297,
0.01849273592233658,
0.01525808870792389,
-0.01664753258228302,
0.008177363313734531,
-0.03593987971544266,
0.01156842801719904,
0.01871855929493904,
0.013038686476647854,
-0.03914259001612663,
0.0314876027405262,
-0.003082848386839032,
0.02527415007352829,
0.03592394292354584,
-0.01396809983998537,
-0.013768532313406467,
0.019260091707110405,
0.007169198710471392,
-0.004415216390043497,
-0.06842581927776337,
-0.05202706903219223,
-0.025545313954353333,
-0.010486829094588757,
0.032304976135492325,
-0.02706691063940525,
0.025740541517734528,
-0.009790029376745224,
0.006790607236325741,
-0.05608455464243889,
-0.017791565507650375,
-0.05399192497134209,
0.021465053781867027,
0.026674650609493256,
-0.038364432752132416,
0.02221137098968029,
0.007989800535142422,
-0.063937708735466,
-0.009144657291471958,
0.012115256860852242,
0.008331695571541786,
-0.036334309726953506,
-0.0068658930249512196,
0.00351658440195024,
0.006715848110616207,
0.04166487976908684,
-0.012750466354191303,
0.0009209378040395677,
0.0036350826267153025,
-0.023099584504961967,
-0.05789787322282791,
0.017251813784241676,
-0.008973999880254269,
0.057983383536338806,
0.051858849823474884,
0.003998900298029184,
-0.009362274780869484,
0.04700016975402832,
-0.008379606530070305,
0.013670521788299084,
0.01883416809141636,
-0.04411328583955765,
-0.008117808029055595,
-0.04837680608034134,
0.020989257842302322,
0.0005163148161955178,
0.016119489446282387,
0.02009495161473751,
0.018358435481786728,
0.01497857179492712,
-0.008878177031874657,
0.003217448014765978,
-0.037025194615125656,
-0.013536738231778145,
0.04362832382321358,
0.050984494388103485,
0.026667045429348946,
0.02634751982986927,
-0.021937957033514977,
0.05113876610994339,
0.02944021299481392,
0.0009426007163710892,
-0.11028074473142624,
-0.026618175208568573,
0.019862713292241096,
-0.0043435534462332726,
0.029690859839320183,
-0.0022066019009798765,
0.020734306424856186,
0.025037311017513275,
-0.07680574059486389,
0.013550527393817902,
-0.038993243128061295,
-0.027195759117603302,
-0.01487941574305296,
-0.01538520585745573,
-0.03451143950223923,
0.04300578683614731,
0.022532308474183083,
0.0366780050098896,
0.003635686356574297,
0.033060599118471146,
0.02193339727818966,
-0.005478436592966318,
-0.02937886118888855,
0.043979063630104065,
-0.03221289813518524,
-0.05070485174655914,
0.09336239099502563,
-0.0013621806865558028,
0.011664951220154762,
0.007267682813107967,
0.037604913115501404,
0.022986412048339844,
-0.009073968045413494,
0.017620032653212547,
-0.020856982097029686,
0.019929658621549606,
0.023193538188934326,
0.0005918681854382157,
-0.04362974315881729,
0.055179886519908905,
0.01470983400940895,
0.044734735041856766,
0.0011621294543147087,
-0.027264339849352837,
0.025240153074264526,
-0.04780438169836998,
-0.013973996043205261,
0.015907466411590576,
-0.046675097197294235,
-0.023332323879003525,
0.007781723514199257,
0.020474160090088844,
0.008734699338674545,
-0.002803374547511339,
0.010646231472492218,
-0.060885265469551086,
-0.013764659874141216,
0.0361064188182354,
0.01271113846451044,
0.0012088714865967631,
-0.024352895095944405,
0.00885415356606245,
-0.012039978057146072,
0.013444685377180576,
0.031075138598680496,
-0.0011120062554255128,
-0.043156981468200684,
0.010095489211380482,
0.008665342815220356,
-0.001953659811988473,
0.005228445399552584,
-0.02803005836904049,
-0.03569167107343674,
0.05574186146259308,
0.015666641294956207,
0.05627919360995293,
-0.04150347784161568,
-0.038006771355867386,
-0.0242081880569458,
-0.03562938794493675,
0.020130222663283348,
-0.016734309494495392,
0.006880246568471193,
-0.025457631796598434,
0.003085954347625375,
-0.002797880908474326,
0.007765218615531921,
0.028382884338498116,
0.016221243888139725,
-0.022585077211260796,
0.029626544564962387,
0.003535788506269455,
0.02260671742260456,
-0.023093992844223976,
-0.011938970535993576,
0.003776839002966881,
-0.02475104108452797,
0.016325311735272408,
-0.013991343788802624,
-0.028227584436535835,
0.01571238785982132,
0.08027790486812592,
0.01068359985947609,
-0.015461966395378113,
-0.02218371443450451,
-0.028692591935396194,
0.06211914122104645,
-0.014814450405538082,
-0.01874265819787979,
0.06663042306900024,
-0.04863184690475464,
0.028595425188541412,
0.02811559848487377,
0.0047967988066375256,
-0.028462335467338562,
0.02070745639503002,
-0.007451529614627361,
-0.029858026653528214,
0.016536403447389603,
-0.019489122554659843,
0.0027167166117578745,
-0.051223915070295334,
0.002430584514513612,
0.021686822175979614,
-0.04292384907603264,
-0.021200090646743774,
0.06538175046443939,
0.015880750492215157,
0.04672554135322571,
0.01142432913184166,
0.01677771471440792,
0.03986482694745064,
0.02163613587617874,
-0.00820943247526884,
0.0552222914993763,
0.06427041441202164,
0.02549164742231369,
-0.011945381760597229,
0.031235894188284874,
-0.025371769443154335,
0.0032316481228917837,
0.03061744198203087,
0.03227147087454796,
-0.028115224093198776,
-0.011839447543025017,
0.026625856757164,
0.01262423675507307,
0.008667344227433205,
0.0007027247338555753,
-0.014463147148489952,
0.09989991784095764,
-0.02285299263894558,
-0.003962122835218906,
-0.02754995785653591,
0.012812514789402485,
-0.045799434185028076,
0.0221396554261446,
-0.018830982968211174,
0.04585834592580795,
0.015393663197755814,
-0.012063354253768921,
-0.02750719152390957,
-0.002277238992974162,
0.021407553926110268,
-0.02134695276618004,
-0.028658268973231316,
-0.01870425045490265,
-0.01562308520078659,
-0.03392765298485756,
-0.005666033830493689,
-0.0010490751592442393,
0.00049719208618626,
0.031534794718027115,
0.048724692314863205,
0.035776957869529724,
-0.0126058179885149,
-0.007528556510806084,
-0.03575366735458374,
0.07749123126268387,
-0.05239446088671684,
-0.008936996571719646,
-0.017830410972237587,
-0.0030651427805423737,
-0.02901887334883213,
-0.045597143471241
] |
<p>How to prove that if a particle performs cyclical motion then its energy loss rate averaged over the period equals averaged radiation intensity?</p>
<p>The energy loss rate is the quantity of energy that the particle loses in unit time. And radiation intensity is an energy which observer detects some time later than it was emitted (due to finitude of light speed).</p>
<p>$$\frac{d E}{d t} = - \int d\Omega \left( 1 - \frac{(\vec n, \vec V(t))}{c}\right)\frac{dI(t)}{d\Omega}$$</p>
<p>where $\vec V(t)$ is the particle's speed, and $\vec n$ is unit vector on sphere $d \Omega$.</p>
<p>One can integrate it over time period $\int_{0}^{T}$ and get averaged energy loss rate $\langle\frac{d E}{d t}\rangle$, averaged intensity $\langle I\rangle$ and $$\int dt \int d\Omega \frac{(\vec n, \vec V(t))}{c}\frac{dI(t)}{d\Omega} $$ which should equals zero in order the initial sentence to be true.</p>
| 10,831 |
[
-0.02067745290696621,
-0.03638174757361412,
-0.004445603117346764,
-0.02517765574157238,
0.037589941173791885,
-0.007423280738294125,
-0.010902607813477516,
-0.00962050911039114,
0.017901230603456497,
-0.029657525941729546,
0.04056214913725853,
0.01248224452137947,
0.059300217777490616,
0.02100074663758278,
-0.007091831415891647,
-0.02878984622657299,
-0.04972919076681137,
0.0023132506757974625,
-0.02470002882182598,
-0.04769835248589516,
0.0178702250123024,
0.007131215650588274,
0.0028298194520175457,
-0.009606268256902695,
-0.03233505040407181,
0.03092668578028679,
0.006348608992993832,
0.003773958422243595,
-0.0023774830624461174,
0.054653555154800415,
-0.012918185442686081,
0.007788511924445629,
0.01740407384932041,
0.03185147047042847,
0.004791385028511286,
0.041192587465047836,
-0.038233961910009384,
-0.0030835135839879513,
0.005876205861568451,
-0.002412948524579406,
-0.0047890557907521725,
-0.015570384450256824,
0.003579082665964961,
0.06446607410907745,
-0.011456845328211784,
0.017133884131908417,
0.054986853152513504,
0.03332028165459633,
0.0797148048877716,
-0.03220484405755997,
0.046192754060029984,
-0.03995579108595848,
0.06810187548398972,
-0.031998634338378906,
0.03736856207251549,
-0.016590265557169914,
0.031974878162145615,
0.06259157508611679,
-0.0024074299726635218,
-0.035515740513801575,
-0.019101295620203018,
-0.004632838070392609,
-0.020315514877438545,
-0.011055825278162956,
0.006533039268106222,
0.013667799532413483,
0.02028486132621765,
-0.02347368188202381,
0.03442176431417465,
0.0032957021612674,
0.00869735050946474,
-0.03125457838177681,
-0.0036593752447515726,
-0.008125766180455685,
-0.004122687038034201,
-0.000980562181212008,
0.01827361062169075,
0.05671589449048042,
0.007562990300357342,
0.023745417594909668,
-0.004298039246350527,
-0.014545789919793606,
0.0058539994060993195,
0.03842988237738609,
0.021448098123073578,
-0.013648327440023422,
0.04349755868315697,
-0.005950503051280975,
0.01712592877447605,
0.04329584538936615,
0.0320158414542675,
0.013949524611234665,
0.021489985287189484,
0.011355758644640446,
-0.03349779173731804,
0.03456799313426018,
-0.005137012340128422,
0.0347919687628746,
-0.003651323262602091,
-0.04424614831805229,
-0.016425058245658875,
-0.028193211182951927,
0.04610271006822586,
0.07024597376585007,
0.003185683861374855,
-0.008529473096132278,
-0.07038526982069016,
0.005328475963324308,
-0.0601145476102829,
-0.010841627605259418,
-0.04157451167702675,
-0.0010080215288326144,
0.018090132623910904,
0.03443843871355057,
-0.016169121488928795,
0.007445988245308399,
-0.004277219995856285,
-0.03388168662786484,
0.05583743005990982,
0.0546673983335495,
0.04452015087008476,
0.007822223007678986,
0.019966715946793556,
-0.011695245280861855,
-0.04055149853229523,
-0.023540567606687546,
0.03741781413555145,
-0.01978609710931778,
-0.050376299768686295,
0.010609575547277927,
0.021979963406920433,
-0.03660179302096367,
-0.004333518445491791,
-0.006416702643036842,
0.01029914803802967,
-0.004321360029280186,
-0.07166697084903717,
-0.02767556719481945,
0.04665052145719528,
-0.038487259298563004,
-0.012367190793156624,
-0.06885041296482086,
0.017097610980272293,
0.05218527838587761,
0.08458276838064194,
0.01835291087627411,
-0.012036711908876896,
-0.0025937461759895086,
0.03482528030872345,
0.011197973042726517,
-0.0172226894646883,
-0.03939908370375633,
0.020204002037644386,
-0.022907745093107224,
-0.010852672159671783,
-0.03173748403787613,
0.04494072124361992,
0.026392096653580666,
-0.0012564314529299736,
-0.001653278712183237,
0.05823100730776787,
-0.017979517579078674,
0.012609750963747501,
-0.007554623298346996,
0.020646151155233383,
-0.04328631982207298,
0.08057557791471481,
0.010973991826176643,
0.0016618536319583654,
-0.004842222202569246,
0.07035506516695023,
0.016809727996587753,
-0.00036345963599160314,
0.01488032378256321,
0.06524108350276947,
-0.07042700052261353,
-0.02916557341814041,
0.012994807213544846,
-0.005135655868798494,
0.020195424556732178,
-0.050796471536159515,
-0.04534875974059105,
-0.01729142665863037,
0.032993607223033905,
-0.013230078853666782,
0.050255466252565384,
0.001195523887872696,
0.029949605464935303,
-0.042290061712265015,
-0.004415886010974646,
0.004479722119867802,
-0.06103440374135971,
0.028692319989204407,
0.023731723427772522,
-0.023109976202249527,
-0.006451266352087259,
-0.015146352350711823,
0.017186377197504044,
-0.005994447041302919,
-0.009266226552426815,
-0.012184347957372665,
0.030168557539582253,
0.005577791947871447,
-0.05443258583545685,
0.014867364428937435,
0.004545144736766815,
0.03998705372214317,
0.011726557277143002,
-0.017814192920923233,
0.006890459451824427,
-0.005674983840435743,
-0.0013140770606696606,
0.010169041343033314,
-0.0019931152928620577,
0.01901027373969555,
-0.005540446378290653,
0.04887177050113678,
-0.02439183183014393,
0.00843464769423008,
0.041487351059913635,
-0.005715119186788797,
0.03717783838510513,
0.043635424226522446,
-0.0024490037467330694,
0.016601817682385445,
0.06298623979091644,
-0.01666085049510002,
0.012217167764902115,
-0.03376905992627144,
-0.06357128918170929,
-0.03696517273783684,
0.009956073015928268,
0.019347716122865677,
0.044351380318403244,
-0.04124487563967705,
0.0033211084082722664,
0.04507224261760712,
0.016580471768975258,
0.005103634670376778,
0.022267881780862808,
0.012379025109112263,
-0.021366426721215248,
0.03755154833197594,
0.04355568811297417,
-0.01773785427212715,
-0.009394440799951553,
0.010998756624758244,
-0.033093199133872986,
-0.024304090067744255,
0.04907151311635971,
-0.025617556646466255,
0.02820739708840847,
0.013457069173455238,
0.016176555305719376,
0.02927733026444912,
-0.010269707068800926,
0.02566218003630638,
-0.011667320504784584,
0.011166469193994999,
0.031060073524713516,
-0.03810657933354378,
0.01081533171236515,
-0.049192532896995544,
0.011959380470216274,
0.022829947993159294,
-0.006296120584011078,
-0.024525467306375504,
-0.03485264256596565,
0.03756942227482796,
-0.025219080969691277,
-0.0017843444366008043,
0.0029607154428958893,
-0.007114774081856012,
-0.027146708220243454,
-0.016113827005028725,
0.020317677408456802,
0.02953706681728363,
-0.008142287842929363,
-0.05954835191369057,
-0.013830265030264854,
-0.02562602423131466,
0.003146631643176079,
-0.02890215627849102,
0.05268119275569916,
-0.036511801183223724,
-0.0037384263705462217,
-0.027822105213999748,
-0.07341499626636505,
0.051320210099220276,
-0.029261408373713493,
-0.020888948813080788,
0.06144056096673012,
0.01566249318420887,
-0.08994591236114502,
-0.005752404220402241,
-0.015122810378670692,
-0.028412282466888428,
-0.06993212550878525,
-0.036065150052309036,
0.055691152811050415,
-0.02789856120944023,
-0.06651275604963303,
0.03076290711760521,
-0.033831026405096054,
-0.05715947970747948,
0.020360909402370453,
-0.0411653034389019,
0.012650484219193459,
-0.04488857835531235,
0.044446565210819244,
0.007167702540755272,
-0.044823188334703445,
-0.008890058845281601,
-0.06685686111450195,
-0.061658699065446854,
0.028765767812728882,
0.0024947160854935646,
0.030155569314956665,
0.009544472210109234,
-0.042230963706970215,
0.057030923664569855,
0.06178344041109085,
0.012450492940843105,
-0.0006667125271633267,
0.011908154003322124,
0.007923873141407967,
-0.05628541484475136,
0.005018717143684626,
0.005417249631136656,
-0.0005391761078499258,
0.0015820212429389358,
0.018522458150982857,
0.017550483345985413,
0.0062591303139925,
0.05493789166212082,
0.00685291038826108,
-0.009680739603936672,
-0.005556387826800346,
0.03133176267147064,
0.00939360074698925,
0.022081665694713593,
-0.03734631463885307,
0.022321606054902077,
0.005119727458804846,
0.03773007169365883,
0.006685555446892977,
-0.06369684636592865,
0.031837478280067444,
0.022079844027757645,
0.003070497652515769,
0.012095474638044834,
0.019568810239434242,
0.015524826012551785,
0.028408663347363472,
-0.00521888816729188,
0.03525461256504059,
0.050864409655332565,
0.0000241453690250637,
0.004821740556508303,
-0.01729445345699787,
0.03169241547584534,
0.014478015713393688,
-0.04172559082508087,
-0.013627746142446995,
0.011222120374441147,
0.009299000725150108,
-0.02891113981604576,
0.0067544798366725445,
0.04139862582087517,
0.019523248076438904,
0.040133606642484665,
0.00030189770041033626,
-0.03199518844485283,
0.01265236921608448,
-0.02602308802306652,
-0.0071347178891301155,
-0.04198099300265312,
0.035014864057302475,
0.027490567415952682,
0.024937042966485023,
0.03483843058347702,
-0.002767335856333375,
0.03690426051616669,
-0.012470003217458725,
-0.06399884819984436,
0.04204973578453064,
0.004052858334034681,
-0.020875830203294754,
-0.021370837464928627,
-0.0028472146950662136,
-0.029826192185282707,
-0.02421436458826065,
-0.017923031002283096,
0.003122558118775487,
-0.015813903883099556,
-0.032820213586091995,
0.009991013444960117,
-0.014655647799372673,
-0.06482274830341339,
-0.04672914370894432,
0.023415597155690193,
0.07342774420976639,
-0.039832379668951035,
0.0031891183461993933,
0.06245662271976471,
-0.008814949542284012,
-0.00042869392200373113,
-0.030028771609067917,
-0.01766357198357582,
0.010509442538022995,
-0.008074810728430748,
0.053840022534132004,
0.023680662736296654,
0.006911888252943754,
-0.007190778851509094,
0.013729928061366081,
0.002227330580353737,
0.013928231783211231,
-0.030051741749048233,
0.00123096804600209,
-0.037928879261016846,
0.01932312361896038,
0.029927333816885948,
0.06620150059461594,
0.03329155594110489,
-0.004125663079321384,
0.032853636890649796,
0.01115249190479517,
0.027227243408560753,
0.040258582681417465,
0.022089822217822075,
-0.04135680943727493,
0.003207569941878319,
-0.02704271860420704,
0.03655602037906647,
-0.017889486625790596,
-0.014361712150275707,
0.0019873403944075108,
-0.02170928195118904,
-0.002208368619903922,
-0.004731057211756706,
-0.0026918393559753895,
0.04315146431326866,
0.0031923905480653048,
0.014581587165594101,
-0.01796106994152069,
0.005151525605469942,
-0.0002026734291575849,
-0.033296551555395126,
0.0074079507030546665,
0.05067909508943558,
0.03423149511218071,
0.006434878334403038,
-0.002993233036249876,
-0.05527796968817711,
-0.03580852970480919,
0.018010912463068962,
0.07625410705804825,
0.0035678346175700426,
0.004081685561686754,
-0.030752094462513924,
-0.032692715525627136,
0.0005940973642282188,
-0.03280530497431755,
-0.0023382108192890882,
0.003616228699684143,
-0.003627220867201686,
-0.03051465004682541,
-0.04577852785587311,
-0.03595584258437157,
0.0016183669213205576,
-0.01721974089741707,
0.023610195145010948,
-0.02704792469739914,
-0.03296322003006935,
0.00041949754813686013,
0.01142716221511364,
0.03255696967244148,
0.018218783661723137,
-0.047882888466119766,
-0.021341146901249886,
-0.0469457171857357,
0.04640456289052963,
-0.02889835461974144,
-0.0783265233039856,
-0.0191341545432806,
0.005266149993985891,
-0.0040337457321584225,
0.05255557596683502,
-0.032390497624874115,
-0.042916908860206604,
0.02301943302154541,
0.05196833983063698,
-0.02307208999991417,
0.020573124289512634,
-0.09873689711093903,
0.04648888111114502,
-0.009884616360068321,
0.00006261861562961712,
0.041249170899391174,
0.056782662868499756,
0.0035053794272243977,
-0.015179450623691082,
0.014451075345277786,
0.0291679035872221,
-0.03141295909881592,
0.01441514864563942,
-0.014290663413703442,
0.010913470759987831,
-0.009688896127045155,
0.045604102313518524,
0.009573228657245636,
-0.016429632902145386,
0.01470991875976324,
-0.0035989684984087944,
0.0028994379099458456,
0.014214234426617622,
-0.02079153247177601,
0.020227650180459023,
0.0032700824085623026,
0.0221866387873888,
0.038576286286115646,
-0.006355212070047855,
0.015555228106677532,
-0.005609248764812946,
-0.020756004378199577,
0.042918477207422256,
0.008087431080639362,
0.04887251555919647,
-0.04847748205065727,
-0.0002547941403463483,
0.024602437391877174,
-0.04029221460223198,
0.03245338797569275,
-0.022154927253723145,
-0.004291668068617582,
0.02060539834201336,
0.02154032327234745,
-0.0431443527340889,
-0.01895809732377529,
-0.021241195499897003,
0.016138477250933647,
-0.05248914286494255,
-0.010803064331412315,
0.006511067505925894,
0.03476065397262573,
-0.08545359969139099,
-0.025106998160481453,
0.007074069697409868,
0.012947908602654934,
-0.024965593591332436,
0.012151295319199562,
-0.0008342718938365579,
-0.037963952869176865,
-0.027295254170894623,
-0.008805643767118454,
0.01731913536787033,
-0.0031807180494070053,
-0.00758322374895215,
0.030877484008669853,
0.030594516545534134,
0.03481652960181236,
-0.03813851252198219,
-0.01885794661939144,
-0.031057847663760185,
-0.0011174057144671679,
-0.05582073703408241,
-0.03956792876124382,
0.061183758080005646,
-0.032912954688072205,
-0.040923554450273514,
-0.014493062160909176,
-0.011980576440691948,
0.005366927478462458,
-0.023660166189074516,
-0.04611612483859062,
0.038073327392339706,
-0.005086392629891634,
-0.013931119814515114,
-0.01576503925025463,
-0.023859882727265358,
0.02328622341156006,
0.04523373395204544,
0.03208374232053757,
-0.011686134152114391,
-0.027880633249878883,
-0.04638263210654259,
0.005437115207314491,
0.006672960706055164,
0.028094330802559853,
-0.011975312605500221,
0.03911849856376648,
0.02036825194954872,
0.016406932845711708,
-0.01018505822867155,
0.01865467242896557,
-0.027451539412140846,
-0.027251334860920906,
0.027393944561481476,
-0.0072531080804765224,
-0.05264531075954437,
-0.02472981996834278,
-0.020189715549349785,
-0.06662089377641678,
0.06050856411457062,
0.059303976595401764,
-0.00031692060292698443,
0.06308194249868393,
-0.00600805040448904,
0.03453265503048897,
-0.012303807772696018,
-0.012512528337538242,
0.012110915035009384,
-0.005511138122528791,
-0.018651561811566353,
0.020005572587251663,
-0.020938968285918236,
-0.027440831065177917,
0.062239788472652435,
0.04224441573023796,
-0.03154171630740166,
0.05650921165943146,
0.003009216394275427,
-0.003091886406764388,
-0.011375918984413147,
0.004885551519691944,
-0.01913583278656006,
0.004101593978703022,
-0.029515907168388367,
0.047628387808799744,
-0.010090290568768978,
-0.011647449806332588,
-0.0032128929160535336,
0.024332309141755104,
-0.0032610842026770115,
-0.028053253889083862,
-0.009964816272258759,
-0.04330732673406601,
0.025093412026762962,
0.030781542882323265,
0.007891439832746983,
0.008922168053686619,
0.01027547288686037,
0.03163750469684601,
0.00020736281294375658,
0.0017499402165412903,
0.015402271412312984,
-0.0343761183321476,
-0.007716674357652664,
-0.03827634081244469,
-0.05726216360926628,
0.022472728043794632,
-0.02543041668832302,
-0.011467565782368183,
-0.005217450670897961,
-0.009996533393859863,
0.03090246208012104,
0.0553617998957634,
0.004901538603007793,
0.046087827533483505,
0.03992714360356331,
0.02349819429218769,
0.03199106082320213,
0.006384697742760181,
0.04141583293676376,
0.1289088875055313,
0.05580274760723114,
-0.0015643551014363766,
-0.02272631786763668,
-0.00204075057990849,
0.010454884730279446,
0.05028606578707695,
-0.050665948539972305,
0.04233301803469658,
-0.011198827996850014,
0.006845513358712196,
0.015975499525666237,
0.02309993840754032,
0.001988127129152417,
-0.023257385939359665,
-0.005447393283247948,
-0.0509013794362545,
0.008706988766789436,
0.006101721432060003,
0.01319305319339037,
0.013162987306714058,
0.008686782792210579,
-0.01390355359762907,
0.02333945222198963,
-0.027234775945544243,
-0.028225034475326538,
-0.022579699754714966,
-0.033466026186943054,
0.026483062654733658,
-0.011729524470865726,
-0.03514071926474571,
0.032302528619766235,
0.011373525485396385,
-0.029920650646090508,
-0.011669867672026157,
0.0011697234585881233,
0.009785282425582409,
0.0021961519960314035,
0.028792116791009903,
0.047267038375139236,
0.040147632360458374,
0.01929672807455063,
0.0605405829846859,
0.05079219490289688,
-0.010214129462838173,
0.01423591934144497,
-0.040944069623947144,
0.06529753655195236,
-0.01767875626683235,
-0.0019239559769630432,
0.021320797502994537,
-0.04072418808937073,
-0.05725586414337158,
-0.09453938901424408,
0.019485777243971825,
0.000567025737836957,
0.005218003410845995,
-0.01113730575889349,
-0.0005130606004968286,
-0.03682301193475723,
-0.015065204352140427,
0.010361217893660069,
0.019916994497179985,
0.013702316209673882,
0.012159271165728569,
-0.0467674620449543,
0.0010721756843850017,
0.05724073201417923,
-0.01761458069086075,
0.014324529096484184,
0.009872758761048317,
-0.0057213627733290195,
-0.02153119258582592,
-0.011280672624707222,
-0.027701782062649727,
-0.01782437413930893,
0.06182458996772766,
0.013556545600295067,
-0.03844315931200981,
-0.00531300762668252,
-0.08808717131614685,
-0.017533548176288605,
0.017891284078359604,
-0.04850175976753235,
-0.018237417563796043,
-0.0024929186329245567,
0.011369762010872364,
0.01996912807226181,
-0.03734529763460159,
0.01705826073884964,
0.00013426740770228207,
0.045129235833883286,
0.05199703201651573,
-0.026144836097955704,
-0.041899148374795914,
-0.00853525847196579,
0.02351565659046173,
0.0011896248906850815,
-0.04267935827374458,
0.020180411636829376,
0.014878558926284313,
0.0035505115520209074,
0.006359773688018322,
0.03538176789879799,
-0.010274235159158707,
-0.012296580709517002,
0.013677465729415417,
-0.027920452877879143,
0.029461435973644257,
0.039492812007665634,
0.04275734722614288,
-0.04730627313256264,
-0.016542257741093636,
-0.04248671978712082,
0.015497707761824131,
0.012149852700531483,
-0.001686054514721036,
-0.05176446586847305,
0.03285839408636093,
-0.05612753704190254,
0.026726074516773224,
-0.038191936910152435,
-0.018327487632632256,
-0.040574878454208374,
0.020835760980844498,
0.00805687252432108,
0.003372487612068653,
-0.013411172665655613,
0.05655592679977417,
-0.015930840745568275,
-0.06142442300915718,
0.05049914866685867,
0.04306057468056679,
-0.017805738374590874,
-0.0019105321262031794,
0.014573725871741772,
0.005510613322257996,
0.04462982341647148,
-0.00025585590628907084,
-0.03839105740189552,
0.029463674873113632,
-0.021926041692495346,
-0.02498643286526203,
0.03134370595216751,
0.007867658510804176,
-0.0027915809769183397,
-0.0015090983361005783,
-0.005538624711334705,
0.009723191149532795,
0.04523385316133499,
-0.008772862143814564,
-0.026158789172768593,
-0.0017625715117901564,
-0.0682353675365448,
-0.026825902983546257,
-0.008932285010814667,
0.027646832168102264,
0.03152941167354584,
0.004156486131250858,
0.02464277297258377,
0.04562683776021004,
-0.01269649900496006,
0.022125015035271645,
-0.012752368114888668,
-0.016608376055955887,
0.004982728511095047,
0.04085263982415199,
0.034011729061603546,
0.012509102933108807,
0.05105096474289894,
-0.020262356847524643,
0.017233023419976234,
-0.005060276947915554,
-0.025702638551592827,
-0.08996271342039108,
0.013839936815202236,
-0.025942683219909668,
0.027972957119345665,
0.025275515392422676,
-0.011273801326751709,
0.035148680210113525,
0.011081344448029995,
-0.054420385509729385,
0.03131254017353058,
-0.022199325263500214,
0.00993795320391655,
-0.030360138043761253,
-0.026274174451828003,
-0.044400278478860855,
0.006431485526263714,
0.028748638927936554,
0.0345437154173851,
0.004060035105794668,
0.036528605967760086,
-0.025122789666056633,
-0.02705620974302292,
-0.013318270444869995,
0.008756640367209911,
0.008732685819268227,
-0.0023325488436967134,
0.0692119374871254,
-0.01376958005130291,
0.011052681133151054,
0.03197750076651573,
-0.009666277095675468,
-0.006760166026651859,
-0.015816375613212585,
0.032556112855672836,
-0.0032200883142650127,
0.02888629212975502,
-0.017127279192209244,
-0.01527059730142355,
-0.00013455412408802658,
-0.004539944231510162,
0.030105503275990486,
-0.015800150111317635,
-0.025437867268919945,
-0.00406489847227931,
0.03730430454015732,
-0.034253962337970734,
-0.05039938539266586,
0.03905763104557991,
0.014456954784691334,
-0.00757355522364378,
0.026113485917448997,
-0.022105896845459938,
0.001331549952737987,
-0.013256753794848919,
0.015589850023388863,
-0.041483864188194275,
0.00004821151742362417,
0.011666023172438145,
0.018035074695944786,
0.0035525315906852484,
-0.044573184102773666,
-0.010677079670131207,
-0.019793611019849777,
0.03740217909216881,
0.03030349500477314,
-0.06580039858818054,
-0.031791120767593384,
0.009710283949971199,
-0.01388121210038662,
0.024039199575781822,
0.007408428471535444,
-0.056309040635824203,
-0.05720297992229462,
0.0040698242373764515,
0.015462998300790787,
0.019030911847949028,
-0.0201882254332304,
-0.019237639382481575,
-0.008002808317542076,
-0.09149173647165298,
0.027840808033943176,
0.005138426087796688,
-0.00007706759060965851,
-0.07017004489898682,
-0.02122950553894043,
-0.0207156203687191,
0.013092887587845325,
0.058497775346040726,
-0.005429689306765795,
-0.043754346668720245,
0.04307286813855171,
-0.0235732514411211,
-0.01259580533951521,
-0.0395897813141346,
0.02579767443239689,
-0.048386674374341965,
-0.03423549234867096,
0.00799857173115015,
-0.006643562577664852,
-0.030979808419942856,
0.01334871631115675,
0.020460665225982666,
0.005995617713779211,
0.04656153544783592,
0.0023523687850683928,
-0.05753941461443901,
0.04187939688563347,
0.013334394432604313,
0.024969523772597313,
0.05891924351453781,
-0.019072046503424644,
0.038300469517707825,
0.037383049726486206,
-0.047877196222543716,
-0.04688753932714462,
0.01391313225030899,
-0.03906511142849922,
-0.02156198024749756,
-0.013361427001655102,
0.0009880297584459186,
0.014040454290807247,
-0.015926923602819443,
0.0009653118904680014,
0.050226882100105286,
-0.024981612339615822,
-0.02264510840177536,
0.05006609112024307,
-0.00588537473231554,
0.04402315989136696,
0.019274841994047165,
0.02121800184249878,
0.014701386913657188,
-0.008887494914233685,
-0.006708342116326094,
0.0741947740316391,
-0.016001135110855103,
-0.021636614575982094,
0.011491868644952774,
0.024451643228530884,
0.008696573786437511,
0.010897167958319187,
0.004182466771453619,
0.03862270712852478,
-0.026891931891441345,
-0.011282365769147873,
0.018708910793066025,
-0.03145212680101395,
-0.06179114803671837,
0.05007370188832283,
0.03656824305653572,
0.026101237162947655,
-0.011027373373508453,
0.028024155646562576,
0.009203613735735416,
-0.06096503511071205,
-0.05470137670636177,
0.03708881139755249,
0.008949840441346169,
0.04957941547036171,
-0.004086279310286045,
0.03140335530042648,
-0.005123164504766464,
-0.01629568263888359,
0.013679270632565022,
-0.058894503861665726,
-0.005671162623912096,
0.043650638312101364,
-0.05116117745637894,
0.0005482318229041994,
0.01727910339832306,
0.0014118312392383814,
-0.04346883296966553,
-0.010766723193228245,
0.021807223558425903,
0.027792906388640404,
-0.01568334922194481,
-0.02129192277789116,
-0.011737734079360962,
0.04784794896841049,
-0.05167759954929352,
0.0022821417078375816,
-0.0285617858171463,
0.07802359014749527,
0.00997406616806984,
-0.04159495607018471
] |
<p>Well, the difference between the two expressions $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is exactly $\Delta p^2$ , i.e. the squared uncertainty (variance) of the momentum,
where the $\hat p$ is momentum operator and uncertainty on the momentum operator is defined by:
$$\Delta p= \sqrt {\langle \hat p^2 \rangle_{\psi} - \langle \hat p \rangle_{\psi}^2}$$.
why the difference between $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is NOT zero?</p>
| 10,832 |
[
0.011420764960348606,
-0.015915991738438606,
-0.0038452777080237865,
-0.03818269446492195,
0.024372858926653862,
0.005286787636578083,
-0.002966257743537426,
-0.04479304701089859,
-0.004773662891238928,
-0.027655724436044693,
0.026713915169239044,
0.035670965909957886,
0.07478634268045425,
-0.016192156821489334,
0.010501019656658173,
0.02815067023038864,
-0.015126783400774002,
-0.006430356297641993,
-0.019539887085556984,
-0.011230891570448875,
-0.0021486333571374416,
0.0547834150493145,
0.01756119169294834,
-0.002484740689396858,
-0.026661401614546776,
0.053803451359272,
0.026883970946073532,
0.02577831596136093,
0.015969768166542053,
0.09545563161373138,
-0.02545422501862049,
0.004796789493411779,
0.0346122644841671,
0.045042455196380615,
0.005332664120942354,
-0.03296808898448944,
-0.023897705599665642,
-0.04776718467473984,
-0.03418583795428276,
0.025027750059962273,
-0.062339913100004196,
-0.00451329629868269,
0.0022709520999342203,
0.038320381194353104,
0.0037238006480038166,
0.003184720641002059,
-0.004102042410522699,
-0.012246628291904926,
0.048160992562770844,
-0.054694343358278275,
0.06823032349348068,
0.01829591765999794,
0.048351868987083435,
0.026403162628412247,
-0.014582488685846329,
0.010966066271066666,
0.06028245389461517,
0.09207818657159805,
-0.030703743919730186,
-0.07366309314966202,
-0.010994148440659046,
-0.02702767215669155,
0.01875535398721695,
-0.016103345900774002,
-0.0333772748708725,
0.029183262959122658,
-0.0045078289695084095,
-0.028934309259057045,
-0.004127184394747019,
-0.013083062134683132,
0.026650240644812584,
0.0025465362705290318,
0.04307202249765396,
-0.03849511593580246,
0.04938973858952522,
-0.044847458600997925,
0.019966676831245422,
0.03373875841498375,
0.046780236065387726,
0.04664565250277519,
0.02017524652183056,
0.007765962742269039,
0.04288842901587486,
-0.005757309962064028,
0.010076782666146755,
-0.005146004259586334,
0.045971885323524475,
-0.005585324950516224,
-0.00038195334491319954,
0.050534263253211975,
0.003715099999681115,
0.020382221788167953,
0.030454332008957863,
-0.026418650522828102,
-0.005581093020737171,
0.04031561687588692,
0.004155247006565332,
0.03992997109889984,
-0.00952138751745224,
-0.050147101283073425,
0.01656327396631241,
-0.035065073519945145,
0.027007142081856728,
0.087989941239357,
-0.000993002438917756,
-0.014178324490785599,
-0.03518480435013771,
0.018737435340881348,
-0.025222554802894592,
-0.015670187771320343,
-0.022351140156388283,
0.027407828718423843,
-0.028890401124954224,
-0.004233999643474817,
0.0031442895997315645,
-0.05678887665271759,
0.020362503826618195,
-0.012432940304279327,
0.04156013950705528,
0.05870296061038971,
-0.00019060178601648659,
-0.017863435670733452,
0.006582727190107107,
-0.03450576588511467,
-0.0641692727804184,
0.049256857484579086,
0.04391304403543472,
-0.018951212987303734,
-0.0752149298787117,
0.001536060473881662,
-0.0015438324771821499,
-0.0032647335901856422,
0.03396426886320114,
0.012039917521178722,
0.0046875267289578915,
-0.013628629967570305,
-0.12371712923049927,
-0.05675731971859932,
0.03128144145011902,
-0.052098482847213745,
-0.009796066209673882,
-0.09015718102455139,
0.014366797171533108,
0.04062798246741295,
0.07090306282043457,
-0.012968556024134159,
0.020578719675540924,
-0.009269420057535172,
0.016385426744818687,
0.016547244042158127,
-0.00867644976824522,
0.0018294494366273284,
0.007709123194217682,
-0.02568717673420906,
-0.00008226226054830477,
-0.05882580578327179,
0.02156459353864193,
0.026401806622743607,
-0.008224180899560452,
0.0013586725108325481,
0.05121641978621483,
-0.03247343376278877,
0.0007768861250951886,
0.0013223389396443963,
0.01765894517302513,
-0.013125420548021793,
0.07158855348825455,
0.05018625408411026,
0.011176921427249908,
0.03282628953456879,
-0.0039655775763094425,
0.02549014985561371,
0.0060256244614720345,
0.025392090901732445,
0.05089040845632553,
-0.03079225867986679,
-0.04396319389343262,
-0.017900338396430016,
0.0106161218136549,
-0.00804270338267088,
-0.05578024685382843,
-0.004676722921431065,
-0.03364497423171997,
0.03125305101275444,
-0.002039064187556505,
0.03190303593873978,
0.003047169419005513,
0.004585345275700092,
-0.007946524769067764,
-0.043732427060604095,
-0.015894338488578796,
-0.08762998878955841,
0.031993426382541656,
0.022832298651337624,
-0.016777103766798973,
0.05375436320900917,
0.022431496530771255,
0.005868409760296345,
-0.011339999735355377,
-0.033852044492959976,
-0.0026093884371221066,
0.017890822142362595,
0.0028446922078728676,
-0.0220088679343462,
0.03711998835206032,
0.046481408178806305,
0.0577034056186676,
-0.0025727623142302036,
0.03991208225488663,
-0.012876221910119057,
-0.04097863286733627,
0.017024986445903778,
0.0058457450941205025,
-0.008744541555643082,
0.02424638904631138,
-0.023640330880880356,
0.017986522987484932,
-0.022814644500613213,
-0.028490278869867325,
0.03689125180244446,
-0.018923774361610413,
0.048284225165843964,
0.04513370990753174,
0.007296308409422636,
0.0037341287825256586,
0.019926760345697403,
0.006180638447403908,
0.02291516773402691,
-0.01593118906021118,
-0.014605292119085789,
-0.021095160394906998,
-0.0022065655793994665,
0.010614491067826748,
0.03970848023891449,
-0.03096422739326954,
0.015915581956505775,
0.03230223432183266,
0.03088492527604103,
0.03736768662929535,
0.032354194670915604,
-0.017309706658124924,
-0.044164687395095825,
0.0100681958720088,
0.012914103455841541,
0.007911882363259792,
0.018528109416365623,
0.021319879218935966,
-0.009015965275466442,
0.04555613920092583,
0.019853195175528526,
-0.016347253695130348,
0.032635390758514404,
-0.04087361320853233,
0.0015777840744704008,
0.022801531478762627,
-0.028824111446738243,
0.024677151814103127,
-0.004832278471440077,
0.007769634947180748,
0.012293677777051926,
-0.0008477719966322184,
-0.01743008755147457,
-0.038159508258104324,
-0.038652993738651276,
0.042558442801237106,
-0.010022355243563652,
-0.024773728102445602,
0.012411629781126976,
-0.0047044591046869755,
-0.00949570257216692,
-0.020667612552642822,
0.00028398583526723087,
-0.007484291214495897,
-0.0537496879696846,
-0.01061124075204134,
0.053373925387859344,
-0.004542259499430656,
0.05972657352685928,
-0.009047451429069042,
-0.04294557869434357,
0.010451843030750751,
-0.025914236903190613,
0.0178633164614439,
-0.007979159243404865,
-0.03898337483406067,
0.017484746873378754,
-0.03390317037701607,
-0.017541641369462013,
0.044769737869501114,
-0.03646927326917648,
0.030213892459869385,
-0.003913116175681353,
-0.028975339606404305,
-0.0285976342856884,
-0.002949340734630823,
-0.041781529784202576,
0.01249734591692686,
0.011423854157328606,
-0.006743593607097864,
0.015138429589569569,
-0.030399290844798088,
-0.029130958020687103,
0.05075046420097351,
-0.01522662304341793,
-0.06920620799064636,
-0.03126297891139984,
-0.003629049751907587,
0.03483567014336586,
-0.059243716299533844,
0.002151059452444315,
0.048044826835393906,
-0.028050081804394722,
-0.016035588458180428,
-0.04398322105407715,
-0.034802261739969254,
0.01917862333357334,
0.007304045371711254,
0.0028764340095221996,
-0.017193684354424477,
-0.026909297332167625,
0.10416804254055023,
0.018626859411597252,
-0.008027489297091961,
-0.0016628160374239087,
0.017944086343050003,
-0.02675609476864338,
-0.03319183737039566,
-0.03306909650564194,
0.03139708936214447,
-0.00012625307135749608,
0.06523400545120239,
0.010574514046311378,
0.017460966482758522,
0.016057327389717102,
0.012606129050254822,
-0.017124202102422714,
-0.00601569376885891,
-0.017829084768891335,
-0.026007724925875664,
0.04350178688764572,
-0.005492962431162596,
-0.02000991627573967,
0.003218703670427203,
0.034089311957359314,
0.01278247032314539,
-0.03806032985448837,
-0.041236743330955505,
0.0517120398581028,
-0.02996865287423134,
0.010989147238433361,
-0.05100981146097183,
0.054547447711229324,
-0.011466373689472675,
-0.020610999315977097,
-0.004311275202780962,
-0.0033801267854869366,
0.04086068645119667,
-0.03396961838006973,
0.0026093439664691687,
0.04600271210074425,
0.0025172794703394175,
-0.0059752087108790874,
-0.022671040147542953,
-0.006000358145684004,
-0.005100103095173836,
0.036714501678943634,
-0.024736599996685982,
-0.060871172696352005,
0.06091306358575821,
0.041981395334005356,
0.029045818373560905,
-0.015027700923383236,
-0.04238124564290047,
-0.0041750636883080006,
-0.04578206315636635,
0.016397031024098396,
-0.00962615106254816,
0.055698785930871964,
-0.005163739901036024,
0.07059606164693832,
0.04103873297572136,
0.01024747546762228,
-0.009026741608977318,
0.004789659753441811,
-0.038638290017843246,
0.015955287963151932,
-0.039220280945301056,
-0.03066076710820198,
-0.015922244638204575,
-0.012860149145126343,
-0.0015358460368588567,
-0.033742666244506836,
-0.004630065988749266,
-0.01890757866203785,
-0.007603845093399286,
-0.030738813802599907,
0.018287142738699913,
-0.020382754504680634,
0.008027884177863598,
-0.031281884759664536,
0.03849990665912628,
0.010388822294771671,
-0.01062279473990202,
0.041096244007349014,
0.05928238853812218,
-0.02919258363544941,
0.024862954393029213,
-0.02865651063621044,
-0.006227385718375444,
0.013635572046041489,
0.0108093386515975,
0.05338185653090477,
0.01301458291709423,
-0.00568432779982686,
-0.0025526653043925762,
-0.02352636493742466,
0.06746601313352585,
0.007148461882025003,
-0.02277236618101597,
0.023727629333734512,
-0.05012078583240509,
-0.012602005153894424,
-0.0151902474462986,
0.043989673256874084,
-0.0017717647133395076,
0.012544377706944942,
0.009761128574609756,
0.0012624278897419572,
0.0023196206893771887,
0.02408774569630623,
0.05706123635172844,
-0.03553604707121849,
0.003106756368651986,
-0.055560801178216934,
0.011668778955936432,
-0.03470023721456528,
-0.04769871383905411,
0.008446680381894112,
-0.014868197031319141,
-0.014715452678501606,
-0.022451138123869896,
0.024454466998577118,
0.0070480844005942345,
-0.03438475728034973,
-0.014060583896934986,
0.02004867047071457,
-0.0022175046615302563,
0.00933034811168909,
0.003239976242184639,
0.009279396384954453,
0.026776010170578957,
0.01895785890519619,
0.001141456887125969,
0.008937429636716843,
-0.036476753652095795,
0.008815928362309933,
0.007971431128680706,
0.03965986892580986,
-0.023385992273688316,
-0.010980107821524143,
-0.032301388680934906,
-0.019574468955397606,
0.05062076821923256,
-0.03654945269227028,
0.02578895539045334,
-0.017051931470632553,
-0.03132648393511772,
-0.01348895113915205,
-0.02382589317858219,
-0.0268268883228302,
0.015183379873633385,
-0.01277600321918726,
0.003315007546916604,
-0.04562733322381973,
-0.009509646333754063,
-0.03349290415644646,
-0.009378114715218544,
0.02304554171860218,
0.052075017243623734,
-0.02165229804813862,
0.00019256302039138973,
-0.00824648141860962,
0.03937404975295067,
-0.022315233945846558,
-0.0914512649178505,
-0.00021175775327719748,
0.02186497487127781,
0.00019766493642237037,
0.07733467221260071,
-0.050574883818626404,
-0.07943708449602127,
-0.003441188018769026,
-0.007864922285079956,
-0.025074459612369537,
0.01136139314621687,
-0.004582260735332966,
0.029188990592956543,
0.037710461765527725,
-0.01321230549365282,
0.06918385624885559,
0.015536191873252392,
-0.0008052000193856657,
-0.012501345947384834,
-0.03172159940004349,
0.049140579998493195,
-0.04151638224720955,
0.0034488483797758818,
-0.04848456010222435,
0.0039879921823740005,
-0.030423596501350403,
0.05422208458185196,
-0.00953794177621603,
0.059588365256786346,
0.006552016828209162,
-0.028752127662301064,
-0.023452278226614,
0.021656237542629242,
0.02792780101299286,
-0.0006942468462511897,
0.006857359316200018,
-0.0055228653363883495,
0.026465747505426407,
-0.023500725626945496,
-0.011003031395375729,
0.03231886029243469,
-0.008145601488649845,
0.014827089384198189,
-0.012636235915124416,
0.05528995767235756,
-0.019948134198784828,
-0.03019803576171398,
-0.000023195738322101533,
-0.02572474628686905,
-0.0018842126009985805,
0.018860504031181335,
0.006378520280122757,
0.009305023588240147,
-0.04787832871079445,
-0.06228891387581825,
0.006832973565906286,
-0.017292078584432602,
0.030370503664016724,
-0.0776083692908287,
0.021678483113646507,
0.005978105589747429,
0.008594545535743237,
-0.0866202712059021,
-0.01240044366568327,
-0.011028761975467205,
0.038009773939847946,
-0.0023512239567935467,
0.000632386771030724,
0.004518396686762571,
-0.019551830366253853,
-0.014380177482962608,
-0.02853337675333023,
0.05648807808756828,
-0.009245245717465878,
-0.03747976943850517,
0.005551583599299192,
-0.00010848943929886445,
0.050679370760917664,
-0.015554332174360752,
-0.004289085511118174,
-0.019093574956059456,
-0.01932239532470703,
0.004475807771086693,
0.032135769724845886,
0.06640652567148209,
-0.019541412591934204,
-0.05034354701638222,
-0.001915234955959022,
-0.0024627840612083673,
0.023922394961118698,
-0.020891040563583374,
0.010373474098742008,
-0.0010260813869535923,
0.018342742696404457,
0.02880326472222805,
-0.010400958359241486,
-0.004412130918353796,
-0.02741549164056778,
0.025748485699295998,
0.0266297347843647,
-0.02266116812825203,
-0.028251152485609055,
-0.0247939545661211,
0.005543192848563194,
0.0016529965214431286,
-0.007967439480125904,
-0.013655112124979496,
0.05194983631372452,
-0.005218499805778265,
0.011967803351581097,
0.03173019364476204,
-0.016094200313091278,
0.008486848324537277,
0.011437245644629002,
0.017332563176751137,
0.01907801814377308,
0.012190714478492737,
-0.01390391681343317,
0.005089359823614359,
-0.040516458451747894,
0.013202951289713383,
0.06325941532850266,
0.00220085890032351,
0.06785707175731659,
0.01262571569532156,
0.012499558739364147,
-0.012442960403859615,
-0.03269096836447716,
-0.025559745728969574,
-0.0004902158980257809,
-0.017253434285521507,
0.03725438937544823,
-0.009570025838911533,
0.022556358948349953,
0.04341481626033783,
0.03050212934613228,
0.009733200073242188,
0.004432625137269497,
0.026443080976605415,
0.04327314347028732,
0.002609911607578397,
-0.028254233300685883,
-0.014398178085684776,
0.05580936744809151,
-0.0360582135617733,
0.015587138012051582,
-0.007088149432092905,
-0.017901398241519928,
0.024667959660291672,
-0.020083647221326828,
-0.026570329442620277,
-0.012008768506348133,
-0.0129218939691782,
-0.03455568850040436,
0.009835639037191868,
0.02762489952147007,
-0.016150062903761864,
-0.01733001507818699,
0.0046655950136482716,
0.004752399865537882,
0.008166809566318989,
0.0198891069740057,
-0.014304998330771923,
-0.060004595667123795,
-0.04486143961548805,
-0.027072008699178696,
-0.02565295808017254,
0.02714390866458416,
-0.03905943036079407,
-0.02934730239212513,
0.00587422214448452,
-0.029383037239313126,
0.04065092280507088,
0.0039220270700752735,
0.011859292164444923,
-0.0390692800283432,
0.0510999858379364,
0.022000839933753014,
0.023904714733362198,
-0.0014032373437657952,
0.008610646240413189,
0.08865432441234589,
0.03522951528429985,
0.03781970962882042,
-0.0505983904004097,
0.0016289870254695415,
-0.022636400535702705,
0.042271196842193604,
-0.03275977075099945,
0.05402118340134621,
0.0020825639367103577,
0.027000252157449722,
-0.008317382074892521,
0.05910857021808624,
0.039363861083984375,
-0.021951649338006973,
0.03848676010966301,
-0.04799368232488632,
-0.037075288593769073,
-0.020449025556445122,
0.020496558398008347,
-0.015234850347042084,
-0.006057212129235268,
-0.019506219774484634,
0.01283175777643919,
-0.03641006723046303,
0.060817278921604156,
-0.011113282293081284,
-0.03210746496915817,
0.021476106718182564,
-0.002722913632169366,
-0.03682693466544151,
-0.00420804601162672,
-0.006921685300767422,
0.017220133915543556,
-0.04616370424628258,
0.010684248991310596,
0.008879532106220722,
-0.020789992064237595,
0.007195725105702877,
0.03448641672730446,
0.015683887526392937,
-0.027624670416116714,
0.004194577224552631,
0.0001503663806943223,
-0.04223746433854103,
-0.017334451898932457,
-0.02835584431886673,
0.09128472954034805,
-0.026229996234178543,
0.011340935714542866,
-0.004567766096442938,
-0.027596762403845787,
-0.03679512068629265,
-0.05010703206062317,
-0.02728979103267193,
0.016703378409147263,
0.023878132924437523,
-0.012996137142181396,
0.02209530957043171,
-0.028324175626039505,
0.022318748757243156,
-0.002333264099434018,
0.021038562059402466,
-0.016637753695249557,
-0.0015511215897276998,
-0.03629501163959503,
0.02553798258304596,
0.008376754820346832,
-0.03872692212462425,
-0.0017181668663397431,
0.01213706936687231,
-0.012229693122208118,
-0.08349277079105377,
-0.03955380618572235,
0.05185532942414284,
0.004877694882452488,
0.0638577938079834,
-0.012029141187667847,
-0.011768478900194168,
-0.01520638819783926,
-0.07784222066402435,
0.033034197986125946,
-0.02883998490869999,
-0.0004366849025245756,
0.020171763375401497,
-0.007703612092882395,
0.042052194476127625,
0.03367970511317253,
-0.02599068358540535,
0.014194859191775322,
0.014981275424361229,
0.026565417647361755,
0.015064460225403309,
-0.051478736102581024,
-0.033476702868938446,
0.043593984097242355,
-0.02044062688946724,
-0.00007989731966517866,
0.002104539657011628,
-0.002860662993043661,
0.03609868139028549,
0.010272813029587269,
-0.023923158645629883,
0.028838394209742546,
-0.02687782794237137,
-0.005114559084177017,
0.029950136318802834,
-0.0059714047238230705,
-0.011979990638792515,
0.06279516220092773,
0.018731042742729187,
-0.019671760499477386,
-0.028989015147089958,
-0.02648100070655346,
0.00012056956620654091,
-0.005941624287515879,
0.011586510576307774,
-0.016291337087750435,
-0.024566583335399628,
-0.007027311250567436,
0.01383223757147789,
-0.02147878333926201,
-0.00825444795191288,
-0.09176738560199738,
0.031056120991706848,
0.013232027180492878,
-0.016711384057998657,
-0.0019448398379608989,
0.0198441781103611,
0.00448970403522253,
-0.030390510335564613,
0.03852543607354164,
0.059927113354206085,
-0.0003097388835158199,
0.0005959774716757238,
0.012693829834461212,
-0.0035158356186002493,
0.01457459107041359,
-0.014825098216533661,
-0.021425800397992134,
0.05414905771613121,
-0.03149804472923279,
-0.06529857963323593,
0.060074541717767715,
0.032079171389341354,
0.03167915716767311,
0.04000542685389519,
-0.018865030258893967,
-0.017410464584827423,
0.08135370165109634,
-0.05217508226633072,
-0.017043232917785645,
-0.005969084333628416,
-0.029883552342653275,
-0.02591542713344097,
-0.024351591244339943,
0.02636054717004299,
-0.01330581121146679,
-0.007330536842346191,
0.032063212245702744,
0.025895798578858376,
-0.013972258195281029,
0.008703120052814484,
0.0022924616932868958,
0.011348248459398746,
0.06915769726037979,
0.048440299928188324,
0.0009166706004180014,
0.002070936607196927,
0.028782518580555916,
-0.04697020724415779,
0.04525265842676163,
0.015645384788513184,
0.04420799762010574,
-0.0994587391614914,
-0.014630977995693684,
-0.004834716208279133,
0.006390727125108242,
0.03724882751703262,
-0.04613163694739342,
0.037426259368658066,
0.05664939433336258,
-0.06386050581932068,
0.0012790539767593145,
-0.05240359529852867,
-0.006002651993185282,
0.0041038175113499165,
0.00760868564248085,
-0.025925228372216225,
0.08228600770235062,
0.02059405855834484,
0.022498443722724915,
0.014191636815667152,
-0.011600825004279613,
0.011944439262151718,
-0.0019620785024017096,
-0.03677516430616379,
0.03184490650892258,
-0.02637907862663269,
-0.014627303928136826,
0.03925316780805588,
-0.03135981783270836,
-0.0028682989068329334,
0.029995333403348923,
0.002832079539075494,
-0.012549668550491333,
-0.02820824459195137,
0.04197392612695694,
0.022274518385529518,
-0.0002485026780050248,
0.007721611298620701,
0.000665818341076374,
-0.017107311636209488,
0.017186902463436127,
0.02814127877354622,
0.028467562049627304,
0.014565185643732548,
-0.020156899467110634,
-0.026160022243857384,
-0.037434931844472885,
-0.033984966576099396,
0.023995164781808853,
0.00781550444662571,
-0.02911258675158024,
0.012911141850054264,
0.023288609459996223,
0.012075933627784252,
-0.04142312705516815,
0.04621759057044983,
-0.06951116770505905,
0.001922799739986658,
0.013135642744600773,
0.010984448716044426,
-0.01999588869512081,
0.021069835871458054,
-0.029749879613518715,
-0.05480843037366867,
0.026754308491945267,
0.02290891297161579,
-0.040366142988204956,
-0.05479875206947327,
-0.01682915911078453,
0.020985834300518036,
-0.0075762830674648285,
0.04853486642241478,
-0.05538194999098778,
-0.05765029415488243,
0.008745341561734676,
-0.017655979841947556,
0.01763712801039219,
-0.02879493683576584,
-0.01230181846767664,
-0.042547378689050674,
-0.08543848246335983,
0.0578031949698925,
0.015261879190802574,
0.00004428052852745168,
-0.04376102611422539,
0.01940908469259739,
-0.022432558238506317,
0.01614065282046795,
0.03531436249613762,
0.012772811576724052,
-0.02927979826927185,
0.009240635670721531,
-0.012983521446585655,
0.022869929671287537,
-0.03756765276193619,
0.002392848953604698,
-0.007032192312180996,
-0.018893305212259293,
-0.008157473988831043,
-0.018438542261719704,
0.017115715891122818,
0.040973562747240067,
0.022003106772899628,
-0.012603840790688992,
0.019382497295737267,
0.003752505872398615,
-0.04723668843507767,
0.06224508583545685,
-0.0073906416073441505,
-0.012969953939318657,
0.08340767025947571,
0.017457127571105957,
0.02793734334409237,
0.015700340270996094,
0.0006091673858463764,
-0.010499189607799053,
0.04827308654785156,
0.0018012207001447678,
-0.017391327768564224,
-0.005615128204226494,
0.020108237862586975,
0.016362076625227928,
-0.0230922382324934,
-0.016671260818839073,
0.028608618304133415,
-0.03453255817294121,
-0.01008614432066679,
0.047925278544425964,
0.03175516426563263,
0.01401116605848074,
0.026772353798151016,
-0.0017684833146631718,
0.03622311353683472,
0.00306545477360487,
0.0167529359459877,
0.01768939383327961,
0.02708044834434986,
0.02171063981950283,
0.03594490513205528,
0.02609577775001526,
-0.029223784804344177,
0.012251880951225758,
0.027457311749458313,
0.0215020552277565,
-0.03665078431367874,
-0.031908921897411346,
0.013048427179455757,
-0.009818613529205322,
-0.0009102013427764177,
-0.0022118957713246346,
-0.030402561649680138,
0.0869753435254097,
-0.012178372591733932,
0.008903720416128635,
-0.022314054891467094,
0.010251257568597794,
0.0023240388836711645,
-0.014519273303449154,
0.018319034948945045,
0.05547916516661644,
-0.01259802095592022,
-0.029425466433167458,
-0.039728205651044846,
0.001962391659617424,
0.00497959041967988,
-0.06373758614063263,
0.01974867656826973,
0.004696529358625412,
-0.029552984982728958,
-0.04326135292649269,
-0.025642551481723785,
-0.012376341968774796,
-0.02951921708881855,
0.03162863105535507,
0.040388450026512146,
0.04364980757236481,
0.005223098676651716,
-0.04637628793716431,
0.011115321889519691,
0.037818387150764465,
-0.04958491399884224,
-0.011557921767234802,
-0.001625600503757596,
0.011610852554440498,
0.0025973354931920767,
-0.011139921844005585
] |
<p>I've recently been working through a lot of physics problems and a lot of them say to assume that the mass of the string used in a problem involving a pulley, for example, is negligible. Why is this important? What would happen if the mass of the string wasn't negligible? </p>
| 10,833 |
[
-0.005541372578591108,
0.012053198181092739,
-0.030244197696447372,
-0.04300044849514961,
-0.003592521883547306,
0.005175027530640364,
-0.02567501924932003,
0.003252546302974224,
0.0008236534195020795,
-0.002366536995396018,
-0.010540702380239964,
0.0361669696867466,
0.026078108698129654,
-0.004702855367213488,
0.0260314904153347,
0.021175432950258255,
0.012483937665820122,
-0.03307224437594414,
0.0016423417255282402,
-0.031961895525455475,
-0.01800377294421196,
0.020274585112929344,
0.03798487037420273,
-0.007705374155193567,
0.000030332203095895238,
0.004948185756802559,
0.02597195841372013,
-0.02556554786860943,
0.025616008788347244,
0.04739027097821236,
-0.004515861161053181,
-0.0026884800754487514,
-0.005029371008276939,
0.04142685979604721,
0.02408706210553646,
0.018886350095272064,
-0.03779464215040207,
-0.010315412655472755,
0.0023288801312446594,
0.03439713269472122,
-0.028519850224256516,
0.005062798038125038,
0.02567388117313385,
0.03114759363234043,
-0.051135431975126266,
0.037450965493917465,
-0.01666485331952572,
-0.05209364369511604,
0.0652548149228096,
-0.06490834057331085,
0.05185871198773384,
0.0027993079274892807,
0.06411145627498627,
0.033834218978881836,
-0.00880512222647667,
-0.009557285346090794,
0.07251513004302979,
0.06334439665079117,
-0.025803789496421814,
-0.09033097326755524,
-0.04639224708080292,
0.0028681904077529907,
-0.027001317590475082,
-0.050820667296648026,
-0.010783345438539982,
0.05846687778830528,
-0.019498605281114578,
-0.00408845953643322,
0.062203194946050644,
0.019159801304340363,
-0.021012669429183006,
0.017026273533701897,
0.04171189293265343,
0.0035685135517269373,
-0.014211881905794144,
-0.008085079491138458,
0.02074240893125534,
0.00035156187368556857,
0.015192973427474499,
0.053535182029008865,
-0.04534931480884552,
-0.01369180902838707,
0.06223127990961075,
0.05524251610040665,
0.009446525014936924,
-0.019673669710755348,
0.059225182980298996,
-0.01174917258322239,
0.025830959901213646,
0.021424857899546623,
-0.0017162685981020331,
-0.027236927300691605,
0.025372879579663277,
-0.03605196252465248,
0.02633177861571312,
0.03661145642399788,
-0.0030952671077102423,
0.030106011778116226,
0.03208623453974724,
-0.015997087582945824,
-0.0306573286652565,
-0.0018661984940990806,
0.03567827492952347,
0.057660847902297974,
0.022096849977970123,
-0.015986276790499687,
-0.01804286241531372,
0.017529945820569992,
-0.01803060807287693,
-0.01797732152044773,
-0.023081185296177864,
0.009489194490015507,
-0.00016554816102143377,
-0.01989484205842018,
0.04232396185398102,
-0.020561348646879196,
-0.009978527203202248,
-0.02307727560400963,
0.045921992510557175,
0.034108202904462814,
0.027695821598172188,
-0.04121464490890503,
0.05209902301430702,
-0.04214548319578171,
-0.022099031135439873,
0.01224272046238184,
0.007640167139470577,
-0.01512954756617546,
-0.037408247590065,
0.02862592414021492,
-0.008651643991470337,
-0.009908203966915607,
0.00250437343493104,
-0.02040962688624859,
0.07233823090791702,
-0.01975836046040058,
-0.07585234940052032,
-0.05725827068090439,
0.041514329612255096,
-0.007713486906141043,
-0.039851970970630646,
-0.05495060235261917,
-0.04040345177054405,
0.045002616941928864,
0.07827775180339813,
-0.0015745109412819147,
0.0101062236353755,
0.02367623895406723,
0.033629149198532104,
-0.011908456683158875,
-0.007087755482643843,
-0.05312475189566612,
0.019374128431081772,
-0.04501309618353844,
0.001185228698886931,
-0.07548303157091141,
0.012561841867864132,
0.025900287553668022,
0.007528000511229038,
-0.0376080721616745,
0.034157149493694305,
-0.013690993189811707,
0.0090683214366436,
0.011286727152764797,
-0.019978679716587067,
-0.029558707028627396,
0.0696374773979187,
0.01653549075126648,
-0.014240030199289322,
0.04853567108511925,
0.024726586416363716,
0.03668420389294624,
0.016855143010616302,
0.013036704622209072,
0.022710949182510376,
-0.03490784764289856,
0.007523545064032078,
-0.016034631058573723,
0.02742083929479122,
-0.017121633514761925,
-0.01579275168478489,
-0.03927459195256233,
0.007729178294539452,
0.013853857293725014,
-0.002989127766340971,
0.05117446556687355,
0.0029652887023985386,
-0.029253538697957993,
0.013176040723919868,
0.0017305038636550307,
-0.008700457401573658,
-0.052085842937231064,
0.038794562220573425,
0.001917851041071117,
0.008052847348153591,
0.035495273768901825,
0.025826258584856987,
-0.0100434310734272,
-0.06811798363924026,
0.034612998366355896,
0.03232719004154205,
0.03556002303957939,
-0.02559465728700161,
-0.02172502689063549,
0.0110539011657238,
0.01417058240622282,
0.0447944812476635,
0.008562035858631134,
0.04040894657373428,
-0.0358266718685627,
-0.058688558638095856,
0.0014540115371346474,
-0.04504638910293579,
0.027431251481175423,
0.01437313947826624,
-0.0008756943279877305,
0.034590400755405426,
-0.06803247332572937,
-0.012584883719682693,
0.05032133683562279,
-0.01772306114435196,
0.07670165598392487,
0.024884391576051712,
-0.013328125700354576,
-0.006919724866747856,
0.007852303795516491,
-0.0006511809187941253,
0.0052424222230911255,
-0.009491058997809887,
-0.05212320014834404,
-0.06950514018535614,
0.01573038287460804,
0.012985632754862309,
0.04948888719081879,
-0.04129683971405029,
0.0047793337143957615,
0.05760636553168297,
0.02101769484579563,
0.019857672974467278,
0.012472325004637241,
-0.021903162822127342,
-0.015911830589175224,
0.03466654568910599,
0.020125070586800575,
-0.011067241430282593,
0.0025000160094350576,
0.027778685092926025,
0.05996989458799362,
0.03273000568151474,
0.006689102854579687,
-0.03058626316487789,
0.056789297610521317,
-0.003270308021456003,
0.059752028435468674,
0.025860106572508812,
-0.02489880844950676,
0.046103157103061676,
-0.03688843920826912,
0.035084888339042664,
0.020755309611558914,
-0.00029930545133538544,
-0.009739366360008717,
-0.0008752234280109406,
-0.02747928351163864,
0.0007243340369313955,
0.0026967735029757023,
-0.013160204514861107,
-0.004193283151835203,
0.02753721922636032,
-0.03349927440285683,
-0.031501226127147675,
-0.029520131647586823,
-0.030167652294039726,
-0.012313274666666985,
0.008683883585035801,
0.02239813469350338,
0.014971326105296612,
0.07901528477668762,
-0.04264824837446213,
-0.0424298420548439,
-0.02053009159862995,
-0.05628780275583267,
-0.021821007132530212,
0.01784617453813553,
-0.035412345081567764,
0.006250109523534775,
-0.03570210561156273,
-0.049949731677770615,
0.06446921825408936,
-0.017100868746638298,
0.02721210941672325,
0.028455790132284164,
-0.008924993686378002,
-0.01914053224027157,
-0.021327070891857147,
-0.02224368415772915,
-0.001509231049567461,
-0.01679804176092148,
0.009430872276425362,
0.044432174414396286,
-0.007798342499881983,
-0.022550493478775024,
0.02691618539392948,
-0.059113431721925735,
-0.06293123960494995,
-0.016621064394712448,
-0.006938614416867495,
0.02073388732969761,
-0.018934085965156555,
0.005298198200762272,
-0.011477775871753693,
-0.03856108337640762,
-0.006517969537526369,
-0.041710998862981796,
-0.0617942176759243,
0.014042666181921959,
0.002879299456253648,
0.03886721655726433,
0.005837947130203247,
-0.05434601381421089,
0.10750174522399902,
0.018723139539361,
-0.02276129275560379,
0.016888927668333054,
-0.03256989270448685,
-0.019403357058763504,
-0.0333971306681633,
0.033035364001989365,
0.011218308471143246,
-0.020939256995916367,
0.0032275572884827852,
0.03582048416137695,
0.04182187467813492,
0.019871383905410767,
0.019204987213015556,
0.0026958587113767862,
-0.022311562672257423,
-0.00042930658673867583,
-0.008600259199738503,
0.030524305999279022,
-0.013699204660952091,
-0.02240000106394291,
0.01890857331454754,
0.008698375895619392,
0.034778084605932236,
-0.014143875800073147,
-0.03450611233711243,
0.08172135800123215,
-0.01158977672457695,
0.03495311737060547,
-0.011280659586191177,
0.0493253692984581,
-0.029358329251408577,
0.0026154308579862118,
0.025620613247156143,
-0.009160731919109821,
0.0348818264901638,
-0.022422505542635918,
0.00641989940777421,
0.006187784019857645,
0.07732480764389038,
-0.005625539924949408,
-0.05603915825486183,
-0.007002509199082851,
0.0004227370664011687,
0.0025624085683375597,
-0.022675978019833565,
-0.033773891627788544,
0.02807227149605751,
0.05315345525741577,
-0.0013832870172336698,
-0.04332765191793442,
-0.03260059282183647,
-0.004347021225839853,
-0.06824583560228348,
-0.006542048882693052,
-0.017158281058073044,
0.014561044052243233,
-0.027476796880364418,
0.014773122034966946,
-0.00035273574758321047,
0.044008687138557434,
-0.008338420651853085,
0.019617924466729164,
-0.08073131740093231,
0.03360079973936081,
-0.08947902172803879,
-0.031206423416733742,
-0.0006915635312907398,
0.014811525121331215,
-0.008590933866798878,
-0.042388465255498886,
-0.00042605382623150945,
-0.014566347934305668,
0.029998594895005226,
-0.0691564530134201,
-0.006214811932295561,
-0.0335741825401783,
-0.04933851584792137,
-0.0037236723583191633,
-0.007738979533314705,
0.0073641277849674225,
0.005598404444754124,
0.015613907016813755,
0.04178324714303017,
-0.020910128951072693,
-0.03487086296081543,
-0.01616145297884941,
-0.013758489862084389,
-0.0015811932971701026,
0.021989518776535988,
0.043009474873542786,
0.03199699893593788,
-0.05137374624609947,
0.0328785665333271,
0.03106115013360977,
0.07299104332923889,
-0.004267259035259485,
-0.018124768510460854,
-0.0075190686620771885,
-0.0816459134221077,
-0.028077680617570877,
-0.03327562287449837,
0.04411093518137932,
-0.03639598190784454,
-0.007021400146186352,
0.04516800120472908,
-0.019376298412680626,
0.014219990000128746,
0.0005495668156072497,
0.04406106472015381,
0.05921359732747078,
-0.01002605352550745,
-0.0677221342921257,
-0.004271029494702816,
-0.05718543007969856,
-0.00785041507333517,
-0.014286577701568604,
0.011530325748026371,
-0.008558194153010845,
0.0004793639818672091,
0.024947257712483406,
0.01381832268089056,
-0.02326185442507267,
0.0006486074416898191,
-0.008374007418751717,
0.027638649567961693,
-0.01984814740717411,
-0.007665220182389021,
0.07509715855121613,
0.012104133144021034,
0.003317308844998479,
-0.02696700394153595,
-0.018974067643284798,
-0.0658305212855339,
-0.018912749364972115,
0.038727954030036926,
0.036479122936725616,
-0.005872630048543215,
-0.007776198443025351,
-0.028296999633312225,
-0.01793701760470867,
0.07594328373670578,
-0.020664503797888756,
0.022339409217238426,
-0.04418826475739479,
0.02579600363969803,
-0.012008619494736195,
-0.009621421806514263,
0.0038396024610847235,
0.03606593236327171,
-0.027136294171214104,
0.024947594851255417,
-0.002079009311273694,
0.015394551679491997,
-0.012283140793442726,
0.027518073096871376,
0.016597913578152657,
0.048368215560913086,
0.02016974426805973,
-0.008786005899310112,
0.022551126778125763,
0.03208865225315094,
-0.023847568780183792,
-0.0637674406170845,
0.0011537297395989299,
-0.005443484988063574,
-0.007821965962648392,
0.007214483339339495,
-0.025860954076051712,
-0.07068324834108353,
0.011397008784115314,
0.009579431265592575,
-0.042147934436798096,
-0.012747271917760372,
-0.03531758114695549,
0.005776599980890751,
0.035920631140470505,
0.004071550443768501,
0.0019416045397520065,
0.03154633194208145,
-0.04890797659754753,
-0.01875055767595768,
-0.02591712772846222,
0.03471560776233673,
-0.024140886962413788,
0.01623278111219406,
-0.05695807933807373,
-0.009472095407545567,
-0.015345302410423756,
0.0476609468460083,
0.005305123049765825,
0.029245665296912193,
-0.0014421251835301518,
-0.03213212266564369,
-0.02286427840590477,
-0.005335810594260693,
0.05679338052868843,
-0.015034862793982029,
0.01338554359972477,
0.0004366354551166296,
0.01878601871430874,
-0.031124092638492584,
0.005181072745472193,
0.03724757209420204,
-0.003856958821415901,
0.0386175699532032,
0.009007474407553673,
0.008931633085012436,
-0.00479755038395524,
-0.04274334758520126,
0.04649755358695984,
-0.05486089736223221,
0.027213215827941895,
-0.015406033024191856,
-0.017586033791303635,
0.01739189773797989,
-0.0437956377863884,
-0.051090069115161896,
-0.010476984083652496,
-0.03978772833943367,
0.03655203431844711,
-0.04154713451862335,
0.03902853652834892,
0.004899873863905668,
0.029789414256811142,
-0.01661255955696106,
-0.039454568177461624,
-0.005225029774010181,
0.011015904136002064,
0.046875208616256714,
0.014029514975845814,
0.014202095568180084,
-0.0023164916783571243,
-0.02538253553211689,
-0.002143370918929577,
0.06008905917406082,
-0.028239335864782333,
-0.00643965695053339,
0.018421359360218048,
-0.008091519586741924,
0.06761226803064346,
-0.0014346045209094882,
-0.030173150822520256,
0.015088425949215889,
-0.06339442729949951,
-0.003462238470092416,
-0.015733445063233376,
0.05624569579958916,
-0.010933028534054756,
-0.04523627087473869,
-0.005482133477926254,
-0.037322476506233215,
0.03582108020782471,
-0.005953039508312941,
0.02029893733561039,
0.026766153052449226,
0.038515523076057434,
0.0036694365553557873,
0.005493462085723877,
0.027706438675522804,
0.00482903653755784,
0.06091969460248947,
0.045192185789346695,
0.005260199308395386,
-0.012064033187925816,
-0.027438245713710785,
0.06257466971874237,
0.02053007110953331,
-0.004245315678417683,
0.018269652500748634,
0.03936232253909111,
-0.009908310137689114,
-0.0230599045753479,
0.0013083993690088391,
-0.012749717570841312,
0.01128463912755251,
-0.013929740525782108,
-0.020068464800715446,
0.0021722172386944294,
0.03748944401741028,
-0.03131714090704918,
-0.03851200267672539,
-0.0293051116168499,
0.014360460452735424,
0.04308690130710602,
-0.04783901944756508,
0.057406652718782425,
-0.0020767594687640667,
-0.026355385780334473,
0.009251373820006847,
-0.0036542541347444057,
-0.020413758233189583,
-0.0019671812187880278,
-0.005135184619575739,
-0.00020561266865115613,
-0.0447511300444603,
-0.002421075478196144,
0.05792737752199173,
0.0012364708818495274,
-0.027849288657307625,
0.0010187907610088587,
0.06700196117162704,
0.029772402718663216,
0.033076174557209015,
-0.012342242524027824,
-0.03841917961835861,
-0.015065009705722332,
-0.012246992439031601,
0.03368924930691719,
-0.01985149458050728,
0.01085083931684494,
0.033265650272369385,
0.0035476915072649717,
-0.021581023931503296,
-0.034928228706121445,
-0.00414698151871562,
-0.0006598897743970156,
0.02258872799575329,
0.020953921601176262,
-0.02694113180041313,
0.016369739547371864,
0.022901669144630432,
0.019238289445638657,
0.010772458277642727,
0.03502495214343071,
-0.018890593200922012,
-0.06413204222917557,
-0.016424916684627533,
-0.050368525087833405,
-0.03463240712881088,
0.03884260356426239,
0.03839828073978424,
-0.03406691551208496,
0.02578561194241047,
-0.009236110374331474,
0.023293234407901764,
0.025394978001713753,
0.016941094771027565,
-0.05881601572036743,
0.05957770720124245,
0.005757912993431091,
0.03576868772506714,
-0.021324397996068,
0.019076678901910782,
0.11028944700956345,
0.0349949449300766,
0.018417082726955414,
-0.04638633877038956,
-0.001582393771968782,
-0.024637669324874878,
0.0059457928873598576,
-0.0169144868850708,
0.00809390563517809,
0.001654193620197475,
0.008998805657029152,
0.007208776660263538,
0.03151663392782211,
-0.04527470842003822,
0.004665100947022438,
0.07176176458597183,
-0.051905643194913864,
-0.05374760553240776,
-0.010447332635521889,
0.0010944565292447805,
0.011062787845730782,
0.026128653436899185,
-0.060281310230493546,
0.02590891346335411,
-0.02713884226977825,
0.013144340366125107,
-0.014264548197388649,
-0.01909041777253151,
0.019565822556614876,
-0.01565900817513466,
-0.04334947466850281,
0.0038934999611228704,
0.024108119308948517,
-0.03220122680068016,
-0.026362061500549316,
0.029779093340039253,
0.038473792374134064,
0.007643270771950483,
0.00350167672149837,
-0.004719259683042765,
-0.019027438014745712,
0.009635557420551777,
-0.0007634059875272214,
0.006943991873413324,
-0.06012623757123947,
0.013444741256535053,
-0.02709411457180977,
0.04635724052786827,
0.008437635377049446,
0.030770009383559227,
0.010942834429442883,
-0.048908304423093796,
0.023252669721841812,
-0.05689277499914169,
-0.028728779405355453,
0.007928786799311638,
0.012411987408995628,
-0.03563704341650009,
0.004504679702222347,
0.006062822416424751,
0.013334277085959911,
0.049830589443445206,
0.033479150384664536,
0.028718624264001846,
-0.0019124747486785054,
-0.008836918510496616,
0.018668007105588913,
0.020146768540143967,
-0.022526651620864868,
-0.044326093047857285,
0.004214457701891661,
-0.025418492034077644,
-0.012790842913091183,
-0.017523687332868576,
-0.011846724897623062,
0.028816699981689453,
0.028561782091856003,
-0.027294402942061424,
0.02373296394944191,
0.006146345753222704,
-0.04383508861064911,
0.0618574358522892,
0.004987531341612339,
-0.008289271965622902,
-0.045245736837387085,
-0.022300908342003822,
0.004205743782222271,
0.04267788305878639,
-0.00711903627961874,
0.006138913333415985,
-0.02104862779378891,
0.02456716261804104,
0.005300845950841904,
-0.013035980053246021,
-0.01520883571356535,
0.017798149958252907,
-0.03784240782260895,
0.03643220290541649,
-0.014514000155031681,
0.01772177405655384,
0.007039153948426247,
0.004254116211086512,
-0.01693554036319256,
0.05556969717144966,
-0.015847953036427498,
-0.0013785096816718578,
0.010265638120472431,
-0.0414147824048996,
-0.016016872599720955,
0.02558089978992939,
0.03691079840064049,
-0.04846157506108284,
-0.009364675730466843,
-0.017377756536006927,
-0.01523894164711237,
0.02802511490881443,
0.034423913806676865,
-0.017981678247451782,
0.057642899453639984,
-0.038162194192409515,
0.034934915602207184,
-0.05261671543121338,
-0.0006076524732634425,
-0.06896280497312546,
-0.004809288308024406,
0.0316891148686409,
-0.02371564507484436,
-0.003926676698029041,
-0.026195431128144264,
-0.03925028815865517,
-0.023634715005755424,
-0.01479368470609188,
-0.003897090209648013,
-0.011618212796747684,
-0.01374722458422184,
0.02800765261054039,
-0.023202283307909966,
0.005969890858978033,
-0.009143269620835781,
-0.0275025125592947,
0.02385474368929863,
-0.036078691482543945,
-0.02083435468375683,
0.015222176909446716,
-0.006452849600464106,
0.034825630486011505,
0.02538643591105938,
-0.049224913120269775,
-0.05618952214717865,
0.02610633708536625,
-0.06610633432865143,
0.0003409904311411083,
-0.015980904921889305,
-0.018417850136756897,
-0.022119443863630295,
-0.0084565794095397,
-0.02652611956000328,
-0.02797292359173298,
-0.013976450078189373,
0.005937349051237106,
0.025546610355377197,
0.0076494584791362286,
-0.017686642706394196,
0.05082661285996437,
0.011161934584379196,
0.011879665777087212,
0.017219820991158485,
0.02071879431605339,
-0.0015622283099219203,
0.06762716919183731,
-0.03957030922174454,
0.0221966914832592,
0.016671739518642426,
0.01104175578802824,
-0.09091439098119736,
-0.016263937577605247,
0.009799023158848286,
-0.0031931728590279818,
0.032131634652614594,
-0.020245932042598724,
0.008210822008550167,
-0.006193983368575573,
-0.042147837579250336,
0.06302878260612488,
-0.04173974320292473,
-0.018220750615000725,
-0.03242446482181549,
-0.032271601259708405,
-0.010599398985505104,
0.059338852763175964,
0.01845347322523594,
0.037455230951309204,
-0.0186469703912735,
0.008185881190001965,
0.002487777965143323,
0.00639572087675333,
0.0175591129809618,
0.03685518726706505,
-0.0307608712464571,
0.02662370167672634,
0.061416976153850555,
0.0077035194262862206,
-0.009369746781885624,
0.015372777357697487,
-0.013678425922989845,
-0.004864852409809828,
-0.013148031197488308,
0.0005825110711157322,
0.01238197647035122,
0.04095450043678284,
0.026076627895236015,
0.008455655537545681,
-0.004867782350629568,
0.01150472555309534,
0.010321150533854961,
0.015884799882769585,
-0.029234660789370537,
0.01579418033361435,
0.0014202356105670333,
-0.055910419672727585,
-0.018762944266200066,
0.014471802860498428,
-0.005117384251207113,
0.011676955968141556,
0.007551621180027723,
0.001714841346256435,
-0.035061758011579514,
-0.015983905643224716,
0.016897814348340034,
-0.0325886495411396,
0.021293649449944496,
0.05881144851446152,
0.011034268885850906,
-0.020761681720614433,
0.040484290570020676,
0.03193286433815956,
-0.006400956306606531,
0.004068647976964712,
0.0178584773093462,
-0.02940121479332447,
-0.06142695993185043,
0.021670594811439514,
-0.0012457775883376598,
0.014058220200240612,
-0.016671720892190933,
-0.06690432876348495,
-0.03302649408578873,
0.05652889609336853,
0.027285261079669,
0.01653771474957466,
-0.004876395221799612,
-0.0495198629796505,
-0.01530061848461628,
-0.09881564974784851,
0.03799344599246979,
0.0004117460339330137,
0.0025597703643143177,
-0.03222529962658882,
0.003185014706104994,
0.008242396637797356,
0.02437877655029297,
0.0328095480799675,
-0.011515217833220959,
0.000037886140489717945,
0.04751255735754967,
-0.031633127480745316,
-0.02282359078526497,
-0.018400762230157852,
0.0007909353589639068,
-0.001079017762094736,
-0.024728715419769287,
-0.017384951934218407,
0.01206883229315281,
-0.000023097880330169573,
-0.0024380364920943975,
0.012003948912024498,
0.02427808754146099,
0.024802694097161293,
-0.028672724962234497,
0.008127196691930294,
0.05999621003866196,
0.024225987493991852,
-0.004308871924877167,
0.0574086531996727,
-0.006537205073982477,
0.0432894229888916,
-0.03859247267246246,
-0.007823193445801735,
-0.037039775401353836,
0.05328086018562317,
-0.014715742319822311,
0.02392471767961979,
-0.00916371215134859,
0.01174846664071083,
0.033402808010578156,
-0.02591886930167675,
-0.009398257359862328,
0.024991700425744057,
-0.033286839723587036,
-0.043535150587558746,
0.032539136707782745,
0.025360234081745148,
0.020793801173567772,
0.0011249904055148363,
0.01307329349219799,
0.05134015157818794,
-0.01365574263036251,
0.014755669049918652,
0.026863794773817062,
0.009312023408710957,
-0.0038981072138994932,
-0.0440705306828022,
0.04352622479200363,
-0.0193321630358696,
0.030058883130550385,
0.0336017906665802,
0.031038379296660423,
-0.06070249527692795,
-0.06070026010274887,
-0.016420677304267883,
-0.023285310715436935,
0.005123653449118137,
0.020458586513996124,
0.005268992390483618,
0.07209412008523941,
0.0375051349401474,
0.01734994538128376,
-0.0010920669883489609,
0.014419619925320148,
0.02866647206246853,
-0.03793539106845856,
-0.005459189414978027,
0.03429783508181572,
0.0067575713619589806,
-0.0054702782072126865,
-0.00600805738940835,
-0.005323069170117378,
0.03707600012421608,
-0.03172529488801956,
0.02788873389363289,
0.03254004567861557,
-0.01364503800868988,
-0.017610879614949226,
-0.01131020300090313,
-0.03955261781811714,
-0.015037700533866882,
0.029915418475866318,
0.06851836293935776,
0.017904724925756454,
-0.019183119758963585,
-0.01835028827190399,
0.0029368794057518244,
0.05314980819821358,
-0.056557100266218185,
0.015797462314367294,
0.016320649534463882,
0.01649128831923008,
-0.0008522973512299359,
0.0018802990671247244
] |
<p>A container filled with fluid is accelerating initially with a1 and instantly changes to a2 (a2 < a1). What would happen to the fluid in the container. </p>
<p>My thoughts on this - If the velocity of the system is v1 when the acceleration changes to a2.
The fluid will, at that instant, have a velocity of v1 while container accelerates (with an accleration a2) to v2 (v2>v1) The fluid in the container is moving backwards relative to the container. So, it would splash against the back wall of the container. Is this logically accurate or am I missing something.</p>
| 10,834 |
[
-0.035599011927843094,
-0.010444475337862968,
-0.04049988090991974,
0.015328170731663704,
0.05683130398392677,
-0.018200455233454704,
-0.009078264236450195,
-0.005848003551363945,
-0.00794984307140112,
0.03745749965310097,
0.013867598958313465,
0.033215127885341644,
0.053423527628183365,
0.0005652659456245601,
0.034246668219566345,
0.011981097050011158,
0.01979546621441841,
-0.036914724856615067,
0.0380864217877388,
-0.015402518212795258,
-0.010027171112596989,
0.002898446749895811,
0.03454780578613281,
-0.037804994732141495,
-0.02900841273367405,
0.04109501093626022,
0.012854380533099174,
-0.05142040178179741,
-0.008019570261240005,
0.019617246463894844,
-0.0294734388589859,
0.014394897036254406,
-0.03337465226650238,
-0.021769285202026367,
0.03408201411366463,
0.04253565892577171,
-0.039069484919309616,
-0.029670029878616333,
0.003945983946323395,
0.04805462434887886,
-0.025983240455389023,
0.006386312190443277,
-0.00011688729136949405,
0.0855487808585167,
-0.043651409447193146,
-0.0012811910128220916,
-0.001694253645837307,
0.018350500613451004,
0.049039147794246674,
-0.06489023566246033,
0.03411051258444786,
-0.015025199390947819,
0.01697390526533127,
0.07033219188451767,
-0.0014437854988500476,
0.03471563383936882,
0.044051747769117355,
0.05854785814881325,
0.015006904490292072,
-0.006430166773498058,
0.009073169901967049,
0.0030863152351230383,
-0.04948562756180763,
-0.017393311485648155,
-0.006062191445380449,
0.012157976627349854,
-0.02074289880692959,
-0.024834882467985153,
0.007346119731664658,
-0.004770280327647924,
-0.016196060925722122,
-0.03314429521560669,
0.035638175904750824,
-0.043338458985090256,
0.051427651196718216,
-0.0414750762283802,
0.021371159702539444,
0.021180538460612297,
0.05466395616531372,
0.0382956825196743,
-0.01122631411999464,
-0.018556011840701103,
0.04549447074532509,
0.05152531713247299,
0.004099444020539522,
-0.037412378937006,
0.04330623894929886,
0.02764134109020233,
0.016742752864956856,
0.0425596758723259,
-0.004222325049340725,
0.043380413204431534,
-0.025671860203146935,
0.028068341314792633,
0.025000333786010742,
0.00999990664422512,
-0.0007234116201288998,
0.058482930064201355,
0.004847411066293716,
-0.03893858939409256,
-0.01416349783539772,
-0.0005822861567139626,
0.006766659207642078,
0.05646875500679016,
-0.006406556814908981,
-0.029694654047489166,
-0.035547539591789246,
-0.017770234495401382,
-0.04856906458735466,
-0.0003838104021269828,
-0.03375594690442085,
-0.020280566066503525,
0.006172261666506529,
0.0018669534474611282,
0.009988437406718731,
-0.03045976348221302,
0.004565842915326357,
0.002233691979199648,
0.04732491075992584,
0.04157509654760361,
0.04794605076313019,
-0.013420764356851578,
0.007276661228388548,
0.018905704841017723,
-0.04185965284705162,
0.000638473778963089,
-0.022636527195572853,
-0.015410547144711018,
-0.03253044933080673,
0.02029314450919628,
-0.0010921899229288101,
-0.014911329373717308,
-0.005924418102949858,
-0.022102516144514084,
0.040496934205293655,
-0.04088575765490532,
-0.08245265483856201,
-0.07112322002649307,
0.04764288663864136,
-0.011374348774552345,
-0.03663339838385582,
-0.07808788120746613,
0.015357013791799545,
0.041708361357450485,
0.07274436205625534,
-0.018047116696834564,
-0.024647181853652,
0.023348327726125717,
0.013280551880598068,
0.022489652037620544,
-0.01195440348237753,
-0.004739763680845499,
-0.015865808352828026,
-0.0439051054418087,
0.0043793017975986,
-0.028601502999663353,
0.01612413302063942,
0.04431645944714546,
0.00541253387928009,
-0.02312575653195381,
0.03031180053949356,
-0.0345960333943367,
0.027305321767926216,
0.03133990615606308,
0.009390728548169136,
-0.004577971529215574,
0.07277286052703857,
0.03373356908559799,
-0.008587175980210304,
0.02791110798716545,
0.057536106556653976,
0.025278618559241295,
-0.023679284378886223,
-0.002718535019084811,
0.0389024093747139,
-0.004312025848776102,
-0.019362688064575195,
-0.02938881143927574,
0.023200344294309616,
-0.025435350835323334,
-0.023017043247818947,
-0.054690923541784286,
-0.035217173397541046,
-0.0014075649669393897,
0.01231188140809536,
0.0019002842018380761,
0.03087146393954754,
0.031205225735902786,
0.008176025934517384,
-0.02256906032562256,
-0.01120186410844326,
-0.07551701366901398,
0.04971668869256973,
-0.014073088765144348,
0.014780833385884762,
0.0183537807315588,
-0.00887222122400999,
0.025103416293859482,
-0.02282695472240448,
0.0032352046109735966,
0.005142011679708958,
-0.013649411499500275,
-0.016109149903059006,
-0.02103959023952484,
-0.016700992360711098,
0.06932061165571213,
0.01414535567164421,
-0.04841030016541481,
-0.02217920497059822,
0.003740853862836957,
0.0020185925532132387,
0.008189663290977478,
-0.008132771588861942,
0.007588714826852083,
-0.026032013818621635,
0.0010642571141943336,
0.026813872158527374,
0.023601427674293518,
0.042807985097169876,
0.011775092221796513,
-0.053390033543109894,
0.10904181003570557,
0.06213237717747688,
-0.004675139673054218,
0.01335978228598833,
0.027157854288816452,
0.009333621710538864,
-0.026309652253985405,
0.05504313111305237,
-0.024874581024050713,
-0.037726424634456635,
-0.007261758204549551,
0.0022992026060819626,
0.016532236710190773,
0.003688926575705409,
0.0037631650920957327,
0.03715194761753082,
-0.0035714590921998024,
0.039182208478450775,
0.008108011446893215,
0.011030171066522598,
-0.047609493136405945,
0.025562990456819534,
0.011174073442816734,
0.04010794311761856,
-0.029690342023968697,
0.0117194764316082,
-0.006929499097168446,
0.05569848045706749,
-0.006559041794389486,
0.007579978555440903,
-0.0007629574392922223,
0.028735272586345673,
0.008604545146226883,
-0.052008409053087234,
-0.04654600843787193,
0.013533046469092369,
0.008958417922258377,
0.004305833950638771,
0.037651050835847855,
0.030196253210306168,
-0.004338819533586502,
-0.04517151042819023,
0.012829657644033432,
0.012621110305190086,
-0.01300971582531929,
-0.029465919360518456,
-0.053769078105688095,
0.027060288935899734,
-0.03972642868757248,
0.025987723842263222,
-0.011388893239200115,
-0.003426515031605959,
-0.025856083258986473,
-0.002419434953480959,
0.004660048522055149,
-0.007009098306298256,
0.008578360080718994,
-0.060160499066114426,
-0.020675649866461754,
-0.013983335345983505,
-0.012814586982131004,
0.0028781909495592117,
0.004077760502696037,
-0.04514158144593239,
0.03985656425356865,
-0.05609966814517975,
-0.06483709067106247,
0.042111121118068695,
0.016972849145531654,
-0.02699562907218933,
0.06416099518537521,
0.00793591607362032,
-0.05148189142346382,
-0.03695439547300339,
-0.029657458886504173,
0.018351569771766663,
-0.0514063760638237,
-0.007392602507025003,
0.05954855680465698,
-0.005855167750269175,
-0.03953782841563225,
0.009184247814118862,
-0.03277944400906563,
-0.037278614938259125,
-0.016895422711968422,
-0.0017625322798267007,
0.015385499224066734,
-0.0384511798620224,
-0.0009219805360771716,
0.03960251063108444,
-0.038317084312438965,
-0.020848410204052925,
-0.0127117233350873,
-0.07243742793798447,
-0.004670554772019386,
0.0060745906084775925,
0.07293016463518143,
-0.007698540575802326,
0.0013472791761159897,
0.03629047051072121,
-0.0073905568569898605,
-0.01674671471118927,
-0.005705318879336119,
0.01852542720735073,
0.00637268740683794,
-0.05351565405726433,
0.017526905983686447,
0.053641874343156815,
-0.018393851816654205,
0.01734294183552265,
0.007337979041039944,
0.026399722322821617,
0.03308224678039551,
0.029102584347128868,
0.025927478447556496,
0.0051642125472426414,
0.04310708865523338,
0.020383987575769424,
0.00263903196901083,
0.015676574781537056,
-0.007050300948321819,
0.029511941596865654,
-0.012693235650658607,
0.023414485156536102,
0.016801226884126663,
-0.04829532653093338,
0.05628511309623718,
-0.005681683775037527,
-0.019296977669000626,
-0.025598077103495598,
0.03616233915090561,
0.000550967815797776,
0.013206841424107552,
-0.0008223111508414149,
0.02436600998044014,
0.02643270045518875,
0.001871626591309905,
0.004723584279417992,
0.03323899954557419,
0.019114065915346146,
-0.04218464717268944,
-0.06902573257684708,
0.01349994633346796,
0.02140657976269722,
0.03730742260813713,
-0.04366423934698105,
0.007529919501394033,
0.05452752113342285,
0.010687720030546188,
0.002247156808152795,
0.006549151614308357,
-0.03655596077442169,
-0.006012048572301865,
-0.06642978638410568,
-0.00031492821290157735,
0.018700771033763885,
0.029041577130556107,
0.010184022597968578,
0.06175125390291214,
0.03622974082827568,
0.04458325728774071,
0.02082897536456585,
0.012250232510268688,
-0.07710320502519608,
0.012816823087632656,
-0.015288742259144783,
-0.037152908742427826,
-0.004111201968044043,
-0.011145037598907948,
-0.004644343163818121,
-0.05963977426290512,
-0.025867559015750885,
0.019888807088136673,
-0.014168718829751015,
-0.05746011435985565,
-0.0015200376510620117,
-0.028207389637827873,
-0.015362650156021118,
-0.01276583131402731,
-0.022162441164255142,
0.021154802292585373,
-0.0031236533541232347,
0.06915827840566635,
0.05107465758919716,
-0.011984669603407383,
0.002801877213642001,
-0.0044859228655695915,
0.01808730699121952,
0.04932614043354988,
0.03895329684019089,
0.05352877452969551,
0.007313848007470369,
0.0016732108779251575,
0.03711003065109253,
0.006439480930566788,
0.02318345569074154,
0.004736346658319235,
0.008480790071189404,
-0.011480758897960186,
-0.03733118996024132,
-0.026110589504241943,
0.02526610903441906,
0.024232646450400352,
0.008166026324033737,
-0.009161519818007946,
0.008448122069239616,
0.006002144888043404,
0.013824257999658585,
0.02055245451629162,
0.07411373406648636,
-0.0019729917403310537,
0.004626968409866095,
-0.055430714040994644,
-0.014132014475762844,
-0.023050813004374504,
-0.022775789722800255,
0.022171787917613983,
0.00414104713127017,
-0.003254486247897148,
0.014203657396137714,
0.006407762411981821,
0.02100839652121067,
-0.02632736973464489,
-0.002844911767169833,
-0.004040994681417942,
0.014035122469067574,
0.015403158031404018,
0.04668605700135231,
0.01940854638814926,
0.026035724207758904,
0.03829048201441765,
0.0014464562991634011,
-0.00824324507266283,
-0.06326714903116226,
-0.010541907511651516,
0.038580700755119324,
0.04647103697061539,
-0.030709128826856613,
-0.0035035163164138794,
-0.043874964118003845,
-0.07163071632385254,
0.03661450371146202,
-0.026481948792934418,
0.03365040570497513,
0.003493343014270067,
0.0019484193762764335,
-0.025035852566361427,
-0.057712454348802567,
-0.0322335883975029,
-0.002384921768680215,
-0.048396263271570206,
-0.014167076908051968,
-0.024846035987138748,
-0.01929558627307415,
-0.006933816242963076,
0.006842480506747961,
0.028215516358613968,
0.010584563948214054,
-0.019554348662495613,
-0.005566055420786142,
-0.04204564541578293,
0.027359511703252792,
-0.0490049310028553,
-0.06826671212911606,
0.0065144132822752,
-0.03140009194612503,
0.0038599635008722544,
0.01790216937661171,
-0.03337189182639122,
-0.020459135994315147,
0.04284321144223213,
0.02954826131463051,
-0.0004454372392501682,
-0.009326341561973095,
-0.021796224638819695,
0.05495993793010712,
0.02739989012479782,
-0.006685024127364159,
0.008396030403673649,
0.005211732815951109,
0.005539038218557835,
-0.0241658017039299,
0.019663715735077858,
0.008810682222247124,
-0.03195187449455261,
0.008360701613128185,
-0.04082025960087776,
0.024807775393128395,
-0.059919506311416626,
0.05579287186264992,
0.0153276938945055,
-0.007692832965403795,
0.003768591908738017,
-0.005530457943677902,
0.017504559829831123,
0.044809792190790176,
0.021293727681040764,
-0.008757139556109905,
-0.03040371462702751,
-0.00043788322363980114,
0.015952561050653458,
0.014569240622222424,
0.019165098667144775,
-0.024080900475382805,
0.020214002579450607,
0.045667268335819244,
-0.02401982992887497,
0.013103323988616467,
-0.005833562929183245,
-0.021890491247177124,
-0.0006043419125489891,
-0.038429707288742065,
0.036830220371484756,
0.030204113572835922,
0.0009591792477294803,
0.03423827141523361,
-0.022557947784662247,
-0.013677835464477539,
0.06708686798810959,
-0.012374179437756538,
0.026389142498373985,
-0.07308273017406464,
0.029294395819306374,
0.003450702643021941,
0.01781523786485195,
-0.06408219784498215,
-0.02720571681857109,
0.051845941692590714,
-0.025650594383478165,
-0.025674792006611824,
-0.046999722719192505,
-0.03298226371407509,
-0.04174033924937248,
-0.02488856017589569,
0.02192533016204834,
0.02558186464011669,
-0.05065295472741127,
-0.010448852553963661,
0.05127328261733055,
-0.0017585497116670012,
0.024665609002113342,
-0.007310173008590937,
-0.0004067876434419304,
-0.009652040898799896,
-0.020626496523618698,
-0.010876858606934547,
-0.02349899336695671,
0.07952021062374115,
-0.023093121126294136,
-0.00016783532919362187,
-0.02063237689435482,
0.00038451218279078603,
0.03771078959107399,
-0.014189939014613628,
0.010658305138349533,
0.0017482726834714413,
0.0010792749235406518,
-0.01803506538271904,
-0.0314473956823349,
0.0053679076954722404,
0.007982329465448856,
0.0022315452806651592,
0.028095299378037453,
-0.004407581407576799,
0.0066749537363648415,
-0.027521200478076935,
-0.004675065167248249,
-0.006235628854483366,
-0.024405337870121002,
-0.006515348330140114,
0.04673789441585541,
-0.021796131506562233,
0.019029388204216957,
0.00805622711777687,
-0.015118706040084362,
0.06655976176261902,
-0.026912391185760498,
-0.05202879384160042,
0.0003765173605643213,
0.0022610353771597147,
-0.03699827566742897,
-0.025377469137310982,
-0.06023357808589935,
-0.032328248023986816,
0.0684872567653656,
-0.0359751433134079,
0.04639732092618942,
0.0072621689178049564,
0.03882686793804169,
-0.02676715888082981,
0.014670365490019321,
-0.00011479506792966276,
0.01171035598963499,
-0.03512025997042656,
0.04988957941532135,
-0.030392317101359367,
-0.021657826378941536,
-0.004718656651675701,
0.01508287712931633,
-0.007894279435276985,
-0.01733051799237728,
0.039330724626779556,
0.009455088526010513,
0.04615180194377899,
0.019011562690138817,
-0.02662704885005951,
0.029857663437724113,
-0.03308603912591934,
0.0182846300303936,
-0.018444815650582314,
-0.020060956478118896,
0.08624482899904251,
0.009573440067470074,
-0.020056286826729774,
-0.0804198607802391,
0.004663906991481781,
-0.05690336227416992,
-0.0009339224197901785,
0.00881519541144371,
0.04065690189599991,
-0.004107742570340633,
0.016497738659381866,
0.05443447828292847,
0.016868537291884422,
-0.0021616804879158735,
-0.006568070035427809,
-0.04105924814939499,
-0.029438799247145653,
-0.019600536674261093,
0.006834342144429684,
0.008609430864453316,
0.015664327889680862,
0.010972359217703342,
-0.0022490231785923243,
-0.03448211029171944,
0.01507317554205656,
0.002220523077994585,
0.053075745701789856,
0.008932653814554214,
0.07632025331258774,
-0.01849265769124031,
0.011219041422009468,
-0.03809422627091408,
0.03370486944913864,
0.1164667084813118,
0.04812830686569214,
0.016249429434537888,
-0.03657715395092964,
0.0042757210321724415,
-0.000025006214855238795,
0.005849909968674183,
-0.032065704464912415,
0.023700065910816193,
-0.013537590391933918,
0.00998824555426836,
0.02263902686536312,
0.07288744300603867,
0.028807753697037697,
-0.02143550105392933,
0.010536842979490757,
-0.05420919135212898,
-0.014746472239494324,
-0.02936064638197422,
-0.009795231744647026,
-0.04480242356657982,
0.03671817481517792,
-0.030636541545391083,
0.03438864275813103,
-0.01807503029704094,
-0.009677918627858162,
-0.03640300780534744,
-0.04621804505586624,
0.023343121632933617,
0.027802253141999245,
-0.0450935959815979,
0.025326598435640335,
0.015504539012908936,
-0.03320646286010742,
-0.05203449726104736,
0.0515090636909008,
-0.005427884869277477,
-0.0004782501491717994,
0.03428838029503822,
0.027047250419855118,
0.03723720461130142,
-0.013541484251618385,
0.012298539280891418,
-0.007725866045802832,
-0.040242649614810944,
0.009937740862369537,
-0.06138944625854492,
0.04596789553761482,
0.018715785816311836,
-0.02507496252655983,
-0.01590583100914955,
-0.009080812335014343,
0.006805951241403818,
-0.07312311977148056,
-0.03698693588376045,
0.037311919033527374,
0.0372462160885334,
0.01767536625266075,
0.04874349385499954,
-0.03404555097222328,
-0.00025959539925679564,
-0.00036464715958572924,
-0.006186702288687229,
-0.007554259151220322,
-0.013778558000922203,
0.012736684642732143,
0.006518784910440445,
0.07043937593698502,
0.009504806250333786,
-0.012610802426934242,
-0.0008644842309877276,
0.009850872680544853,
-0.07577069103717804,
0.008558981120586395,
0.02819528430700302,
0.03481601923704147,
0.04507657513022423,
-0.004067638423293829,
0.003993561025708914,
-0.015214222483336926,
-0.06117066368460655,
0.03805551305413246,
0.003628451842814684,
0.006943820975720882,
-0.05670037865638733,
0.00007558095967397094,
0.023863108828663826,
0.030796842649579048,
-0.01361507922410965,
-0.022939536720514297,
-0.006429971661418676,
0.0732746571302414,
0.009589916095137596,
0.01980683021247387,
0.007618282921612263,
0.006863974034786224,
-0.026636051014065742,
-0.0020114986691623926,
0.005615970119833946,
0.05129765719175339,
0.020901799201965332,
-0.002816546941176057,
0.02195127308368683,
-0.016861164942383766,
-0.03806246444582939,
0.020563539117574692,
0.03790311515331268,
-0.002078278921544552,
-0.030554862692952156,
0.018051888793706894,
0.027043329551815987,
-0.00556568568572402,
-0.03659675642848015,
-0.03647465631365776,
-0.022364133968949318,
-0.045975614339113235,
0.02538434788584709,
-0.011094431392848492,
0.02999678999185562,
-0.0159269031137228,
0.040296025574207306,
-0.03809881955385208,
0.004702884238213301,
-0.028512729331851006,
-0.011513100005686283,
0.019728517159819603,
-0.01738518662750721,
-0.04889937862753868,
0.049984291195869446,
-0.05253637209534645,
0.006445714738219976,
0.004017869010567665,
0.00803751777857542,
-0.008317173458635807,
-0.016810957342386246,
0.03579241782426834,
-0.02752952091395855,
0.03802192956209183,
-0.041993238031864166,
-0.05199107900261879,
0.03649583458900452,
-0.004224011674523354,
-0.0313824899494648,
0.02218477614223957,
-0.008157379925251007,
0.016186246648430824,
0.020254915580153465,
-0.02007586881518364,
-0.01770985685288906,
0.11491803824901581,
-0.012589982710778713,
-0.0034261206164956093,
0.013723575510084629,
-0.034217264503240585,
-0.04397158697247505,
0.008350081741809845,
0.02401215024292469,
0.0014538493705913424,
0.0031379025895148516,
0.03380489721894264,
0.04390975087881088,
-0.009916809387505054,
0.001539650373160839,
-0.015994425863027573,
-0.031189896166324615,
0.03099479153752327,
0.026697581633925438,
-0.0024441303685307503,
0.02006295695900917,
0.036139171570539474,
-0.024934502318501472,
-0.0005087704048492014,
-0.007015516050159931,
-0.015034820884466171,
-0.1104736253619194,
0.023147672414779663,
0.0074465395882725716,
0.003519037738442421,
0.010336657986044884,
-0.04454527422785759,
-0.0008281189948320389,
0.06410517543554306,
-0.0685906782746315,
-0.012331707403063774,
-0.048595234751701355,
-0.009370039217174053,
-0.03508562222123146,
0.020118610933423042,
-0.03293449804186821,
0.049425676465034485,
0.028782369568943977,
-0.0028370253276079893,
-0.0038998343516141176,
-0.024944841861724854,
-0.03020683489739895,
0.004163834266364574,
0.013977477326989174,
0.0452604703605175,
-0.011052078567445278,
0.02394605427980423,
0.0492175854742527,
-0.00869828462600708,
-0.03538498282432556,
0.008432918228209019,
-0.014551266096532345,
-0.005278861150145531,
-0.008601956069469452,
0.012497524730861187,
-0.012428680434823036,
0.021241355687379837,
-0.002210110891610384,
0.0370183065533638,
0.014259873889386654,
0.021665332838892937,
0.025293637067079544,
0.04345586523413658,
-0.02045849710702896,
-0.010047238320112228,
0.007928162813186646,
-0.02091718651354313,
-0.01630895771086216,
0.01728716865181923,
-0.014084646478295326,
0.014367463998496532,
-0.0032594462390989065,
0.021670488640666008,
-0.013799874112010002,
-0.00899005401879549,
-0.011434359475970268,
-0.02782098576426506,
0.010685870423913002,
0.05509345605969429,
0.001985881244763732,
-0.013448263518512249,
-0.011732746846973896,
-0.03875519707798958,
0.017519919201731682,
-0.02638876810669899,
-0.0023880077060312033,
-0.03675602748990059,
-0.05744435638189316,
-0.025751546025276184,
-0.030695224180817604,
-0.03632610663771629,
-0.016400115564465523,
-0.03986407443881035,
0.01621090993285179,
0.05473104491829872,
0.026645487174391747,
0.041000187397003174,
0.02938009984791279,
-0.048527706414461136,
-0.017190707847476006,
-0.0805511474609375,
0.05062210559844971,
-0.0004861826018895954,
-0.03981437161564827,
-0.04106806218624115,
-0.010873870924115181,
0.024773158133029938,
0.05347374081611633,
0.027409762144088745,
-0.0009187626419588923,
-0.00841677188873291,
0.0010189220774918795,
-0.027144016698002815,
0.03365923464298248,
-0.006552061531692743,
-0.005808249581605196,
-0.02513461373746395,
-0.03183610737323761,
0.031237879768013954,
0.004447097424417734,
0.0130561962723732,
-0.025912897661328316,
0.012082724831998348,
-0.06364643573760986,
0.02267625369131565,
-0.0019453678978607059,
-0.05233298987150192,
0.015550185926258564,
0.015511760488152504,
-0.03309786692261696,
0.1146879643201828,
0.01927732303738594,
0.015406772494316101,
0.023319300264120102,
0.0037454275880008936,
-0.05415754392743111,
-0.0013562495587393641,
-0.030509674921631813,
0.029212888330221176,
-0.023207247257232666,
-0.051093317568302155,
0.008671620860695839,
-0.039205413311719894,
0.04530402272939682,
0.006165284663438797,
-0.07579799741506577,
0.010796337388455868,
0.041453808546066284,
0.016463208943605423,
0.023999590426683426,
0.005436094477772713,
0.04115614667534828,
0.025049278512597084,
0.02943604253232479,
0.001981013687327504,
0.03390539437532425,
0.021079208701848984,
-0.011664383113384247,
0.013102756813168526,
0.05640435591340065,
-0.02553098089993,
-0.00100114312954247,
0.004647469148039818,
-0.0006951151299290359,
-0.02481396310031414,
-0.010242754593491554,
-0.0077793593518435955,
-0.028755880892276764,
0.031691066920757294,
0.045886553823947906,
0.0018538846634328365,
0.05118214711546898,
-0.052592933177948,
0.022895729169249535,
-0.017815517261624336,
0.005322514101862907,
-0.021315090358257294,
0.01236384455114603,
0.008429933339357376,
-0.022733407095074654,
-0.0069364639930427074,
0.003122732974588871,
0.004453867673873901,
-0.03247401863336563,
0.037377480417490005,
-0.046054769307374954,
-0.0070262388326227665,
-0.006021637935191393,
0.009443632327020168,
-0.0005589888314716518,
-0.0039926087483763695,
-0.02832466922700405,
-0.014355121180415154,
0.02997361309826374,
0.009714305400848389,
0.038695693016052246,
-0.002772281179204583,
-0.0021330611780285835,
-0.022945402190089226,
0.049636125564575195,
-0.0587959960103035,
-0.0038567527662962675,
-0.00970340147614479,
0.019015811383724213,
0.0024929451756179333,
-0.016017429530620575
] |
<p>I wonder if someone can help me with the following problem.</p>
<p>I send a light beam to a distant galaxy which then bounces back to me.</p>
<p>I measure the travel time of the lightbeam using say a light clock of fixed size which I assume measures conformal time $\tau=\int dt/a(t)$.</p>
<p>Is the proper distance of the galaxy at the moment that I receive the lightbeam given simply by:
$$L = \frac{c\ \tau}{2}?$$</p>
| 10,835 |
[
0.034950532019138336,
-0.023050960153341293,
-0.009954883717000484,
-0.02422538585960865,
0.07269598543643951,
-0.009362864308059216,
-0.019700078293681145,
-0.0035463932435959578,
-0.004113832488656044,
0.005715576466172934,
0.05008397623896599,
0.05000433698296547,
0.07950600236654282,
0.030857998877763748,
0.05671489238739014,
0.010194451548159122,
-0.03918419033288956,
0.012302027083933353,
-0.035446614027023315,
-0.060224395245313644,
0.06608513742685318,
0.013745741918683052,
-0.011907665058970451,
-0.05196670442819595,
-0.02106035128235817,
0.02605322375893593,
-0.003305942052975297,
-0.020778430625796318,
0.0007207042654044926,
0.058687709271907806,
-0.03812551125884056,
-0.011460352689027786,
0.02946959063410759,
0.024174001067876816,
0.0017400681972503662,
0.012408401817083359,
-0.035121846944093704,
-0.018884869292378426,
0.005259814206510782,
0.013078311458230019,
-0.04998384416103363,
-0.029743148013949394,
0.02802298590540886,
0.06035175547003746,
0.01836608164012432,
0.009118528105318546,
-0.03588377684354782,
-0.01087258942425251,
0.05537768453359604,
-0.01754796877503395,
0.0811680480837822,
-0.012029223144054413,
0.011743960902094841,
-0.011531470343470573,
0.01301945373415947,
-0.016284719109535217,
0.07886753231287003,
0.04673765227198601,
-0.027539577335119247,
-0.025932861492037773,
-0.012100856751203537,
-0.017086569219827652,
-0.0064479573629796505,
-0.012164189480245113,
-0.010896407067775726,
-0.0030204139184206724,
-0.04647275432944298,
0.003792431904003024,
0.030666766688227654,
-0.011746878735721111,
-0.005593336187303066,
0.016060154885053635,
0.01280701532959938,
-0.022683147341012955,
-0.0009253298630937934,
-0.02189946547150612,
-0.003083036281168461,
0.03627612441778183,
0.025470206514000893,
0.015422441996634007,
-0.022209908813238144,
0.01001644041389227,
0.019336402416229248,
0.04525190219283104,
0.005075032357126474,
-0.026818178594112396,
0.05337626487016678,
-0.02383737452328205,
0.012568056583404541,
0.028582632541656494,
-0.014946299605071545,
0.023362822830677032,
0.022010233253240585,
0.010795197449624538,
-0.01081666350364685,
0.051955193281173706,
0.012674916535615921,
0.0559825599193573,
-0.011101139709353447,
-0.04717663675546646,
-0.016759781166911125,
-0.039313897490501404,
0.0150385033339262,
0.049052055925130844,
-0.005839341785758734,
0.004313149023801088,
-0.04816029220819473,
0.008025447838008404,
-0.030687468126416206,
-0.008871928788721561,
-0.0397760383784771,
0.021984795108437538,
-0.00500420480966568,
0.03491799905896187,
0.01769443228840828,
-0.033964671194553375,
-0.012423585169017315,
-0.006012571044266224,
0.06768527626991272,
0.03341512009501457,
0.0601285845041275,
-0.030339401215314865,
0.04069707542657852,
-0.01940186135470867,
-0.060899294912815094,
0.025418775156140327,
0.025121990591287613,
-0.00562653411179781,
-0.022780708968639374,
0.041737474501132965,
0.03270306810736656,
-0.021011345088481903,
0.014425184577703476,
-0.007197539787739515,
0.02595372125506401,
-0.03787751868367195,
-0.05813511088490486,
-0.08741214871406555,
0.0031160530634224415,
-0.0037902058102190495,
-0.012597569264471531,
-0.09359948337078094,
-0.00431636581197381,
0.018300864845514297,
0.08810006082057953,
0.03304174169898033,
0.009551610797643661,
0.0049671451561152935,
0.028378793969750404,
-0.017539789900183678,
-0.03886958956718445,
-0.012464359402656555,
-0.011093617416918278,
-0.03152089565992355,
0.03305879607796669,
-0.043861024081707,
-0.016163459047675133,
0.017761647701263428,
0.016191717237234116,
-0.029356593266129494,
0.07551634311676025,
-0.004886141046881676,
0.008756488561630249,
0.010728999972343445,
0.020173607394099236,
-0.02005046233534813,
0.09171581268310547,
0.011575993150472641,
-0.04403424263000488,
0.044294267892837524,
0.0040843854658305645,
-0.0028972888831049204,
-0.02570037730038166,
0.0047356435097754,
0.05242467299103737,
-0.04011495038866997,
-0.01735629141330719,
0.029170114547014236,
-0.014253400266170502,
0.004416543524712324,
0.014844104647636414,
-0.018841763958334923,
-0.01323650311678648,
0.022769616916775703,
0.028455952182412148,
0.0301379207521677,
-0.0004306635819375515,
0.022130075842142105,
0.027289168909192085,
-0.026297101750969887,
0.016537044197320938,
-0.029517551884055138,
0.020545026287436485,
0.007980582304298878,
-0.004997641779482365,
0.013662386685609818,
-0.006351414602249861,
0.0026219640858471394,
0.03189190477132797,
-0.01493234932422638,
-0.010307783260941505,
0.02394421398639679,
0.03707501292228699,
0.005630445666611195,
0.02202431857585907,
0.04200420156121254,
0.07127242535352707,
-0.0022166266571730375,
0.003974598832428455,
0.007019186858087778,
0.018369244411587715,
-0.019535409286618233,
-0.004180006217211485,
0.03490496426820755,
-0.02686811238527298,
0.014195233583450317,
-0.02160917967557907,
-0.0009787857998162508,
0.0291767418384552,
0.06533469259738922,
-0.022674407809972763,
0.05142781883478165,
0.050258535891771317,
0.016678640618920326,
0.018956203013658524,
0.022342223674058914,
-0.012125914916396141,
-0.01585736870765686,
0.0035662520676851273,
-0.06459397077560425,
-0.035465702414512634,
-0.006460776086896658,
0.04152138531208038,
0.03841204568743706,
-0.005880079232156277,
-0.00761630292981863,
0.07825560867786407,
0.003028721548616886,
0.029784154146909714,
0.022030770778656006,
-0.05017179250717163,
-0.07176340371370316,
0.015779707580804825,
0.018868502229452133,
-0.018263820558786392,
0.007220136001706123,
0.014665142633020878,
-0.009349970147013664,
0.021825069561600685,
-0.007287395186722279,
-0.0041807531379163265,
0.0019945872481912374,
-0.02164861187338829,
-0.002526801312342286,
0.008816876448690891,
-0.008841254748404026,
0.06377284973859787,
0.00867426861077547,
0.010227516293525696,
0.05340389162302017,
-0.034242480993270874,
0.009695468470454216,
-0.022428760305047035,
-0.0028851854149252176,
0.0231374129652977,
0.019863909110426903,
-0.01904001459479332,
-0.04222273826599121,
0.029177747666835785,
-0.024912267923355103,
0.03522555157542229,
-0.012334100902080536,
-0.004896373488008976,
-0.014780841767787933,
-0.004305965732783079,
0.018614646047353745,
0.04965946823358536,
0.0003791107446886599,
-0.04095656797289848,
-0.05528883635997772,
0.01600094884634018,
-0.004320248961448669,
0.0045935302041471004,
0.009320225566625595,
-0.03427113592624664,
0.027482816949486732,
-0.009536855854094028,
-0.013580292463302612,
0.01075834035873413,
-0.0018821799894794822,
0.04512106627225876,
0.02306312881410122,
-0.016833633184432983,
-0.05577700957655907,
-0.029930051416158676,
-0.023231029510498047,
0.014417629688978195,
-0.04051128029823303,
0.0005457910010591149,
0.0430307537317276,
0.02428467385470867,
-0.016120824962854385,
0.0202009454369545,
-0.0729534775018692,
-0.023560289293527603,
-0.008335552178323269,
-0.0043496848084032536,
0.028960272669792175,
-0.03470087796449661,
0.05615580454468727,
-0.011642588302493095,
-0.01128421537578106,
0.0018686839612200856,
-0.06238760054111481,
-0.05464264750480652,
0.031505923718214035,
0.007101321592926979,
0.01624971814453602,
0.006233017425984144,
-0.02990110218524933,
0.09606301039457321,
0.03468514606356621,
-0.00834349263459444,
-0.014435350894927979,
-0.001281064236536622,
0.00012635589519049972,
-0.05081116780638695,
-0.010345418006181717,
0.0086510656401515,
-0.046605534851551056,
0.031403131783008575,
0.017782535403966904,
0.052495695650577545,
0.06383467465639114,
0.012964981608092785,
-0.003441388485953212,
0.003690893528982997,
-0.014205141924321651,
0.0022399546578526497,
0.044906120747327805,
0.02003883756697178,
-0.023568326607346535,
0.014841876924037933,
-0.018883733078837395,
0.022653445601463318,
0.010058263316750526,
-0.0884472206234932,
0.013839712366461754,
-0.0020939696114510298,
-0.0026201775763183832,
-0.002577269682660699,
0.017910778522491455,
0.006321418099105358,
-0.009426559321582317,
0.004978418815881014,
0.023992225527763367,
0.030436787754297256,
-0.012523270212113857,
0.012760580517351627,
0.05634697154164314,
0.009838580153882504,
0.02166428416967392,
-0.028159556910395622,
-0.009764089249074459,
-0.027910279110074043,
-0.0060048396699130535,
-0.0128477206453681,
-0.025235554203391075,
0.03731423243880272,
0.05389087274670601,
0.014195858500897884,
-0.018738456070423126,
-0.044762786477804184,
-0.0010004540672525764,
-0.036389969289302826,
0.0021186107769608498,
-0.006904227659106255,
0.05530703440308571,
0.016661595553159714,
0.002885370282456279,
0.0683436170220375,
-0.022063184529542923,
0.041985176503658295,
-0.01345420628786087,
-0.06953290104866028,
0.012662735767662525,
-0.05033604055643082,
-0.024790484458208084,
-0.01803712546825409,
-0.015100349672138691,
0.004808337893337011,
-0.03201521933078766,
0.011754277162253857,
0.0027296494226902723,
-0.0011081394040957093,
-0.026662781834602356,
-0.004038503859192133,
-0.050330787897109985,
-0.04423242434859276,
-0.03401574864983559,
0.02017083764076233,
0.047921378165483475,
0.0028212436009198427,
0.012485694140195847,
0.03376450389623642,
-0.01275724545121193,
-0.020883947610855103,
0.00018156653095502406,
-0.010321998037397861,
-0.015076490119099617,
0.03798774257302284,
0.05348098278045654,
0.0065512447617948055,
-0.032337941229343414,
0.03677046671509743,
0.030971966683864594,
0.02821003459393978,
-0.000601012259721756,
0.005390394013375044,
-0.03443455323576927,
-0.06493237614631653,
0.00652353884652257,
0.0037081988994032145,
0.05281991884112358,
-0.013351993635296822,
-0.008611664175987244,
0.04662342742085457,
0.00859969574958086,
-0.002438447205349803,
0.023124510422348976,
0.04948866367340088,
-0.01890656165778637,
-0.04411173611879349,
-0.03329843655228615,
-0.037758968770504,
-0.013059858232736588,
-0.0013487517135217786,
0.02083153836429119,
-0.011516878381371498,
0.008138224482536316,
-0.023481309413909912,
0.008197920396924019,
0.0021662202198058367,
0.0037048051599413157,
-0.010098027996718884,
0.0024901360739022493,
-0.004776857793331146,
0.024930428713560104,
-0.016140885651111603,
0.006768241990357637,
0.051243651658296585,
0.03763612359762192,
0.018259529024362564,
-0.0011159474961459637,
-0.06855427473783493,
-0.04480065405368805,
0.011841843836009502,
0.06845784187316895,
-0.00953175500035286,
-0.019434403628110886,
-0.069024458527565,
-0.01716827042400837,
0.07044751197099686,
-0.01892365887761116,
0.05175704136490822,
-0.007521338295191526,
-0.007479702588170767,
0.02389298565685749,
-0.00795943383127451,
-0.017539415508508682,
0.037684760987758636,
0.03449180722236633,
-0.0015272833406925201,
-0.033799588680267334,
0.021216725930571556,
0.004740607459098101,
-0.019471026957035065,
0.0316181518137455,
0.02878788858652115,
0.00826349575072527,
-0.0025233502965420485,
0.02402685210108757,
0.02653614804148674,
-0.018789684399962425,
-0.030603695660829544,
0.013246677815914154,
0.0021167201921343803,
-0.032779257744550705,
0.022543739527463913,
-0.016458889469504356,
-0.010888513177633286,
0.04521441087126732,
0.026990974321961403,
0.015906330198049545,
0.02095954865217209,
-0.04287262260913849,
0.023073909804224968,
0.019317302852869034,
0.012139608152210712,
0.03641379624605179,
0.05632834509015083,
0.02501693181693554,
-0.002506393939256668,
0.00892232358455658,
0.053330011665821075,
-0.036824047565460205,
0.0005546202301047742,
-0.012741964310407639,
-0.037529926747083664,
-0.04637698084115982,
0.05580822005867958,
-0.020035210996866226,
-0.005310149397701025,
0.012256440706551075,
-0.027515681460499763,
0.01834796741604805,
0.054965440183877945,
-0.019769465550780296,
0.009668559767305851,
-0.019514327868819237,
-0.007310693617910147,
0.002057691104710102,
-0.003072280902415514,
-0.010745176114141941,
-0.01667136698961258,
0.002106918254867196,
-0.008983779698610306,
0.032932452857494354,
0.02504299022257328,
-0.023213310167193413,
-0.006405604537576437,
0.018849028274416924,
-0.042058065533638,
0.031420327723026276,
0.00894605927169323,
-0.00425168639048934,
0.006201049312949181,
-0.02767886407673359,
-0.01954200118780136,
-0.015007751993834972,
-0.03954549878835678,
0.017329879105091095,
-0.06131167709827423,
0.01194135844707489,
0.005936722736805677,
0.024306144565343857,
-0.08248578011989594,
0.003107266966253519,
0.006088525056838989,
0.005902706179767847,
-0.007238660007715225,
-0.028783686459064484,
-0.014363248832523823,
-0.04190889745950699,
-0.013536042533814907,
-0.026350559666752815,
0.05499871075153351,
0.016573011875152588,
-0.024728955700993538,
-0.026299254968762398,
0.00654718978330493,
0.02503078244626522,
0.008707807399332523,
0.01619175262749195,
0.007183664944022894,
0.008865026757121086,
-0.036410462111234665,
-0.0032742421608418226,
0.08610350638628006,
-0.03620437905192375,
-0.03851553425192833,
-0.0087753776460886,
0.0015090461820363998,
0.014001833274960518,
-0.028757501393556595,
-0.005798231810331345,
-0.0010841523762792349,
0.0058746784925460815,
-0.018645210191607475,
0.02290823869407177,
0.008692484349012375,
0.014941961504518986,
-0.008529993705451488,
-0.041187211871147156,
-0.0171405840665102,
-0.01850433461368084,
-0.02963593788444996,
0.04234951734542847,
0.0049287243746221066,
0.042740073055028915,
-0.018017513677477837,
0.04453834891319275,
0.025538111105561256,
-0.027369219809770584,
0.00489032082259655,
0.026956604793667793,
-0.0170060433447361,
-0.0056093051098287106,
-0.013601018115878105,
0.046834930777549744,
-0.0346209779381752,
-0.035335004329681396,
-0.019669311121106148,
-0.014629891142249107,
-0.007731535471975803,
0.11205044388771057,
-0.025000981986522675,
0.06033140793442726,
-0.022012311965227127,
0.007245420943945646,
-0.016402697190642357,
-0.00039218453457579017,
-0.03987693414092064,
0.01375788263976574,
0.023657510057091713,
0.019597705453634262,
-0.051331549882888794,
-0.05165800079703331,
0.007454617414623499,
0.01958419382572174,
-0.005964426323771477,
0.0023812216240912676,
0.01149966474622488,
0.02317900024354458,
0.006464903708547354,
0.006086783017963171,
-0.02529532089829445,
-0.002528322394937277,
-0.029484787955880165,
0.031145762652158737,
-0.010456631891429424,
0.01807999424636364,
0.04248310998082161,
0.03486255183815956,
0.02465299889445305,
-0.024668216705322266,
-0.0018438523402437568,
-0.05288512259721756,
-0.035073988139629364,
0.035477615892887115,
-0.019756769761443138,
0.008732629008591175,
0.028259193524718285,
0.03191012889146805,
-0.003257719799876213,
0.029807426035404205,
-0.0034375221002846956,
-0.07575102895498276,
-0.016654571518301964,
-0.036983244121074677,
-0.033091671764850616,
0.06875203549861908,
0.009987182915210724,
-0.015628544613718987,
0.022762494161725044,
-0.045926764607429504,
-0.010533362627029419,
0.03482016175985336,
0.007559194695204496,
-0.023292334750294685,
0.09721469134092331,
-0.02094888873398304,
0.020793993026018143,
-0.03048897348344326,
0.014524661004543304,
0.0846739113330841,
0.04881361126899719,
-0.014922888949513435,
-0.07072830200195312,
0.04418477788567543,
-0.0266546793282032,
-0.001315198838710785,
-0.06547247618436813,
0.041009802371263504,
-0.01748161017894745,
-0.03543991595506668,
0.038606010377407074,
0.05236820504069328,
-0.00831664726138115,
-0.029463179409503937,
0.02300793118774891,
-0.01827661693096161,
-0.03927359730005264,
0.040750257670879364,
0.0014428819995373487,
-0.021717624738812447,
-0.006209906190633774,
-0.036339566111564636,
0.057615458965301514,
-0.04518201947212219,
0.01998191699385643,
-0.03019731305539608,
-0.04193628951907158,
-0.006429930217564106,
-0.03371024131774902,
-0.014523310586810112,
0.014830310828983784,
-0.00007267521868925542,
-0.04401842877268791,
-0.02704763412475586,
0.02822074480354786,
0.024316968396306038,
-0.0037907666992396116,
0.04297798499464989,
0.03456404432654381,
0.0173463337123394,
0.019064808264374733,
-0.006930692587047815,
0.00040845206240192056,
-0.04635615646839142,
-0.025021424517035484,
0.00612646946683526,
0.057882893830537796,
-0.02774575538933277,
0.005227942951023579,
0.008896753191947937,
0.02921905368566513,
0.03403177857398987,
-0.06104375049471855,
0.02751591056585312,
0.01559433713555336,
0.01445798110216856,
0.007791879121214151,
-0.0038819657638669014,
-0.007403131574392319,
0.03377991169691086,
-0.03168747201561928,
0.0027016662061214447,
0.008001440204679966,
0.04095534607768059,
0.023363694548606873,
-0.021578524261713028,
0.043118756264448166,
-0.015861451625823975,
-0.027871806174516678,
-0.029292544350028038,
0.02444889210164547,
-0.04038788005709648,
0.030943790450692177,
0.015408916398882866,
0.009849871508777142,
-0.019389325752854347,
-0.003902589436620474,
-0.021847853437066078,
-0.04680854082107544,
-0.09422248601913452,
0.020745091140270233,
-0.027674922719597816,
-0.030156606808304787,
-0.012613405473530293,
-0.018562957644462585,
0.05240655690431595,
0.040591608732938766,
0.0029997152741998434,
-0.018667491152882576,
-0.018806446343660355,
0.05190584063529968,
0.0388338603079319,
-0.02340332791209221,
-0.0024784128181636333,
0.0168472807854414,
-0.01334842387586832,
0.02518349327147007,
-0.052357207983732224,
0.04158824309706688,
0.029117800295352936,
0.04324369877576828,
-0.004273668862879276,
0.002726469188928604,
-0.05549149215221405,
0.010465229861438274,
0.02071487158536911,
-0.029518263414502144,
-0.01236147154122591,
-0.027396373450756073,
0.04132992774248123,
-0.015243074856698513,
-0.043275926262140274,
0.007004956249147654,
-0.0400947630405426,
0.0030582246836274862,
-0.0021480051800608635,
-0.01344085019081831,
0.01459908951073885,
-0.011157483793795109,
-0.06609037518501282,
-0.08556576073169708,
0.043502096086740494,
-0.0350273996591568,
0.030490078032016754,
-0.033225689083337784,
-0.005582829471677542,
-0.03494688868522644,
0.04159640148282051,
-0.009351368993520737,
-0.045978132635354996,
0.002296596998348832,
0.00040563559741713107,
-0.007706868462264538,
-0.013469358906149864,
-0.005894537549465895,
-0.0016191040631383657,
0.07044237107038498,
-0.023152561858296394,
-0.0183291994035244,
0.04059871658682823,
-0.04005904495716095,
-0.04470391571521759,
0.045008085668087006,
-0.003541276091709733,
0.02159295417368412,
0.011386414989829063,
-0.0084296315908432,
-0.018798792734742165,
0.06841462850570679,
0.003401050576940179,
-0.018196137621998787,
0.006125941872596741,
-0.03510501608252525,
0.026086939498782158,
0.005732792429625988,
0.029653746634721756,
-0.025724273175001144,
-0.009395943954586983,
-0.0019830160308629274,
0.049914244562387466,
-0.0175277478992939,
0.04459625482559204,
-0.026277165859937668,
-0.027498465031385422,
-0.027999863028526306,
-0.02383923903107643,
0.007928435690701008,
0.011205632239580154,
0.07159881293773651,
-0.007308322470635176,
0.03722909092903137,
0.040032681077718735,
0.0029099788516759872,
-0.09389562904834747,
0.03730238601565361,
-0.007009109016507864,
0.037043556571006775,
0.05663073807954788,
-0.07177997380495071,
0.009768565185368061,
0.032834652811288834,
-0.028807340189814568,
0.04463538900017738,
-0.045040298253297806,
-0.029205214232206345,
-0.025509202852845192,
-0.02558710426092148,
-0.03403937444090843,
0.03866046294569969,
0.04074225574731827,
0.02053404599428177,
0.032459408044815063,
0.004976764786988497,
0.017955277115106583,
-0.064210444688797,
0.023362651467323303,
0.016792230308055878,
0.035368457436561584,
0.0009035008260980248,
0.03655672445893288,
-0.0007787087233737111,
-0.04209519177675247,
0.05966024845838547,
0.009724325500428677,
0.028133507817983627,
-0.03482809662818909,
-0.022432180121541023,
0.020742151886224747,
0.016502195969223976,
0.009177918545901775,
-0.014409140683710575,
0.006433485541492701,
-0.008774939924478531,
0.010514437220990658,
-0.02933555096387863,
0.00013236614177003503,
-0.002917724661529064,
-0.015864338725805283,
-0.05073970556259155,
-0.043905485421419144,
0.04886860400438309,
0.00765952467918396,
-0.0052354298532009125,
0.008160267025232315,
-0.02969437837600708,
0.022994134575128555,
-0.06694725155830383,
0.00457617687061429,
-0.027055732905864716,
0.019718555733561516,
0.04647361859679222,
0.035171978175640106,
-0.05274683237075806,
-0.013231378048658371,
-0.018058456480503082,
-0.024415520951151848,
0.02524915337562561,
0.017374595627188683,
-0.012334048748016357,
-0.028660738840699196,
-0.055762145668268204,
-0.03124981001019478,
-0.0019283974543213844,
0.020039768889546394,
-0.032042261213064194,
-0.027061570435762405,
0.04473008215427399,
-0.025646725669503212,
0.013595486991107464,
-0.008466344326734543,
0.001455188263207674,
-0.005308694671839476,
-0.06726977229118347,
0.009629768319427967,
-0.023486239835619926,
0.0018030119827017188,
-0.04313674569129944,
-0.02445308305323124,
-0.03703586757183075,
0.014223165810108185,
0.050289932638406754,
0.0026581953279674053,
0.003320063930004835,
0.0018752862233668566,
-0.03763356804847717,
-0.008135718293488026,
-0.06582124531269073,
-0.026132524013519287,
-0.014797951094806194,
-0.01603066921234131,
-0.014109677635133266,
-0.025108538568019867,
-0.02984955720603466,
0.0027456649113446474,
0.012168939225375652,
0.024210339412093163,
0.03613346070051193,
0.02708381414413452,
-0.028410309925675392,
0.02451651357114315,
-0.0014535696245729923,
0.017813576385378838,
0.06482259929180145,
0.02311551570892334,
0.003588785883039236,
0.05908540263772011,
-0.022728873416781425,
-0.040684621781110764,
0.03933030366897583,
-0.04241221398115158,
-0.03639933839440346,
-0.03024851344525814,
0.024116219952702522,
0.003112411592155695,
-0.04694097489118576,
-0.052058663219213486,
0.04976040869951248,
0.0042047989554703236,
-0.009450936689972878,
0.012380018830299377,
0.00983556266874075,
0.03556479513645172,
-0.012729865498840809,
0.025564691051840782,
0.01331363059580326,
0.019337955862283707,
0.011596654541790485,
0.020681364461779594,
-0.0038109389133751392,
-0.013944040052592754,
-0.0045662494376301765,
-0.0022130124270915985,
-0.01577957347035408,
0.016193034127354622,
-0.05327242985367775,
0.04991256073117256,
-0.022791005671024323,
-0.004728346131742001,
0.008465769700706005,
-0.010294919833540916,
0.002213484374806285,
-0.007311385124921799,
0.01654934324324131,
0.05808352306485176,
-0.03460626304149628,
0.039986755698919296,
-0.011540833860635757,
-0.043115146458148956,
-0.005791178904473782,
0.05537444353103638,
0.014446712099015713,
0.012909963726997375,
-0.023113958537578583,
-0.008970113471150398,
-0.03470107167959213,
-0.019436703994870186,
0.035001546144485474,
-0.05054963752627373,
-0.007865043357014656,
0.008210543543100357,
-0.03327447548508644,
0.002302793553099036,
-0.021966734901070595,
-0.014821604825556278,
-0.010386775247752666,
-0.012304399162530899,
0.0419243648648262,
0.019434858113527298,
-0.026783237233757973,
0.01821131817996502,
0.009610390290617943,
0.055502232164144516,
-0.04862530529499054,
-0.014269731938838959,
-0.028676440939307213,
0.03493161126971245,
-0.02318650856614113,
-0.00012400446576066315
] |
<p>I was playing with some High-Voltage the other day, when a question popped into my head. Can you calculate length of an electrical arc? It probably would be proportional to :-<br>
1. Voltage of the source<br>
2. Spark gap<br>
3. Relative Humidity (in air only)<br>
4. Resistivity of Medium<br>
5. Shape of the Electrodes<br>
Can anyone come up with a dimensional formula from this...?</p>
| 10,836 |
[
-0.03600693121552467,
-0.0318073071539402,
0.034523192793130875,
-0.0007911594584584236,
0.054951928555965424,
-0.03602791950106621,
-0.07615531980991364,
0.0036178079899400473,
0.03170691430568695,
0.003562378929927945,
0.046066269278526306,
0.009514844045042992,
0.03722619265317917,
0.05533347651362419,
0.02056310512125492,
0.02018672227859497,
0.04404259845614433,
0.02866240218281746,
0.026500415056943893,
-0.024757085368037224,
0.004777200985699892,
-0.023816576227545738,
0.015986142680048943,
-0.010994669049978256,
-0.023097574710845947,
0.07806724309921265,
0.04850137233734131,
0.001419930369593203,
0.02268175780773163,
0.02755759097635746,
-0.017823094502091408,
-0.0033665939699858427,
0.06938683986663818,
0.019783953204751015,
0.003014190820977092,
0.008326183073222637,
-0.02139398269355297,
-0.029089322313666344,
-0.027974866330623627,
0.03364036977291107,
0.015627730637788773,
-0.018504073843359947,
-0.0010785347549244761,
0.007399064023047686,
-0.04677126556634903,
0.012576018460094929,
-0.03417418524622917,
-0.03812102973461151,
0.042290639132261276,
-0.05637642741203308,
0.05999378114938736,
-0.02565467171370983,
0.05607007443904877,
0.03103984147310257,
-0.02091958560049534,
0.013593514449894428,
0.0820022001862526,
0.020243076607584953,
-0.009731539525091648,
-0.04884231835603714,
-0.00870099849998951,
-0.013488988392055035,
-0.018132776021957397,
-0.025720832869410515,
-0.009832740761339664,
0.030500175431370735,
-0.0389535054564476,
-0.029598236083984375,
0.004449945408850908,
-0.019893845543265343,
0.021025925874710083,
0.026409409940242767,
-0.004862472880631685,
0.01224066223949194,
-0.010978084988892078,
0.01925908774137497,
0.027963152155280113,
0.01902850717306137,
0.0477091446518898,
0.06121636927127838,
-0.051569074392318726,
-0.010313506238162518,
0.038419563323259354,
-0.0009066644124686718,
0.014663905836641788,
-0.008849730715155602,
0.06789270788431168,
-0.016091283410787582,
0.017185991629958153,
0.0068622734397649765,
-0.0013610362075269222,
0.03228339925408363,
0.03775797039270401,
0.016572188585996628,
0.01851903833448887,
0.046838708221912384,
0.004521061200648546,
0.045962050557136536,
-0.0016696845414116979,
-0.011411456391215324,
0.008497273549437523,
0.011985495686531067,
0.024393992498517036,
0.05743509903550148,
-0.017822887748479843,
-0.03643461689352989,
0.01343242172151804,
0.03551923856139183,
0.02085086889564991,
-0.011259390041232109,
-0.0483705960214138,
0.01393320132046938,
0.013468848541378975,
0.005517968442291021,
-0.007267529144883156,
-0.006347417365759611,
0.038586728274822235,
-0.015190435573458672,
0.019487574696540833,
0.0574684701859951,
-0.015352954156696796,
-0.041105568408966064,
0.02735271118581295,
-0.014604732394218445,
-0.07238758355379105,
0.005422058515250683,
0.02504546567797661,
-0.016418857499957085,
0.0061382208950817585,
0.04229336977005005,
-0.022334346547722816,
-0.012727834284305573,
0.02790728583931923,
0.014030085876584053,
0.03449004143476486,
0.004328498616814613,
-0.0665101408958435,
-0.0699867233633995,
0.0034847056958824396,
0.02169991284608841,
-0.06658151745796204,
-0.06220852583646774,
0.03992839530110359,
0.03529577702283859,
0.05983046069741249,
0.009045479819178581,
0.012873915024101734,
-0.04639489948749542,
-0.0011446200078353286,
0.005098862107843161,
-0.02140643820166588,
-0.016690202057361603,
0.032569240778684616,
-0.029503079131245613,
0.024062078446149826,
-0.024524912238121033,
-0.004055984318256378,
0.015265804715454578,
0.01712700165808201,
-0.011996245943009853,
0.036788929253816605,
0.01117639522999525,
-0.01261941622942686,
-0.009055105969309807,
-0.0011620523873716593,
-0.07635267078876495,
0.06803043931722641,
-0.010667645372450352,
-0.029802877455949783,
-0.004616867750883102,
0.0031459250021725893,
-0.01528287585824728,
0.006140490528196096,
-0.00956082995980978,
0.08059683442115784,
-0.002862783847376704,
-0.04757975786924362,
-0.011632214300334454,
0.0150271225720644,
0.012929271906614304,
-0.06437600404024124,
-0.02690623700618744,
0.03535044565796852,
-0.0009018456912599504,
0.008305240422487259,
0.05747044086456299,
0.00608031963929534,
0.002658900571987033,
-0.026530692353844643,
-0.010267352685332298,
-0.027169790118932724,
-0.0690883919596672,
0.0373358279466629,
0.005955537781119347,
0.00166786287445575,
-0.013258806429803371,
-0.023125875741243362,
0.014914643950760365,
-0.03708610311150551,
-0.019343385472893715,
-0.016909735277295113,
0.045550387352705,
0.009477818384766579,
-0.017237547785043716,
0.011746605858206749,
0.03583793714642525,
0.028556006029248238,
-0.011621600948274136,
0.036851923912763596,
-0.02041374333202839,
-0.028108635917305946,
-0.05180463567376137,
-0.06698092818260193,
0.0598406046628952,
0.004434595350176096,
-0.002070876071229577,
0.02223203517496586,
0.0021968428045511246,
-0.009632517583668232,
0.0353507436811924,
0.010389847680926323,
0.07261274009943008,
0.040908701717853546,
0.033934950828552246,
0.011263083666563034,
0.028422057628631592,
0.011512243188917637,
0.00600481079891324,
0.03542657941579819,
-0.02350878342986107,
-0.013741827569901943,
-0.008564175106585026,
0.029698355123400688,
0.014584077522158623,
-0.033783212304115295,
0.02438807673752308,
0.0061839791014790535,
0.0472487136721611,
0.005817611701786518,
-0.0020871739834547043,
0.0063638268038630486,
-0.01097206398844719,
-0.0339803621172905,
-0.009694474749267101,
-0.00001616897134226747,
-0.021756665781140327,
0.020564822480082512,
0.06033904477953911,
0.019143961369991302,
-0.02266656793653965,
-0.012900088913738728,
0.010091432370245457,
-0.02088998444378376,
-0.010785740800201893,
0.004977202042937279,
-0.04147026687860489,
0.06736396998167038,
-0.06576702743768692,
0.01334671676158905,
0.0265324879437685,
0.013821244239807129,
0.03327920660376549,
-0.028998810797929764,
0.010797758586704731,
0.00836945604532957,
0.011103491298854351,
-0.0010992215247824788,
-0.0071016340516507626,
0.01905883476138115,
-0.02182702161371708,
-0.002834990853443742,
-0.024434231221675873,
0.005538556259125471,
-0.03633671626448631,
-0.017179790884256363,
0.033566106110811234,
0.045482855290174484,
0.03315810486674309,
0.036025382578372955,
-0.0487380214035511,
0.005858113057911396,
-0.0189063660800457,
0.0071901362389326096,
-0.004499633330851793,
-0.029164481908082962,
-0.022201672196388245,
0.012521237134933472,
-0.018664630129933357,
0.025997672230005264,
0.003901699325069785,
0.0011032142210751772,
0.04884742200374603,
-0.01778837852180004,
-0.026485227048397064,
0.015762044116854668,
0.02426801063120365,
0.016600994393229485,
-0.023405207321047783,
0.012464744038879871,
0.02141270600259304,
-0.019852641969919205,
-0.047134533524513245,
0.003629345213994384,
-0.031414907425642014,
-0.041723307222127914,
-0.03712531179189682,
0.034040097147226334,
0.03508821129798889,
-0.004209727514535189,
0.031401313841342926,
0.030450450256466866,
-0.020816093310713768,
-0.007184653542935848,
-0.03126545622944832,
-0.02946791797876358,
0.006789736915379763,
-0.0018476498080417514,
0.039152100682258606,
-0.007989621721208096,
-0.034584660083055496,
0.06581386178731918,
0.03494463488459587,
-0.0691380575299263,
-0.04546988755464554,
-0.02159549482166767,
0.007944944314658642,
-0.01567140594124794,
-0.005165908485651016,
0.0330372117459774,
0.008733016438782215,
-0.02376372553408146,
0.009695298969745636,
0.07201214134693146,
0.02425403892993927,
0.01156154926866293,
0.026185709983110428,
-0.005661088041961193,
-0.010692399926483631,
-0.01602795720100403,
0.025007009506225586,
0.019243808463215828,
0.0004274088714737445,
0.031929630786180496,
-0.008241062052547932,
0.07127892225980759,
0.04765862226486206,
-0.03389229252934456,
0.009037434123456478,
-0.02240024320781231,
0.009795673191547394,
-0.025344161316752434,
0.02127309888601303,
0.0000690995148033835,
-0.019425339996814728,
-0.015314145013689995,
0.05010111629962921,
0.03618447110056877,
-0.02895301952958107,
-0.0073486203327775,
0.038297388702631,
0.05015064775943756,
-0.0192758496850729,
-0.0534917414188385,
0.015769178047776222,
0.0007489584968425333,
0.025189731270074844,
-0.02429499477148056,
-0.0399789959192276,
0.04525875300168991,
0.009872560389339924,
0.03340327367186546,
0.023344796150922775,
-0.04080023616552353,
-0.0055550173856318,
-0.10332109779119492,
0.00047969658044166863,
-0.01679563708603382,
0.04539627954363823,
-0.0068460507318377495,
0.05484732985496521,
0.005501971114426851,
0.020190546289086342,
0.02245357632637024,
0.003064606338739395,
-0.10096970200538635,
-0.0017531299963593483,
-0.05589570105075836,
-0.005081489682197571,
-0.02232080139219761,
0.03064020350575447,
-0.01805473491549492,
0.0067990971729159355,
0.00017612460942473263,
0.01311532873660326,
-0.001702792476862669,
-0.056543320417404175,
0.022206278517842293,
-0.012685088440775871,
-0.013400792144238949,
-0.04185667261481285,
0.03074176423251629,
0.03332885354757309,
-0.020652445033192635,
0.03018265590071678,
0.007063597906380892,
0.019517920911312103,
-0.024786535650491714,
-0.02532057650387287,
-0.011476547457277775,
0.009377098642289639,
0.06501215696334839,
0.006204025354236364,
0.003997412975877523,
-0.002456605900079012,
0.01933780126273632,
-0.000558704836294055,
0.045005932450294495,
0.016061333939433098,
0.003835184033960104,
-0.05121901258826256,
-0.040396012365818024,
0.0055413153022527695,
0.007479419931769371,
0.04935777187347412,
-0.014295986853539944,
0.03972543776035309,
0.014799654483795166,
-0.04799581691622734,
-0.01765836402773857,
0.005220463965088129,
0.04272732138633728,
0.036670196801424026,
-0.022587556391954422,
-0.016283288598060608,
-0.03209111839532852,
-0.04482774809002876,
0.004998459480702877,
-0.008516825735569,
0.0029925452545285225,
-0.03185556083917618,
-0.02664584293961525,
0.024344077333807945,
-0.011405766010284424,
-0.0006691751768812537,
0.022951019927859306,
-0.01880826987326145,
0.006124336272478104,
-0.022929955273866653,
0.016505824401974678,
0.02008887194097042,
-0.034738145768642426,
0.036620356142520905,
-0.015428355894982815,
-0.017218483611941338,
-0.1188340112566948,
-0.0009899932192638516,
0.025202708318829536,
0.053780701011419296,
-0.020198676735162735,
0.0038092348258942366,
-0.04634716361761093,
-0.029117487370967865,
0.08218378573656082,
-0.021423133090138435,
0.008471648208796978,
-0.0488068163394928,
0.030488744378089905,
0.012065940536558628,
-0.03357403352856636,
-0.0026016097981482744,
0.03362062945961952,
0.06482112407684326,
0.026382198557257652,
-0.029914768412709236,
-0.01789572276175022,
0.009344790130853653,
0.03396669775247574,
0.037193696945905685,
0.06130935251712799,
0.04208831861615181,
0.0038357125595211983,
-0.0017218199791386724,
0.001986823044717312,
0.018866797909140587,
-0.056524284183979034,
-0.006775978021323681,
0.01462671160697937,
-0.0077181304804980755,
0.03609684109687805,
-0.0238480307161808,
-0.03414033353328705,
0.03156935051083565,
-0.008337300270795822,
-0.016317080706357956,
-0.0026487286668270826,
-0.029094429686665535,
0.024223322048783302,
0.01526738703250885,
0.00516212172806263,
0.039604563266038895,
0.043012335896492004,
-0.04778086394071579,
0.01964828372001648,
-0.0369955338537693,
0.052555885165929794,
0.01174918282777071,
-0.028000351041555405,
-0.004590038675814867,
0.0054213302209973335,
-0.04244901239871979,
0.04195269197225571,
-0.016169287264347076,
0.03331584483385086,
-0.01376793347299099,
-0.017480717971920967,
0.01382704358547926,
0.020657893270254135,
-0.00010813486733241007,
-0.007913623936474323,
0.015386072918772697,
0.013059500604867935,
0.006708434782922268,
-0.04811180755496025,
-0.005355906672775745,
-0.0007982251117937267,
0.05739300325512886,
0.013907559216022491,
-0.02136286161839962,
-0.023325953632593155,
-0.03097938373684883,
0.009841548278927803,
0.011351109482347965,
-0.023627445101737976,
0.07316122949123383,
-0.04859618470072746,
-0.019322877749800682,
0.030589399859309196,
-0.046383630484342575,
-0.01538078859448433,
0.006026696413755417,
0.001989608397707343,
0.0647735446691513,
-0.0389917753636837,
0.036219365894794464,
-0.02519233711063862,
-0.01541205309331417,
-0.06619692593812943,
-0.03151953965425491,
0.015637515112757683,
0.05775756388902664,
-0.028488442301750183,
-0.04551587253808975,
-0.028297435492277145,
-0.013129950501024723,
-0.061199359595775604,
0.009970752522349358,
0.03938804566860199,
-0.031128020957112312,
-0.021894190460443497,
0.02137589640915394,
-0.023487921804189682,
0.08339798450469971,
0.018849195912480354,
0.005002084653824568,
-0.034480780363082886,
-0.03277621790766716,
-0.013955860398709774,
0.017743736505508423,
0.032563358545303345,
-0.02934117615222931,
-0.05046720802783966,
0.0029403127264231443,
-0.031578179448843,
0.014302083291113377,
-0.04061254858970642,
-0.028101762756705284,
0.01667098142206669,
0.0039520300924777985,
-0.0036903959698975086,
-0.02813047170639038,
0.04817532002925873,
0.0092814601957798,
0.015408551320433617,
-0.008705440908670425,
-0.022042972967028618,
-0.08502459526062012,
0.002543240087106824,
-0.05024152249097824,
0.04290151596069336,
0.04584397375583649,
0.0040053981356322765,
-0.009202052839100361,
-0.05170189589262009,
-0.007145931012928486,
0.06752747297286987,
0.015855636447668076,
0.045352473855018616,
-0.02502310648560524,
-0.014894850552082062,
0.04435884207487106,
0.029695624485611916,
-0.03146125003695488,
-0.05464791879057884,
-0.015196569263935089,
-0.011672107502818108,
0.04928377643227577,
-0.014017226174473763,
0.0381082184612751,
0.0000012535099358501611,
-0.01657138578593731,
0.009220059029757977,
0.008023316040635109,
0.01638699509203434,
0.025085045024752617,
0.02729327604174614,
0.008654162287712097,
-0.01400959212332964,
0.04991267994046211,
-0.00417562760412693,
0.040360696613788605,
-0.01588626578450203,
-0.010428717359900475,
-0.018089473247528076,
0.024899210780858994,
0.01843353733420372,
0.013678405433893204,
-0.03821994736790657,
0.0248784851282835,
-0.002447891514748335,
0.016455797478556633,
0.03255556523799896,
0.022886844351887703,
0.07192926853895187,
-0.043661441653966904,
-0.01482406910508871,
-0.03912243992090225,
0.011959417723119259,
-0.008761625736951828,
0.004267677664756775,
0.04097569361329079,
0.03005145862698555,
-0.00466615566983819,
0.020382458344101906,
0.013076098635792732,
-0.026096923276782036,
0.025265421718358994,
-0.02362324483692646,
-0.05001416429877281,
-0.013484861701726913,
-0.014950769022107124,
-0.03570031002163887,
0.04950347915291786,
0.015037238597869873,
-0.023373637348413467,
-0.025800976902246475,
-0.016415415331721306,
0.04631400480866432,
0.02508540078997612,
0.052273962646722794,
0.020793016999959946,
0.06396488845348358,
-0.03304978832602501,
-0.008998654782772064,
-0.0634457990527153,
0.04045450687408447,
0.12145259976387024,
0.03799393028020859,
0.009731330908834934,
-0.016928892582654953,
0.020098745822906494,
-0.04226481541991234,
-0.006511212792247534,
-0.032191067934036255,
0.021466966718435287,
-0.07357504963874817,
-0.005847953259944916,
0.056082408875226974,
0.048865363001823425,
-0.01578177511692047,
0.016269437968730927,
0.04340202361345291,
-0.022418741136789322,
-0.054015517234802246,
-0.006122124847024679,
0.008198653347790241,
0.002317935461178422,
0.03833269327878952,
-0.04151762276887894,
0.03442993387579918,
-0.004705409519374371,
-0.0007081477669999003,
-0.03160513937473297,
-0.00335253425873816,
0.027430860325694084,
-0.013733471743762493,
-0.030883319675922394,
-0.006974149029701948,
0.043384525924921036,
-0.004883493296802044,
-0.03355974704027176,
-0.006636444479227066,
0.0344037301838398,
0.0008581759757362306,
-0.021772734820842743,
0.039451126009225845,
0.025051282718777657,
0.013254756107926369,
-0.022025873884558678,
0.022255219519138336,
-0.014139795675873756,
-0.042593032121658325,
-0.03161244839429855,
0.005023241974413395,
0.010847575031220913,
0.041127149015665054,
-0.01313431654125452,
0.0037747828755527735,
0.01173193845897913,
-0.03840433806180954,
-0.029286852106451988,
-0.016646575182676315,
0.045418933033943176,
-0.014161151833832264,
-0.018660014495253563,
-0.049696363508701324,
0.054490700364112854,
-0.003980307839810848,
0.010298029519617558,
-0.00687969196587801,
0.002027172828093171,
0.0017377800540998578,
-0.018676044419407845,
0.03256534785032272,
0.004409751854836941,
-0.06228957697749138,
-0.04744414985179901,
-0.023370927199721336,
-0.012329702265560627,
-0.008785616606473923,
-0.018387887626886368,
0.05658848211169243,
-0.014547773636877537,
-0.009008831344544888,
-0.003921751864254475,
0.007059733383357525,
-0.06342770904302597,
0.0175581444054842,
0.008787404745817184,
0.004972720984369516,
-0.01270888838917017,
0.02454555220901966,
-0.008181999437510967,
0.030551960691809654,
-0.012304162606596947,
0.01984177529811859,
0.010071353986859322,
0.03355367109179497,
0.032254863530397415,
-0.06448355317115784,
0.018097760155797005,
-0.006913113873451948,
-0.04238448664546013,
0.021465836092829704,
0.02141496352851391,
0.04253234341740608,
0.011200584471225739,
0.014234456233680248,
0.04374279826879501,
0.03924638405442238,
-0.03565719723701477,
0.0015147995436564088,
-0.0056627364829182625,
-0.017353015020489693,
0.011046336032450199,
-0.031055863946676254,
-0.018938181921839714,
-0.06264239549636841,
-0.03564915806055069,
-0.032919593155384064,
0.0007611517212353647,
0.013772983103990555,
0.007592581212520599,
-0.04592260345816612,
0.014422806911170483,
-0.0010108461137861013,
0.017679106444120407,
-0.02662326768040657,
0.0063832723535597324,
-0.00400063069537282,
-0.019071098417043686,
-0.0029835477471351624,
-0.025477271527051926,
0.022512534633278847,
0.0074477605521678925,
-0.03442958742380142,
-0.019068490713834763,
0.013028817251324654,
0.019079213961958885,
0.03257986158132553,
-0.04899054020643234,
-0.00953394640237093,
0.0023297874722629786,
0.02224213443696499,
-0.03883737698197365,
-0.027643436565995216,
0.024170774966478348,
-0.035916537046432495,
-0.02894030697643757,
0.035051293671131134,
-0.05518043413758278,
0.0234895758330822,
0.026319049298763275,
-0.018766101449728012,
-0.003798974212259054,
0.07171815633773804,
-0.013440987095236778,
0.013665828853845596,
-0.012264210730791092,
0.004273549187928438,
0.0028242631815373898,
-0.003383616916835308,
-0.03349815681576729,
-0.009497093968093395,
0.0014671460958197713,
0.03815092891454697,
0.0024092213716357946,
0.014621615409851074,
-0.016498077660799026,
0.05838261544704437,
-0.007459316868335009,
-0.01616480015218258,
0.02283022552728653,
-0.012685675173997879,
0.012871268205344677,
0.04271448403596878,
-0.018733514472842216,
0.029125718399882317,
0.010210615582764149,
0.009157548658549786,
-0.1042570099234581,
0.0070939697325229645,
0.02789900079369545,
0.03451313078403473,
0.0018867352046072483,
-0.05873826518654823,
-0.0034271867480129004,
0.010614633560180664,
-0.09536825865507126,
-0.027884654700756073,
-0.03114975243806839,
-0.037541650235652924,
0.001778433914296329,
-0.017691006883978844,
0.004483383614569902,
-0.0035678434651345015,
0.01420288160443306,
0.05601420998573303,
0.022026289254426956,
0.0018346511060371995,
-0.027726883068680763,
-0.07337376475334167,
-0.026100611314177513,
0.04078647121787071,
0.0017618720885366201,
-0.03721506521105766,
0.05833582952618599,
-0.061198752373456955,
0.018087683245539665,
-0.005915235728025436,
-0.021281840279698372,
0.017923884093761444,
0.00445865374058485,
0.012183434329926968,
-0.017944449558854103,
0.03465725854039192,
0.0015077353455126286,
-0.02648072876036167,
-0.020194627344608307,
-0.01354725006967783,
-0.012622220441699028,
-0.015214018523693085,
-0.003856657538563013,
-0.00219086860306561,
0.1006917878985405,
-0.022370440885424614,
-0.03552214056253433,
0.022323178127408028,
-0.02558186650276184,
-0.03481109067797661,
-0.015449871309101582,
0.006123736500740051,
0.01722627505660057,
-0.02306174486875534,
-0.012773759663105011,
-0.0457988940179348,
-0.01628738082945347,
0.0269386675208807,
-0.024555852636694908,
-0.018949342891573906,
0.004735887050628662,
-0.012995772063732147,
-0.05398445576429367,
-0.0013754216488450766,
0.025647733360528946,
-0.04049566015601158,
-0.03691650182008743,
0.0018786154687404633,
0.00898751337081194,
-0.0018131027463823557,
0.03417456895112991,
-0.017201555892825127,
-0.018063699826598167,
0.020894285291433334,
0.02417769841849804,
0.0037963055074214935,
0.04048582538962364,
-0.04314472898840904,
-0.017355063930153847,
-0.021436836570501328,
0.025208765640854836,
-0.014325008727610111,
-0.04443983733654022,
-0.03933103010058403,
-0.023596812039613724,
0.014928627759218216,
0.008231548592448235,
0.06228349357843399,
-0.02933625318109989,
-0.014185336418449879,
-0.0071540153585374355,
0.005973925814032555,
0.007703990209847689,
-0.01566176302731037,
-0.021862758323550224,
0.05747618526220322,
-0.03652063012123108,
-0.006138809956610203,
-0.007746053859591484,
0.011211882345378399,
-0.031497351825237274,
-0.01622047647833824,
-0.010079208761453629,
-0.03223501145839691,
-0.03466229513287544,
-0.031104164198040962,
0.0020737575832754374,
-0.010244778357446194,
-0.05249115452170372,
0.07911859452724457,
-0.006938494276255369,
-0.01711351051926613,
-0.004442599602043629,
-0.0056067281402647495,
-0.025747625157237053,
0.000994296045973897,
-0.028114039450883865,
0.018456749618053436,
-0.015754912048578262,
0.022410612553358078,
0.04016712307929993,
-0.034697696566581726,
0.0018823962891474366,
0.03811027109622955,
-0.0043738181702792645,
-0.01601855829358101,
0.05700324475765228,
0.019818151369690895,
-0.0012523694895207882,
-0.02310044877231121,
0.0003438075364101678,
0.04539139196276665,
0.02143728733062744,
-0.031094854697585106,
0.042070165276527405,
0.057216838002204895,
-0.03325844556093216,
0.00317453988827765,
0.026308732107281685,
-0.006372535601258278,
0.025709744542837143,
0.015851318836212158,
0.015061339363455772,
-0.009175648912787437,
-0.020769407972693443,
-0.0028626020066440105,
0.0013302332954481244,
-0.005960649810731411,
0.026132788509130478,
-0.06097590923309326,
0.07900483906269073,
0.04089975357055664,
-0.017237458378076553,
-0.022374993190169334,
0.030390571802854538,
-0.037223510444164276,
0.012631602585315704,
0.00678972527384758,
0.023157894611358643,
0.02103940211236477,
0.01472512912005186,
0.0054689194075763226,
0.026763353496789932,
0.04152625426650047,
-0.04988047480583191,
0.00113905209582299,
-0.026047034189105034,
0.014291487634181976,
0.005954552907496691,
0.018259480595588684,
-0.04001958668231964,
0.01152727846056223,
0.039042916148900986,
0.012661791406571865,
0.0028773266822099686,
0.014342311769723892,
-0.010392438620328903,
0.00852256454527378,
0.05588890612125397,
-0.05542067810893059,
-0.04978904128074646,
-0.018738295882940292,
0.00807254109531641,
0.013531961478292942,
-0.0006791080813854933
] |
<p>This photo was published at <a href="http://www.stern.de/bdt/bilder-des-tages-gefaehrliche-tropfen-1501450-4a50503e928f997c.html" rel="nofollow">stern magazine online</a>.
<img src="http://i.stack.imgur.com/Ryhyi.jpg" alt="contaminated water leaks out of vessel"></p>
<p>I wonder which information about the physical quantities could be reconstructed or computed given this photograph, the exposure time, and the detector size.</p>
<p>The white dots in the image correspond to particle traces on the imaging sensor. Thus by just counting the number of white dots, we know how many gamma photons interacted with the sensor while passing through. I will neglect the fact that the white pixels could also be caused by defect pixels aka "dead pixels". Let's assume the photo was taken with a non-stationary new camera. </p>
<p>So the only physical quantity I could come up is: </p>
<p>$$\frac{\text{# of white dots}}{12\pi \text{sr}\ \text{sensor_area}\cdot \text{exposure_time}}$$</p>
<p>Is there a way to find out more with some very conservative assumptions about the environment? What would these assumptions be?</p>
| 10,837 |
[
-0.0202474482357502,
-0.06392043083906174,
0.008989164605736732,
-0.01798672415316105,
0.06151934340596199,
0.02509605512022972,
-0.029740436002612114,
-0.011352086439728737,
-0.0031247141305357218,
-0.055857446044683456,
0.039730045944452286,
0.04232286289334297,
0.043695248663425446,
0.037902235984802246,
-0.014065571129322052,
0.012020526453852654,
-0.011693782173097134,
-0.034126557409763336,
-0.02981085143983364,
-0.038483746349811554,
0.03688718378543854,
0.033676911145448685,
-0.00645485008135438,
-0.01317980419844389,
-0.029406992718577385,
0.007668779697269201,
-0.015546455979347229,
-0.019806278869509697,
0.010673623532056808,
0.05570792034268379,
-0.026935094967484474,
-0.045416466891765594,
-0.015410557389259338,
0.0017255727434530854,
-0.0021056695841252804,
0.02010318450629711,
-0.00237696198746562,
-0.05730919539928436,
-0.009794021025300026,
0.05243833363056183,
-0.001571595435962081,
-0.0017244770424440503,
0.011265098117291927,
0.02996348775923252,
-0.02947636879980564,
0.009778428822755814,
-0.020517529919743538,
-0.025257304310798645,
0.04541877284646034,
-0.04746957868337631,
0.05069490522146225,
-0.00017121958080679178,
0.05639469996094704,
0.021810857579112053,
0.0017155915265902877,
-0.017230691388249397,
0.06396877765655518,
0.08039578795433044,
-0.02461840584874153,
-0.037957582622766495,
0.018758470192551613,
0.018301626667380333,
0.022485746070742607,
-0.01671575754880905,
0.004245345946401358,
-0.025421734899282455,
-0.01957598514854908,
-0.039673976600170135,
0.026962190866470337,
0.025188226252794266,
0.03909807279706001,
0.020487859845161438,
0.06791332364082336,
0.024802591651678085,
0.01793297566473484,
-0.01303799357265234,
0.026554780080914497,
0.05140472203493118,
0.006776878144592047,
0.010258084163069725,
-0.028321467339992523,
-0.007234503980726004,
-0.0014622407034039497,
0.03245538845658302,
0.04139312356710434,
-0.021220145747065544,
0.07418844103813171,
0.0054032206535339355,
0.039836425334215164,
0.003415101207792759,
0.009698123671114445,
0.041370291262865067,
0.009517991915345192,
0.0018981869798153639,
-0.030034802854061127,
0.03565595671534538,
-0.0014722236664965749,
0.068776935338974,
0.0076227691024541855,
-0.011615577153861523,
0.0586986280977726,
-0.01048471312969923,
-0.01880807802081108,
0.06290395557880402,
-0.015029379166662693,
-0.005534058902412653,
-0.029751218855381012,
0.0146143464371562,
-0.02768530137836933,
0.0032691603992134333,
-0.06706999987363815,
0.01767595484852791,
0.031456056982278824,
-0.04009120538830757,
0.009079284965991974,
0.017039913684129715,
-0.010606715455651283,
0.014385856688022614,
0.08228013664484024,
0.04637525975704193,
0.01585347391664982,
-0.02166750654578209,
0.0031824803445488214,
-0.019422387704253197,
-0.07182441651821136,
0.058821361511945724,
0.02572021819651127,
-0.03153151273727417,
-0.06431318819522858,
0.05852338671684265,
-0.004319879226386547,
0.0018113830592483282,
0.03862641751766205,
-0.0017683589830994606,
0.018130239099264145,
-0.0009084995253942907,
-0.07123307138681412,
-0.07802190631628036,
0.029694022610783577,
0.014732127077877522,
-0.008341117762029171,
-0.07001059502363205,
0.008592263795435429,
0.030351577326655388,
0.05364304408431053,
-0.04039013758301735,
0.007006094790995121,
0.0025100703351199627,
0.03381321579217911,
-0.054930999875068665,
-0.016654087230563164,
-0.0035761138424277306,
0.03084389492869377,
-0.012662588618695736,
-0.011514834128320217,
-0.043152473866939545,
0.02614767849445343,
0.0629771500825882,
0.0005667060031555593,
-0.05678007751703262,
0.048792216926813126,
0.023134028539061546,
0.016087256371974945,
0.017461035400629044,
-0.03943086788058281,
-0.06386860460042953,
0.05366739630699158,
0.002096675569191575,
-0.012510848231613636,
-0.012803561985492706,
0.0022866528015583754,
0.041639167815446854,
-0.0010053891455754638,
-0.020143525674939156,
0.049239978194236755,
-0.0009684654651209712,
-0.004861068446189165,
-0.006733592599630356,
0.03272552043199539,
0.014602039009332657,
-0.018641062080860138,
-0.06941653788089752,
-0.027367044240236282,
0.023526174947619438,
0.03621629998087883,
0.001702752779237926,
0.014230144210159779,
-0.03693423792719841,
0.003454050747677684,
-0.01085430383682251,
-0.02006988227367401,
-0.06074634566903114,
-0.024884121492505074,
-0.01916775107383728,
-0.007175086997449398,
0.024195566773414612,
-0.057363204658031464,
0.011399971321225166,
-0.001681628986261785,
-0.04136551544070244,
-0.0019021035404875875,
-0.015293686650693417,
0.025571970269083977,
-0.004753662273287773,
0.012979261577129364,
0.06438234448432922,
0.010857587680220604,
0.0343509316444397,
0.018397711217403412,
-0.026028653606772423,
0.00491988193243742,
-0.02398321032524109,
-0.05531783774495125,
0.027478136122226715,
-0.00598496338352561,
-0.025226546451449394,
0.010021787136793137,
-0.014897981658577919,
0.0007104015094228089,
-0.006762890610843897,
0.016827357932925224,
0.0675683468580246,
0.022605979815125465,
-0.0023250875528901815,
-0.009437493048608303,
-0.004278750624507666,
0.013605772517621517,
0.017523106187582016,
-0.0322086475789547,
-0.059571508318185806,
-0.06534767150878906,
-0.02576274238526821,
0.039401825517416,
0.00017147390462923795,
-0.012624389491975307,
0.03298363834619522,
0.031898852437734604,
0.02579236775636673,
0.009832262061536312,
0.009688599966466427,
-0.03561384230852127,
-0.000863048539031297,
-0.0195437204092741,
0.029704740270972252,
-0.03420636057853699,
-0.029505854472517967,
-0.025905899703502655,
0.01010777149349451,
0.027678217738866806,
0.007754082791507244,
0.04523565247654915,
0.0005945322336629033,
-0.022082658484578133,
0.020715774968266487,
-0.0757119283080101,
-0.0002714508445933461,
0.06069308891892433,
-0.013953889720141888,
0.029001839458942413,
-0.012221045792102814,
-0.016844168305397034,
0.017908819019794464,
-0.0414283387362957,
-0.0660652369260788,
0.009194117039442062,
0.004104380030184984,
-0.028198586776852608,
0.008553869090974331,
0.013175661675632,
-0.03408999368548393,
0.01765616238117218,
-0.033379629254341125,
0.0073290662840008736,
-0.012479825876653194,
0.0025121858343482018,
0.04246850311756134,
0.016207102686166763,
0.012946371920406818,
-0.07444485276937485,
-0.028130389750003815,
-0.0004832480335608125,
0.018846459686756134,
-0.009445912204682827,
0.04473142698407173,
-0.028930408880114555,
-0.020858032628893852,
-0.005495402030646801,
0.0024996325373649597,
0.011094488203525543,
-0.0025521088391542435,
-0.007542023900896311,
0.048858653753995895,
0.014707088470458984,
-0.023380693048238754,
0.004314900375902653,
-0.00973972026258707,
-0.0008880746900103986,
-0.04380771145224571,
-0.0363578237593174,
0.03500514104962349,
0.01720564439892769,
-0.025986043736338615,
0.030350295826792717,
-0.01777493953704834,
-0.030695652589201927,
-0.028716500848531723,
0.018806496635079384,
0.018646659329533577,
-0.054840847849845886,
0.036099810153245926,
0.0021056809928268194,
0.009079771116375923,
0.007332629058510065,
-0.025564929470419884,
-0.06413763016462326,
0.05242922529578209,
-0.0063219196163117886,
0.031001966446638107,
-0.05353168770670891,
-0.041591111570596695,
0.07627595216035843,
0.02070513926446438,
-0.02558944560587406,
-0.017501914873719215,
0.00462748110294342,
-0.025762632489204407,
-0.008313718251883984,
-0.021982675418257713,
-0.0009552176343277097,
0.028243182227015495,
0.03889419510960579,
-0.018541013821959496,
0.026418481022119522,
0.04009184613823891,
0.022773180156946182,
-0.0008152061491273344,
0.015110786072909832,
0.0013016390148550272,
0.011437204666435719,
0.05707716941833496,
0.017729004845023155,
0.01388956606388092,
0.0006303046829998493,
-0.024581169709563255,
0.022725872695446014,
0.028393583372235298,
-0.04531284049153328,
0.0290437713265419,
0.028597306460142136,
0.00015392863133456558,
-0.03913090378046036,
0.005075980443507433,
-0.007677433080971241,
-0.004563711117953062,
-0.0013424694770947099,
0.0153018394485116,
0.043132517486810684,
0.0020263802725821733,
-0.0020583306904882193,
0.033983081579208374,
0.06835238635540009,
0.011572213843464851,
-0.02766803465783596,
0.0006382035790011287,
0.007338935974985361,
-0.00007559179357485846,
-0.02089291252195835,
-0.020144173875451088,
0.05742016062140465,
0.02712550014257431,
0.05101761594414711,
-0.01023887936025858,
-0.03618014603853226,
-0.02076015993952751,
-0.05573640763759613,
-0.046303633600473404,
-0.01584511063992977,
0.046443693339824677,
0.02670290134847164,
0.011042582802474499,
0.019633891060948372,
-0.0012680853251367807,
0.016723578795790672,
0.002794958185404539,
-0.05242525786161423,
-0.007899033837020397,
0.03246412053704262,
-0.025576338171958923,
0.009431693702936172,
-0.0254336129873991,
0.015865860506892204,
-0.030674682930111885,
-0.04916597157716751,
0.03693917766213417,
0.04312406852841377,
-0.0638258159160614,
0.018710754811763763,
-0.04633425176143646,
-0.023287642747163773,
-0.02351197600364685,
0.05021670088171959,
0.03575583174824715,
-0.010793115012347698,
-0.02561529539525509,
-0.006227484904229641,
0.023594731464982033,
-0.007999486289918423,
-0.025047603994607925,
0.01281324028968811,
-0.024684231728315353,
0.026022903621196747,
0.004010720178484917,
0.036202892661094666,
-0.03828407824039459,
-0.0284709595143795,
0.015660157427191734,
0.02321731112897396,
-0.0004518693021964282,
0.006164980586618185,
-0.03805378079414368,
-0.024129647761583328,
0.01347255427390337,
0.03169574216008186,
0.01789289526641369,
-0.027269791811704636,
0.029744718223810196,
0.043738462030887604,
-0.01791009120643139,
-0.034893881529569626,
0.030358662828803062,
0.05396808311343193,
0.02473500743508339,
0.0232542734593153,
-0.0566856823861599,
-0.019517790526151657,
-0.000642747210804373,
-0.02558979205787182,
0.038997385650873184,
0.05468546226620674,
0.023267200216650963,
-0.01566062495112419,
0.03860624134540558,
0.04531239718198776,
-0.04854603484272957,
-0.024040432646870613,
-0.0014002122916281223,
0.009924882091581821,
-0.008387390524148941,
-0.01672689989209175,
0.017367077991366386,
0.055974893271923065,
0.06225593388080597,
0.003879501484334469,
-0.03503712639212608,
-0.09732264280319214,
-0.05355846509337425,
0.0282193124294281,
0.041100066155195236,
0.026734257116913795,
-0.012297273613512516,
-0.04545052722096443,
-0.012994615361094475,
0.04161962494254112,
-0.02361496165394783,
0.001273379661142826,
0.004932623356580734,
0.00588266784325242,
0.02328396774828434,
-0.03557877242565155,
-0.01343457493931055,
-0.001989259384572506,
-0.004913371056318283,
0.010758276097476482,
-0.04118318855762482,
-0.018975498154759407,
0.02337201125919819,
0.03865864500403404,
0.030389606952667236,
0.05627439543604851,
0.00444844551384449,
0.016047272831201553,
-0.019638901576399803,
0.002269583521410823,
-0.030311623588204384,
-0.0765237882733345,
0.03931856155395508,
-0.0160157922655344,
-0.004477460402995348,
0.07690560817718506,
-0.020533189177513123,
-0.030673187226057053,
0.03109867498278618,
0.026833804324269295,
-0.026446253061294556,
-0.0007200007094070315,
-0.08634047955274582,
0.016511237248778343,
0.0496189258992672,
0.02367124892771244,
0.04518839716911316,
0.021924030035734177,
-0.0007356943096965551,
0.038260623812675476,
-0.03336002677679062,
0.017440129071474075,
-0.027849040925502777,
-0.0026680531445890665,
-0.006497893948107958,
0.018270034343004227,
0.008483684621751308,
0.06651247292757034,
0.005256396718323231,
-0.006586560048162937,
0.0166108850389719,
-0.040130313485860825,
0.02939470484852791,
0.0021692446898669004,
-0.058900486677885056,
-0.004958715755492449,
-0.03643995150923729,
0.03661150857806206,
0.02196411043405533,
-0.01776904985308647,
-0.0008425827254541218,
-0.0227606650441885,
0.004415399860590696,
-0.0012512922985479236,
0.010248835198581219,
0.004743336699903011,
-0.06034011393785477,
0.01894482783973217,
0.014711685478687286,
-0.012041151523590088,
0.06432656943798065,
-0.009498624131083488,
0.007992837578058243,
0.0036470927298069,
-0.061764128506183624,
0.0011580658610910177,
-0.030311353504657745,
-0.011247729882597923,
0.03865320608019829,
-0.023236384615302086,
0.040751513093709946,
-0.0016266005113720894,
0.019560225307941437,
-0.09156445413827896,
-0.0262515377253294,
0.01598355360329151,
0.014415884390473366,
0.0033395886421203613,
-0.023738138377666473,
0.010004335083067417,
-0.005359861068427563,
-0.026418522000312805,
0.0061411927454173565,
0.01841251365840435,
-0.006446926388889551,
-0.03628856688737869,
0.009185452945530415,
0.0072028455324471,
0.06732939183712006,
-0.0477779284119606,
0.007692514918744564,
0.05340191349387169,
-0.0011216796701774001,
-0.04647094011306763,
0.020402509719133377,
-0.009524594061076641,
-0.030488930642604828,
-0.03345485404133797,
-0.023319119587540627,
-0.005916493013501167,
0.05488740652799606,
-0.04538670927286148,
-0.0262195635586977,
0.012668113224208355,
0.021466875448822975,
0.02312423102557659,
0.0062049091793596745,
0.0318538174033165,
0.01026487909257412,
0.056490927934646606,
-0.011162642389535904,
-0.018248438835144043,
-0.01949933171272278,
-0.011133495718240738,
0.04280434176325798,
0.0018824883736670017,
-0.026754720136523247,
0.003484149230644107,
0.03149742633104324,
0.01493830792605877,
-0.02558927610516548,
0.01756667159497738,
-0.018594257533550262,
0.04135482758283615,
-0.0422508530318737,
0.028982246294617653,
0.024490265175700188,
0.01895490102469921,
-0.034289129078388214,
-0.033160146325826645,
-0.07512341439723969,
-0.028768759220838547,
0.058492619544267654,
-0.013972938992083073,
0.039641015231609344,
-0.03028854914009571,
-0.01230144128203392,
0.03018706850707531,
-0.0036864338908344507,
0.005780687090009451,
0.028602920472621918,
-0.008108150213956833,
0.01574736461043358,
-0.02556043677031994,
-0.04373138025403023,
0.01169741339981556,
0.05153466761112213,
-0.005138387903571129,
0.047865670174360275,
0.0047931913286447525,
0.012685898691415787,
0.0047107869759202,
-0.05738358944654465,
-0.05931515619158745,
0.01264479011297226,
-0.030208054929971695,
0.028479300439357758,
0.001948464778251946,
-0.009384926408529282,
0.08920937776565552,
0.0032454326283186674,
-0.010774108581244946,
-0.03632063791155815,
-0.02250300720334053,
-0.041448257863521576,
-0.00720281433314085,
-0.0038363486528396606,
-0.00850715022534132,
-0.024760767817497253,
0.007424970623105764,
0.011230070143938065,
-0.018093936145305634,
0.005668605677783489,
-0.007562377490103245,
-0.05429234355688095,
-0.008723877370357513,
-0.025104720145463943,
-0.012062925845384598,
0.07198268175125122,
-0.01786508783698082,
-0.010998588055372238,
-0.0051215579733252525,
-0.05222245678305626,
0.015670588240027428,
0.04303637519478798,
0.07568632066249847,
-0.021182948723435402,
0.04194485768675804,
-0.022373951971530914,
0.030881276354193687,
0.0009281402453780174,
0.03677994757890701,
0.12468606233596802,
0.0755021870136261,
0.0006722970283590257,
-0.009622694924473763,
-0.009419891983270645,
-0.024596786126494408,
0.00789259746670723,
0.0017742558848112822,
0.007829475216567516,
0.005295976065099239,
-0.0361575186252594,
0.019462229683995247,
0.02420840412378311,
-0.009381579235196114,
-0.005444440059363842,
-0.0021950136870145798,
-0.04100228101015091,
-0.016999373212456703,
0.034260790795087814,
0.03834530711174011,
-0.006554853171110153,
-0.0009601641213521361,
-0.03796174377202988,
0.03503131866455078,
-0.01622292399406433,
-0.012151935137808323,
0.010385015979409218,
-0.04988797754049301,
0.02336220070719719,
0.012455256655812263,
-0.05234844610095024,
-0.0068445815704762936,
-0.018379172310233116,
0.0013182166730985045,
-0.03264738991856575,
0.032854218035936356,
0.012758470140397549,
0.0314670093357563,
-0.006199214607477188,
-0.00003572591958800331,
0.024999147281050682,
-0.013198954984545708,
0.02006382867693901,
-0.008059149608016014,
-0.028401121497154236,
-0.016186632215976715,
0.001266231294721365,
0.0527089461684227,
-0.017540765926241875,
-0.014280826784670353,
-0.03169122338294983,
-0.022753708064556122,
0.00274451170116663,
-0.07962941378355026,
-0.02250136248767376,
0.01705120876431465,
-0.008531569503247738,
0.002621597843244672,
-0.02422073483467102,
-0.001311156083829701,
0.03847932070493698,
0.005582536570727825,
0.05041838809847832,
0.027391809970140457,
0.0054960972629487514,
-0.027866287156939507,
-0.017791999503970146,
0.07152983546257019,
0.034884583204984665,
-0.01813628152012825,
-0.03221079707145691,
-0.043319810181856155,
-0.0329882875084877,
-0.05270080640912056,
0.015870027244091034,
0.010682939551770687,
0.026431553065776825,
0.026480551809072495,
-0.017479248344898224,
-0.0002682439226191491,
-0.05650153383612633,
0.034340862184762955,
-0.009806828573346138,
-0.017015425488352776,
-0.03219231963157654,
-0.022161690518260002,
-0.01719115674495697,
0.041990768164396286,
-0.006359677296131849,
0.007270750589668751,
0.010565592907369137,
0.08671122789382935,
0.018805233761668205,
-0.045513369143009186,
0.00017948746972251683,
0.02873680740594864,
-0.011030563153326511,
0.00956498272716999,
-0.007272886112332344,
0.01441421639174223,
0.0001856024464359507,
-0.008562427014112473,
0.04824141412973404,
-0.0020479110535234213,
-0.04606032371520996,
-0.0071275983937084675,
0.017177004367113113,
0.006732399109750986,
-0.029887063428759575,
-0.011794399470090866,
0.028292790055274963,
-0.015363176353275776,
-0.003959619905799627,
-0.006012801546603441,
-0.02799317054450512,
-0.0005575129762291908,
0.012354811653494835,
0.00862293504178524,
0.009719784371554852,
-0.05032472312450409,
-0.0024724905379116535,
0.010668576695024967,
-0.019906090572476387,
-0.0515892431139946,
0.015264693647623062,
0.00238821585662663,
0.0014234433183446527,
-0.02910354733467102,
-0.0037064652424305677,
0.023723801597952843,
-0.029163789004087448,
0.021572144702076912,
0.016593191772699356,
0.011314066126942635,
0.0006677667261101305,
0.005893402267247438,
0.014879235066473484,
0.0593140535056591,
-0.0023098012898117304,
-0.023915860801935196,
0.02586701512336731,
-0.003771448042243719,
-0.01763777993619442,
0.0336853452026844,
-0.020640553906559944,
0.024124233052134514,
0.015620676800608635,
0.0077162752859294415,
-0.012050826102495193,
0.06724543869495392,
-0.0037914554122835398,
-0.031204696744680405,
0.0013366398634389043,
-0.015579398721456528,
-0.016795404255390167,
-0.05821356922388077,
0.031672894954681396,
0.03271310031414032,
-0.004517740104347467,
0.032815057784318924,
-0.02819628082215786,
0.0188522320240736,
0.016627663746476173,
-0.00015146014629863203,
-0.04828547313809395,
-0.0046264114789664745,
-0.02929117903113365,
-0.00227952073328197,
0.0314212441444397,
0.04038425534963608,
-0.03728668391704559,
-0.00038043007953092456,
0.00031592778395861387,
-0.025044312700629234,
-0.1167697161436081,
-0.0037239619996398687,
0.01464838720858097,
0.04875534400343895,
0.03510046750307083,
-0.04944012314081192,
0.019076814875006676,
0.03663312643766403,
-0.0919351577758789,
-0.006021745502948761,
-0.02750462479889393,
-0.005822385661303997,
-0.058609023690223694,
0.040734805166721344,
0.0005018058000132442,
0.021955644711852074,
0.013156778179109097,
0.05323219671845436,
0.03150865063071251,
0.045272938907146454,
0.0021077455021440983,
-0.05376887321472168,
-0.022500352934002876,
0.04167559742927551,
0.009483014233410358,
-0.01867503486573696,
0.03856205940246582,
0.0037123817019164562,
0.0010426582302898169,
-0.03510047867894173,
-0.010156910866498947,
0.03276793658733368,
-0.03288361430168152,
0.009009766392409801,
0.002953161485493183,
0.019531358033418655,
0.017553020268678665,
0.014640051871538162,
0.013703403063118458,
-0.025688536465168,
0.01646033488214016,
0.0038714008405804634,
0.0116202924400568,
0.026753395795822144,
0.019823361188173294,
-0.012973244301974773,
-0.025351565331220627,
0.031012987717986107,
-0.003969550598412752,
-0.022183211520314217,
0.03517488017678261,
-0.010862247087061405,
0.0007244673324748874,
-0.04536142200231552,
0.029990147799253464,
-0.0622781477868557,
0.027868997305631638,
0.020843522623181343,
0.0255582295358181,
-0.017933987081050873,
-0.007310104556381702,
0.011991789564490318,
-0.05300859734416008,
0.011161020956933498,
-0.00750254699960351,
-0.005216778255999088,
-0.028238389641046524,
0.011863408610224724,
0.01903671957552433,
0.01694573648273945,
0.021009214222431183,
-0.010990871116518974,
-0.07003645598888397,
0.0405702143907547,
0.014869226142764091,
-0.010438164696097374,
0.021928295493125916,
-0.024281006306409836,
0.008922616951167583,
-0.07662969827651978,
0.01161281205713749,
0.01732391119003296,
-0.017153998836874962,
-0.024214671924710274,
-0.004591773264110088,
-0.0029023003298789263,
0.022522050887346268,
0.05463405326008797,
-0.02121145650744438,
-0.007111487444490194,
0.0063358875922858715,
0.011816208250820637,
0.00479962769895792,
-0.05864051356911659,
0.027997970581054688,
-0.03122374601662159,
-0.0014995428500697017,
-0.01048409566283226,
-0.003241359954699874,
-0.007967771030962467,
0.018901394680142403,
0.02111215330660343,
-0.00005348375634639524,
0.018615471199154854,
-0.01468876376748085,
-0.01038709282875061,
0.0640236958861351,
0.0005438137450255454,
0.023043418303132057,
0.06394544243812561,
0.01560593955218792,
0.017777107656002045,
0.050829969346523285,
0.0076349470764398575,
-0.04269034042954445,
0.013448403216898441,
-0.005104253999888897,
-0.03474271297454834,
0.030574684962630272,
-0.01819443888962269,
0.021264489740133286,
-0.07529372721910477,
-0.002600025851279497,
0.03276721388101578,
-0.0000833564845379442,
-0.027214709669351578,
0.043920230120420456,
0.010027794167399406,
0.026644088327884674,
0.008008185774087906,
0.026343801990151405,
0.05281820520758629,
0.00386453652754426,
-0.03905855864286423,
0.01623944565653801,
0.013227581977844238,
-0.025158898904919624,
0.03505473956465721,
0.006480006966739893,
0.013146031647920609,
-0.017951564863324165,
-0.0036870548501610756,
0.013137620873749256,
-0.024268141016364098,
-0.008207307197153568,
0.018352879211306572,
-0.011692377738654613,
-0.010484191589057446,
0.01337568648159504,
-0.001625993405468762,
0.09043357521295547,
0.014676271937787533,
-0.0008303161012008786,
-0.05967862531542778,
-0.024367960169911385,
-0.025113755837082863,
0.03169035539031029,
0.019172100350260735,
0.037686094641685486,
-0.007887364365160465,
-0.006761325057595968,
-0.039056435227394104,
0.017339974641799927,
-0.013952258974313736,
-0.048662152141332626,
0.03156745433807373,
0.013513248413801193,
-0.005189051385968924,
0.010377692990005016,
-0.018104545772075653,
-0.029277797788381577,
0.005492477212101221,
0.0007519980426877737,
0.019711477681994438,
-0.025131400674581528,
0.020851226523518562,
-0.04162149876356125,
-0.045986536890268326,
0.06446367502212524,
-0.05933748930692673,
-0.005493844859302044,
-0.010648945346474648,
0.00010055866732727736,
-0.016703713685274124,
-0.03523517772555351
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.